{ "cells": [ { "cell_type": "markdown", "id": "adaptive-weekly", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# A simple epidemic model for Covid 19 and its numerical solution\n", "**André Massing**\n", "\n", "Date: **March 26, 2021**\n", "\n", "$\\newcommand{mb}[1]{\\mathbf{#1}}$\n", "If you want to have a nicer theme for your jupyter notebook,\n", "download the [cascade stylesheet file tma4125.css](https://www.math.ntnu.no/emner/TMA4125/2020v/part_II/notebooks/tma4125.css)\n", "and execute the next cell:" ] }, { "cell_type": "code", "execution_count": 1, "id": "seasonal-video", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/html": [ " \n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import ipywidgets as widgets\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from IPython.core.display import HTML\n", "from ipywidgets import fixed, interact\n", "from numpy import pi\n", "from numpy.linalg import norm, solve\n", "\n", "\n", "def css_styling():\n", " try:\n", " with open(\"tma4125.css\") as f:\n", " styles = f.read()\n", " return HTML(styles)\n", " except FileNotFoundError:\n", " pass # Do nothing\n", "\n", "\n", "# Comment out next line and execute this cell to restore the default notebook style\n", "css_styling()" ] }, { "cell_type": "markdown", "id": "broken-theory", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "As always, we start by calling the necessary modules: And of course we want to import the required modules.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "respiratory-running", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "\n", "# Use a funny plotting style\n", "plt.xkcd()\n", "\n", "newparams = {\n", " \"figure.figsize\": (6.0, 6.0),\n", " \"axes.grid\": True,\n", " \"lines.markersize\": 8,\n", " \"lines.linewidth\": 2,\n", " \"font.size\": 14,\n", "}\n", "plt.rcParams.update(newparams)" ] }, { "cell_type": "markdown", "id": "essential-connectivity", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Plan for the day\n", "\n", "* Part I: Extension of the SIR model\n", "* Part II: Numerical solution of SIR-like models" ] }, { "cell_type": "markdown", "id": "corporate-korean", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Part I: Extending the SIR model for disease spreading\n", "\n" ] }, { "cell_type": "markdown", "id": "accurate-milwaukee", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Review of the SIR model\n", "\n", "Motivated by the ongoing corona virus pandemic, we considered\n", "the simplest ODE model describing how an an infectious disease spread in a population.\n", "\n", "The model goes under the name [[SIR model]](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model)\n", "and a particular example of a **compartmental model in epidemiology**.\n", "An overview over more complicated model can be for example found on [[wikipedia]]( https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#Elaborations_on_the_basic_SIR_model)." ] }, { "cell_type": "markdown", "id": "interesting-carrier", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The SIR models divides the population into three\n", "population classes or **compartments**, namely\n", "* S(t): number individuals **susceptible** for infection,\n", "* I(t): number **infected** individuals, capable of transmitting the disease,\n", "* R(t): number **removed** individuals who cannot be infected due death or to immunity \n", " after recovery\n", "\n", "The model is of the spreading of a disease is based\n", "on moving individual from $S$ to $I$ and then from $S$ to $R$, in short-hand notation\n", "\n", "$$\n", "S \\to I \\to R\n", "$$" ] }, { "cell_type": "markdown", "id": "impaired-booking", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "We assume a \n", " * birth rate and rate of death not caused by Covid 19 can be neglected (no vital dynamics)\n", " * no incubation time, immediately transition from $S$ to $I$\n", " * large population so we model it $N, I, R$ as continuous functions \n", "\n", "Note that we then have that the total population/number of individuals $N(t)$ satisfies\n", "$$\n", "S(t) + I(t) + R(t) = N(t) = \\mathrm{const}\n", "$$\n", "and we assume that we have rescaled the population number such that $N = 1$, so $I, S, R$ measures the proportion of susceptible, infectious and removed inviduals." ] }, { "cell_type": "markdown", "id": "fresh-times", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The final ODE system is given by\n", "\n", "\\begin{align}\n", "S' &= - \\beta S I\n", "\\\\\n", "I' &= \\beta S I - \\gamma I\n", "\\\\\n", "R' &= \\gamma I,\n", "\\end{align}\n", "\n", "where \n", "\n", "* $\\beta$ denotes the **infection rate**, and\n", "* $\\gamma$ the **removal rate**. \n", "\n", "Having this ODE in mind, an epidemic model can be simply specified by writing\n", "down a *state transition diagram*\n", "\n", "$$\n", "S \\overset{\\beta}{\\to} I \\overset{\\gamma}{\\to} R\n", "$$" ] }, { "cell_type": "markdown", "id": "jewish-aircraft", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A closer look at the derivation of the SIR model\n", "We give a brief motivation for the SIR model following the presentation \n", "in [[Chapter 8.3]](https://link.springer.com/chapter/10.1007/978-3-030-16877-3_8https://link.springer.com/chapter/10.1007/978-3-030-16877-3_8) of\n", "the book [[Programming for Computations - Python]](https://link.springer.com/book/10.1007/978-3-030-16877-3https://link.springer.com/book/10.1007/978-3-030-16877-3)." ] }, { "cell_type": "markdown", "id": "higher-subscriber", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Question**: How can we derive this model?\n", "\n", "Starting from a number of susceptible inviduals $S(t)$ and infectious individuals $I(t)$\n", "at some time $t$ we want to know how many susceptible inviduals get infected during \n", "a time interval $\\Delta t$.\n", "\n", "The change during this time interval $\\tau$ can be described a\n", "\\begin{align}\n", "S(t+\\Delta t) - S(t) = - \\beta \\Delta t S(t) I(t) \n", "\\tag{1}\n", "\\label{eq} \n", "\\end{align}\n", "What is the meaning behind the right-hand side term of \\eqref{eq}? " ] }, { "cell_type": "markdown", "id": "southwest-ozone", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " * First, we have a negative sign since $S$ is decreasing due to infections.\n", " " ] }, { "cell_type": "markdown", "id": "possible-lloyd", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " * Second, the term $$ S(t)I(t).$$\n", " is simply the number of **all possible contact pairs** between susceptible and infectious \n", " individuals.\n", " " ] }, { "cell_type": "markdown", "id": "durable-transformation", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " * Third the infection rate $\\beta$ is composed of two factor $$ \\beta = p \\mu$$ where\n", " * $p$ is probality with which a $S$-$I$ actually occur per unit time interval, so $p \\Delta t\n", " S(t)I(t)$ measures the number of **actual** contacts between susceptible and infectious \n", " individuals. \n", " * $\\mu$ is the probabilty with which an $S$ individual gets infected during an $S$-$I$ contact" ] }, { "cell_type": "markdown", "id": "polyphonic-spray", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Thus the total number of people newly infected during the time period $\\Delta t$ is thus $$\\underbrace{\\mu p \\Delta}_{:=\\beta} t S(t) I(t)$$ and therefore\n", "$$\n", "S(t+\\Delta t) - S(t) = - \\beta \\Delta t S(t) I(t) \\Leftrightarrow - \\beta S(t) I(t)\n", "= \\dfrac{S(t+\\Delta t) - S(t)}{\\Delta t} \\to S'(t) \\quad \\text{for } \\Delta t \\to 0.\n", "$$" ] }, { "cell_type": "markdown", "id": "humanitarian-alert", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### $R_0$ number and start of outbreaks\n", "\n", "Looking at $$ I' = \\beta S I - \\gamma I$$ we see that an outbreak of a disease (read: increase of number of infections) can only occur\n", "if $I'(0) > 0$, but this is of course equivalent to \n", "$$\n", "0 < \\beta S(0) I(0) - \\gamma I(0) \\Leftrightarrow \\underbrace{\\dfrac{\\beta}{\\gamma}}_{:=R_0} S(0) > 1 \n", "$$" ] }, { "cell_type": "markdown", "id": "guilty-staff", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "$$\n", " \\dfrac{\\beta}{\\gamma} =: R_0\n", "$$\n", "is known as the **basic reproduction number** and corresponds basically to the number of individuals infected by each infectious individual." ] }, { "cell_type": "markdown", "id": "tropical-instruction", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "The $R_0$ can be affected by e.g. social distancing, (temporal) immunization, vaccination campaign etc. It also determines the treshold for flock immunity. If for instance the basic reproduction number is $2$, the fraction of susceptible individual should be less that $0.5$ to avoid\n", "an outbreak in the presence of infected individuals." ] }, { "cell_type": "markdown", "id": "exact-bishop", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Breakout session (20 min)\n", "\n", "1. **Warm-up discussion**: \n", " * How many people have you met *physically* since Monday? \n", " * How can *social distancing* be taken into account in SIR model? (The person in the group who has met the least number of people since Monday will be the appointed as group leader :)" ] }, { "cell_type": "markdown", "id": "processed-conducting", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "2. **Challenge**: To prevent the collapse of our health care system, we need to predict the number of additional hospitalized patients (caused by Covid 19) at any point in time. Discuss in your group how to incorporate the dynamics of the fraction $H(t)$ of hospitalized patients into the SIR model to arrive at a $SIHR$ model. **Hint**: With which population category with $H$ interact? " ] }, { "cell_type": "markdown", "id": "dressed-concert", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "3. **Cool-down**: The SIR and even the SIHR model are very simplified models for diseaese spreading. Discuss possible effects/phenomena/parameters one might want to include in these models (e.g natural birth and death rates...) in a more accurate model. You can think of anything which somehow impact the population number or course of disease. Collect keywords on the [[mentimeter]](https://www.menti.com) word cloud, the group leader will quickly summarize (some) ideas." ] }, { "cell_type": "markdown", "id": "posted-turning", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Feeback: Discussion, ipad solution and mentimeter poll\n", "\n", "* Draw state diagram A, B, C and perform poll\n", "* Present final ODE model\n", "* Activate word cloud and discuss extensions" ] }, { "cell_type": "markdown", "id": "integrated-senegal", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Part II: An adaptive Runge-Kutta method for the SIHR model\n", "\n", "In this part we want to implement an adaptive Runge-Kutta method to solve the\n", "extended $SIHR$ model numerically." ] }, { "cell_type": "markdown", "id": "criminal-barrier", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Review: Runge-Kutta methods" ] }, { "cell_type": "markdown", "id": "consistent-checkout", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Explicit** Runge-Kutta schemes are specified in the form of a **Butcher table**:\n", "\n", "\\begin{equation*}\n", "\\begin{array}{c|ccc}\n", "c_1 & a_{11} & \\cdots & a_{1s}\n", "\\\\ \n", "\\vdots & \\vdots & & \\vdots\n", "\\\\ \n", "c_s & a_{s1} & \\cdots & a_{ss}\n", "\\\\ \n", "\\hline\n", "& b_1 & \\cdots & b_s\n", "\\end{array}\n", "\\end{equation*}\n", "\n", "with $c_1 = 0$ and $a_{ij} = 0$ for $j \\geqslant i$." ] }, { "cell_type": "markdown", "id": "micro-representation", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "So starting from $y_i, t_i$ and chosen step size $\\tau_i$\n", "the discrete solution at $t_{i+1}$ is computed as follows\n", "\n", "* Compute stage derivatives $k_j$ for $j=1,\\ldots,s$:\n", " \\begin{equation*}\n", " k_{j} =\n", " f(t_i + c_j \\tau, y_i + \\tau \\sum_{l=1}^{j-1} {a}_{jl} k_l)\n", " \\end{equation*}\n", "* Compute the next time step via\n", " \\begin{equation*} \n", " y_{i+1} = y_{i} + \\tau \\sum_{j=1}^s b_j k_j\n", " \\end{equation*}" ] }, { "cell_type": "code", "execution_count": 3, "id": "lasting-montgomery", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "class ExplicitRungeKutta:\n", " def __init__(self, a, b, c):\n", " self.a = a\n", " self.b = b\n", " self.c = c\n", "\n", " def __call__(self, y0, t0, T, f, Nmax):\n", " # Extract Butcher table\n", " a, b, c = self.a, self.b, self.c\n", "\n", " # Stages\n", " s = len(b)\n", " ks = [np.zeros_like(y0, dtype=np.double) for s in range(s)]\n", "\n", " # Start time-stepping\n", " ys = [y0]\n", " ts = [t0]\n", " dt = (T - t0) / Nmax\n", "\n", " while ts[-1] < T:\n", " t, y = ts[-1], ys[-1]\n", "\n", " # Compute stages derivatives k_j\n", " for j in range(s):\n", " t_j = t + c[j] * dt\n", " dY_j = np.zeros_like(y, dtype=np.double)\n", " for l in range(j):\n", " dY_j += a[j, l] * ks[l]\n", "\n", " ks[j] = f(t_j, y + dt * dY_j)\n", "\n", " # Compute next time-step\n", " dy = np.zeros_like(y, dtype=np.double)\n", " for j in range(s):\n", " dy += b[j] * ks[j]\n", "\n", " ys.append(y + dt * dy)\n", " ts.append(t + dt)\n", "\n", " return (np.array(ts), np.array(ys))" ] }, { "cell_type": "markdown", "id": "acknowledged-lightning", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Usage example** \n", "\n", "We use the class above to create a Runge-Kutta solver based on Heun's method\n", "which is specified by \n", "\\begin{equation*}\n", " \\begin{array}{c|cc}\n", " 0 & 0 & 0 \\\\ \n", " 1 & 1 & 0 \n", " \\\\ \n", " \\hline \n", " & \\frac{1}{2} & \\frac{1}{2} \n", "\\end{array}\n", "\\end{equation*}\n", "and the ODE\n", "$$\n", "y' = \\lambda y\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "id": "familiar-private", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "# Define Butcher table for Heun\n", "a = np.array([[0, 0], [1.0, 0]])\n", "b = np.array([1 / 2, 1 / 2.0])\n", "c = np.array([0.0, 1])\n", "\n", "# Create a new Runge Kutta solver\n", "rk2 = ExplicitRungeKutta(a, b, c)\n", "\n", "# Initial time, stop time\n", "t0, T = 0, 1\n", "\n", "# Initial value\n", "y0 = 1\n", "\n", "# Number of steps\n", "Nmax = 10\n", "\n", "# rhs of IVP\n", "lam = 1\n", "f = lambda t, y: lam * y\n", "\n", "# solver can be simply called as function:\n", "ts, ys = rk2(y0, t0, T, f, Nmax)" ] }, { "cell_type": "code", "execution_count": 5, "id": "blocked-translator", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ts, ys, \"c--o\", label=r\"$y_{\\mathrm{heun}}$\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "broke-timothy", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Review: Runge-Kutta method with stepsize control" ] }, { "cell_type": "markdown", "id": "seven-samuel", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Given $t_n, \\mb{y}_n$ and a step size $\\tau_n$. \n", "* Do one step with the method of choice, and find an error estimate $\\mb{le}_{n+1}$. \n", "\n", "* if $\\|\\mb{le}\\|_{n+1} < \\text{Tol}$\n", "\n", " * Accept the solution $t_{n+1}, \\mb{y}_{n+1}$.\n", "\n", " * If possible, use increased step size $\\tau_{n+1} := \\tau_{new}$ for the next step.\n", "\n", "* else\n", "\n", " * Repeat the step from $(t_n,\\mb{y}_n)$ with a reduced step size $\\tau_n := \\tau_{new}$.\n", "\n", "In both cases the the new time-step suggestion $\\tau_{new}$ is computed by\n", "$$\n", "\\tau_{new} \\approx \\mathrm{fac} \\left( \\frac{\\text{Tol}}{\\|\\mb{le}_{n+1}\\|} \\right)^{\\frac{1}{p+1}} \\tau _{n}.\n", "$$\n", "where $\\mathrm{fac} = 0.8$ is a safety factor." ] }, { "cell_type": "markdown", "id": "found-oakland", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "A Runge - Kutta methods with an error estimate are usually called **embedded Runge - Kutta methods** or **Runge - Kutta pairs**, and\n", "the coefficients can be written in a Butcher tableau as follows\n", "\n", "$$\n", "\\begin{array}{c|ccccl}\n", " c_1 & a_{11} & a_{12} & \\cdots & a_{1s} \\\\ \n", " c_2 & a_{21} & a_{22} & \\cdots & a_{2s} \\\\ \n", " \\vdots & \\vdots &&&\\vdots \\\\ \n", " c_s & a_{s1} & a_{s2} & \\cdots & a_{ss} \\\\ \\hline\n", " & b_1 & b_2 & \\cdots & b_s & \\qquad\\text{Order $p$}\\\\ \\hline\n", " & \\widehat{b}_1 & \\widehat{b_2} & \\cdots & \\widehat{b}_s & \\qquad\\text{Order $\\widehat{p}= p+1$}\n", " \\end{array}.\n", "$$\n", " " ] }, { "cell_type": "markdown", "id": "flush-civilization", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The error is simply estimated by $$\\| \\mb{le}_{n+1}\\|$$ with \n", "$$ \\mb{le}_{n+1} = \\tau_n\\sum_{i=1}^s (\\widehat{b}_i - b_i)\\mb{k}_i.\n", "$$" ] }, { "cell_type": "markdown", "id": "responsible-monitor", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Breakout session 2 (20 min): Implementing an adaptive Runge-Kutta solver\n", "Now we ask you to \n", "* Extend the Runge-Kutta class to include adaptive time-stepping\n", "* Run a first quick test using the example above: $y' = y$, $y(0)$ with the exact solution $y(t) = e^t$ with $tol=10^{-3}$ to see whether you get a meaningful result " ] }, { "cell_type": "code", "execution_count": null, "id": "sufficient-poison", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "class EmbeddedExplicitRungeKutta:\n", " # TODO: Extend __init__ so that it also takes in 'bhat' and 'order' as additional argument\n", " def __init__(self, a, b, c):\n", " self.a = a\n", " self.b = b\n", " self.c = c\n", " ...\n", " ...\n", "\n", " # TODO: Extend previous __call__ routine to take in toleranse tol as well:\n", " def __call__(self, y0, t0, T, f, Nmax):\n", " # TODO: Extract Butcher table and\n", " a, b, c, bhat, order = ...\n", "\n", " # Stages\n", " s = len(b)\n", " ks = [np.zeros_like(y0, dtype=np.double) for s in range(s)]\n", "\n", " # Start time-stepping\n", " ys = [y0]\n", " ts = [t0]\n", "\n", " # TODO: What is a simple choice for the initial time step?\n", " dt = ...\n", "\n", " # Counting steps\n", " N = 0\n", " N_rej = 0\n", "\n", " while ts[-1] < T and N < Nmax:\n", " t, y = ts[-1], ys[-1]\n", " N += 1\n", "\n", " # Compute stages derivatives k_j\n", " for j in range(s):\n", " t_j = t + c[j] * dt\n", " dY_j = np.zeros_like(y, dtype=np.double)\n", " for l in range(j):\n", " dY_j += a[j, l] * ks[l]\n", "\n", " ks[j] = f(t_j, y + dt * dY_j)\n", "\n", " # Compute next time-step\n", " dy = np.zeros_like(y, dtype=np.double)\n", " for j in range(s):\n", " dy += b[j] * ks[j]\n", "\n", " # bhat was not given then fall back to a standard RKM witu uniform step size\n", " if bhat is None:\n", " ys.append(y + dt * dy)\n", " ts.append(t + dt)\n", " # TODO:\n", " # Compute yhat or dyhat, estimate error,\n", " # decide whether to accept step or not, compute new time step\n", " else:\n", " # TODO: Compute dyhat\n", " dyhat = ...\n", "\n", " # TODO: Error estimate, use norm() function for this\n", " err = ...\n", "\n", " # TODO: Accept time-step\n", " if err <= tol:\n", " ...\n", " ...\n", "\n", " else:\n", " print(f\"Step is rejected at t = {t} with err = {err}\")\n", " N_rej += 1\n", "\n", " # TODO: Compute New step size\n", " dt = ...\n", "\n", " print(f\"Finishing time-stepping reaching t = {ts[-1]} with final time T = {T}\")\n", " print(f\"Used {N} steps out of {Nmax} with {N_rej} being rejected\")\n", "\n", " return (np.array(ts), np.array(ys))" ] }, { "cell_type": "markdown", "id": "veterinary-stuff", "metadata": {}, "source": [ "**Solution.**" ] }, { "cell_type": "code", "execution_count": 6, "id": "least-struggle", "metadata": {}, "outputs": [], "source": [ "class EmbeddedExplicitRungeKutta:\n", " def __init__(self, a, b, c, bhat=None, order=None):\n", " self.a = a\n", " self.b = b\n", " self.c = c\n", " self.bhat = bhat\n", " self.order = order\n", "\n", " def __call__(self, y0, t0, T, f, Nmax, tol=1e-3):\n", " # Extract Butcher table\n", " a, b, c, bhat, order = self.a, self.b, self.c, self.bhat, self.order\n", "\n", " # pessisimistic factor used in the new time-step computation\n", " fac = 0.8\n", " # some more advanced parameters for better controlling of time-step choice for higher-order methods\n", " eps = 1e-15 # machine precision\n", " facmax = 5.0 # Maxima\n", " facmin = 0.1\n", "\n", " err = 0\n", "\n", " # Stages\n", " s = len(b)\n", " ks = [np.zeros_like(y0, dtype=np.double) for s in range(s)]\n", "\n", " # Start time-stepping\n", " ys = [y0]\n", " ts = [t0]\n", "\n", " # Simple choice for initial time step\n", " dt = (T - t0) / Nmax\n", " # Counting steps\n", " N = 0\n", " N_rej = 0\n", "\n", " while ts[-1] < T and N < Nmax:\n", " t, y = ts[-1], ys[-1]\n", " N += 1\n", "\n", " # Compute stages derivatives k_j\n", " for j in range(s):\n", " t_j = t + c[j] * dt\n", " dY_j = np.zeros_like(y, dtype=np.double)\n", " for l in range(j):\n", " dY_j += a[j, l] * ks[l]\n", "\n", " ks[j] = f(t_j, y + dt * dY_j)\n", "\n", " # Compute next time-step\n", " dy = np.zeros_like(y, dtype=np.double)\n", " for j in range(s):\n", " dy += b[j] * ks[j]\n", "\n", " if bhat is None:\n", " ys.append(y + dt * dy)\n", " ts.append(t + dt)\n", " else:\n", " dyhat = np.zeros_like(y, dtype=np.double)\n", " for j in range(s):\n", " dyhat += bhat[j] * ks[j]\n", "\n", " # Error estimate\n", " err = dt * norm(dy - dyhat)\n", "\n", " # Accept time-step\n", " if err <= tol:\n", " # ALTERNATIVE: more robust, activate this one for FEHLBERG\n", " # if err <= tol + tol*norm(y):\n", "\n", " ys.append(y + dt * dyhat)\n", " ts.append(t + dt)\n", " else:\n", " # print(f\"Step is rejected at t = {t} with err = {err}\")\n", " N_rej += 1\n", "\n", " # Compute new step size\n", " dt = fac * (tol / err) ** (1 / (order + 1)) * dt\n", " # Decrease time-step further if we go beyond T\n", " dt = min(dt, abs(T - ts[-1]))\n", " # ALTERNATIVE: more robust, activate this one for FEHLBERG\n", " # dt = min(dt*min(facmax, max(facmin, fac*(tol/err)**(1/(order+1)))),abs(T-ts[-1]))\n", "\n", " print(f\"Finishing time-stepping reaching t = {ts[-1]} with final time T = {T}\")\n", " print(f\"Used {N} steps out of {Nmax} with {N_rej} being rejected\")\n", "\n", " return (np.array(ts), np.array(ys))" ] }, { "cell_type": "markdown", "id": "comic-crazy", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Test example 1:**\n", "Solve\n", "$$\n", "y'(t) = y(t), \\quad y(0) = 1\n", "$$\n", "until $T=1$ with \n", "and the Heun-Euler pair which is is given by\n", "$$\n", "\\begin{array}{c|cc} 0 & & \\\\ 1 & 1 & \\\\ \\hline & 1 & 0 \\\\ \\hline \\displaystyle & \\frac{1}{2} & \\frac{1}{2} \n", " \\end{array}\n", "$$" ] }, { "cell_type": "code", "execution_count": 7, "id": "quick-punishment", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Finishing time-stepping reaching t = 1.0 with final time T = 1\n", "Used 12 steps out of 10000 with 0 being rejected\n" ] } ], "source": [ "## Test solver\n", "# Initial time, stop time\n", "t0, T = 0, 1\n", "# Initial value\n", "y0 = 1\n", "# Number of steps\n", "Nmax = 1000\n", "\n", "# rhs of IVP\n", "lam = 1\n", "f = lambda t, y: lam * y\n", "\n", "# Heun-Euler\n", "a = np.array([[0, 0], [1.0, 0]])\n", "bhat = np.array([1 / 2, 1 / 2.0])\n", "b = np.array([1, 0.0])\n", "c = np.array([0.0, 1])\n", "order = 1\n", "\n", "# Run method\n", "Nmax = 10000\n", "tol = 1.0e-2\n", "euler_heun = EmbeddedExplicitRungeKutta(a, b, c, bhat, order)\n", "ts, ys = euler_heun(y0, t0, T, f, Nmax, tol)" ] }, { "cell_type": "code", "execution_count": 8, "id": "latest-terror", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.close()\n", "plt.plot(ts, ys, \"-o\", label=\"$y_{heun}$\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "dangerous-practitioner", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A SIR model class\n", "Next, similar to the *ExplicitRungeKutta* class above, we will wrap the SIR model \n", "\\begin{align}\n", "S' &= - \\beta S I\n", "\\\\\n", "I' &= \\beta S I - \\gamma I\n", "\\\\\n", "R' &= \\gamma I,\n", "\\end{align}\n", "into a little SIR class of the following form:" ] }, { "cell_type": "code", "execution_count": 9, "id": "grateful-lotus", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "class SIR:\n", " def __init__(self, beta, gamma):\n", " self.beta = beta # infectional rate\n", " self.gamma = gamma # removal rate\n", "\n", " def __call__(self, t, y):\n", " return np.array(\n", " [\n", " -self.beta * y[0] * y[1],\n", " self.beta * y[0] * y[1] - self.gamma * y[1],\n", " self.gamma * y[1],\n", " ]\n", " )" ] }, { "cell_type": "markdown", "id": "exciting-greensboro", "metadata": {}, "source": [ "To create a new SIR model for some given parameters, you instatiate an object as follows:" ] }, { "cell_type": "code", "execution_count": 10, "id": "smooth-sugar", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "# Data for the SIR model\n", "# denote basic reproduction number by r0\n", "r0 = 2\n", "gamma = 1 / 18.0\n", "beta = r0 * gamma\n", "\n", "# Define a model\n", "sir = SIR(beta=beta, gamma=gamma)" ] }, { "cell_type": "markdown", "id": "documentary-planning", "metadata": {}, "source": [ "The ```sir``` object can now simply used as the right-hand side in our ODE solver, e.g. ```sir(t0, y0)```:" ] }, { "cell_type": "code", "execution_count": 11, "id": "entire-dancing", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-5.55552778e-07 2.77775000e-07 2.77777778e-07]\n" ] } ], "source": [ "# Trondheim has 200.000 inhabitants we start with 1 infected person\n", "I_0 = 1 / 200000\n", "S_0 = 1 - I_0\n", "R_0 = 0\n", "\n", "y0 = np.array([S_0, I_0, R_0])\n", "\n", "t0, T = 0, 365 # days, we consider a whole year\n", "\n", "# Illutrating how sir can be called like a function\n", "print(sir(t0, y0))" ] }, { "cell_type": "markdown", "id": "ecological-source", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Testing our ```EmbeddedExplicitRungeKutta``` solver using either the Heun-Euler defined by\n", "$$\n", "\\begin{array}{c|cc} 0 & & \\\\ 1 & 1 & \\\\ \\hline & 1 & 0 \\\\ \\hline \\displaystyle & \\frac{1}{2} & \\frac{1}{2} \n", " \\end{array}\n", "$$\n", "or \n", "the\n", "embedded Runge-Kutta 4(3) variant\n", "due to **Fehlberg**:\n", "$$\n", "\\begin{array}{c|ccccc}\n", " 0 & 0 & 0 & 0 & 0 & 0\n", " \\\\ \n", " \\frac{1}{2} & \\frac{1}{2} & 0 & 0 & 0 & 0\n", " \\\\ \n", " \\frac{1}{2} & 0 & \\frac{1}{2} & 0 & 0 & 0\n", " \\\\\n", " 1 & 0 & 0 & 1 & 0 & 0\n", " \\\\\n", " 1 & \\frac{1}{6} & \\frac{1}{3} & \\frac{1}{3} & \\frac{1}{6} & 0 \n", " \\\\\n", " \\hline \n", " & \\frac{1}{6} & \\frac{1}{3} & \\frac{1}{3} & 0 & \\frac{1}{6} \n", " \\\\\n", " \\hline \n", " & \\frac{1}{6} & \\frac{1}{3} & \\frac{1}{3} & \\frac{1}{6} & 0\n", "\\end{array}\n", "$$" ] }, { "cell_type": "code", "execution_count": 12, "id": "hungarian-dividend", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Finishing time-stepping reaching t = 365.0 with final time T = 365\n", "Used 741 steps out of 10000 with 3 being rejected\n" ] } ], "source": [ "### NB: If your solver doesn't work just uncomment the next line\n", "#### after you have fetched rkm.py\n", "# from rkm import EmbeddedExplicitRungeKutta\n", "\n", "# Heun-Euler\n", "a = np.array([[0, 0], [1.0, 0]])\n", "bhat = np.array([1 / 2, 1 / 2.0])\n", "b = np.array([1, 0.0])\n", "c = np.array([0.0, 1])\n", "order = 1\n", "\n", "# Run method\n", "Nmax = 10000\n", "tol = 1.0e-5\n", "euler_heun = EmbeddedExplicitRungeKutta(a, b, c, bhat, order)\n", "ts, ys = euler_heun(y0, t0, T, sir, Nmax, tol)" ] }, { "cell_type": "code", "execution_count": 13, "id": "marked-pastor", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Fraction of population')" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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U1im/q1Vg0mkw6bWcfmBPrp4yAIB1JbXc8+katGoVBp0ajVqNXqPGYtBgNWi5cGI/Zf8UFtfi8gWwm8OtEykmrRQVQogOES33xbUA8Pv96PX6Jl/LysoiKyuLRYsWcfDBByvPf//99wCMHTu20fIzZ85k5syZTa7r/fffB6Curq7J1/eWSqXCqNMoTf3NOfOgXpx5UK+o68u2Gdl47/SoywGcuH93Tty/e0zL5keJrzNTq1WkmnWNCg6TXsN5E/rE9P7pw/PolWGh1u2jzuPH4QoXaW5fALWq8Rl+hkWPw2bA6Q2/7g+GqPcGqPcG8AZ2zy1e4nDz7bqmiwqAU8b2UOJ9/Ov1fLKySHnNoFWTk2IkL9XIuH4ZXHVEuKgIhUKU13nJtOqlQBBCtAmrNdy/qrncF9cCID09vdmJCjQaDSeccALPPfccF154ISkpKVRXV3Pfffdx4IEHkpqa2qrPAfZ6ICHRdXVLM0Ut0CLevnBco9/9gSAuXwCnN4CxQZ+CwXkpvHj2WPzBEB5/gEAwhMcfpN7jp87tJ8W4u1jpYTczLD+Fqvpwa0Wdx8+2SifbKp2kNShqyuu8jL3nS6wGLf1zrAzKTWFQro1h+akMz09Fr5WOkEKI1omW++JSAKxZs4bzzz+f1atXEwgEGD9+PN999x0qlYoTTjiBuXPnMmrUKG677TY+/fRTBg8ezJFHHsnChQvZtWsXX3/9das+L9LRsKKioj02RyQorUaNTaPGZmx8uSPTamDSoNhuQb1x2iBunDZI+b3e46fY4WZXtQuzfvefX2mtmzSzjmqnj2Xbqlm2rVp5zahT89p5BzKmt33fNkgIkVSi5b64FAAZGRmccMIJHHfccYRCIdLT09FoNFRWVvLxxx9jt9t56aWX6NGjB6tXr+a+++5j5cqVHHvssVx33XX06NEj+oc00PA6iBDxZDFo6ZdlVW59jBjaLZXld0ylos7D2uJa1hbXUljsYMnWKjaX19M/26Yse+eHf1Be72XK4BwOG5hFmrnpy2hCiOQWLffFpQDIzs7muuuu2+P5jIwMqqqqlKAhvAH33nvvPn1e5DpIbW3zt6MJ0RlkWA0cXGDg4IJM5blqp1fpUxAKhfj09yLK67x8urIIjVrFxP6ZnDymB4cPzpbbH4UQimi5L659AJqSlpbW5uuM3P7Q2jkEhOgMGp7hq1Qq3rv4YL5cU8KXa0r4dXMl3xSW8U1hGWlmHf88YThHDc+LY7RCiM4iWu7rdAVAe9Drwz2r3W53vEMRYp/1zDBz7oQ+nDuhDxV1Hj5Yvot3Fm9nbXEtPTN23+vr8gYw6aVFQIhkFS33JUUBoFKpsFqtbX4boBDxlmE1cN6EPpw3oQ/rSmoZkLO7r8BZL/yKUa/hxmkDGdot9rtmhBCJIVruS4oCAMKXFmRCIJHIGib/XdUuVu2qod4b4Pv1ZZwwKp/rpg6M+ZZIIURiaCn3Jc3NxSaTSfoAiKTRLc3E9zcezjkH90arVvHe0p0c/tBCnvl2I/4GgxoJIRJbS7kvaQoAg8GAx+OJvqAQCcJu0XPnsUP58ppDOXp4Hm5fkH9+vpaTn/mp0XDTQojE1VLukwJAiATXK8PCk6eP5qVzxpKfZuKwgdldbhprIcTeaSn3JU0fAK1Wi9/vj76gEAnqsIHZfHH1xEazNa7YXk3vDEvMkzsJIbqWlnJf0rQAaDSaZqcMFiJZWAxaZV6BXdUuzn7xV45+/HvWlcggWUIkopZyX1IVAMGgdH4SIiIEdE83s6PKxYn/WcSijeXxDkkI0cZayn1JUwAIIRrLTzPxzkXjOGpYLrUeP2e98Cv/t2RHvMMSQnSQpCkAAoEAanXSbK4QMTHqNDxx2mjOn9AHXyDEde+s4NnvNsU7LCFEG2kp9yVNRvT7/Wi1SdPnUYiYadQqbjtmCHOPGwrAPz9fQ2Gx9AkQIhG0lPuSJiP6fD50OunpLERzzhrfG4shfEgYmGuLsrQQoitoKfclTQHg9XrR62XedCFactL+3Rv97vYFMOpkQiEhuqqWcl/SXALweDwYjcZ4hyFEl7FkayWHPvgNCwtL4x2KEGIvtZT7kqYA8Hq9cglAiFb4trCMEoeHS15fyqpdNfEORwixF1rKfUlTAEgfACFa5+opAzhhVD5Ob4ALXllCRZ0MpS1EV9NS7kuaAqC+vh6LxRLvMIToMlQqFf/823D265HGzmoX18xbQVAmERKiS2kp9yVFARAMBnE4HKSlpcU7FCG6FKNOw1NnjCbdrOPbdWW88OPmeIckhIhRtNyXFAVAdXU1oVAIu90e71CE6HLyUk3cd+IIAO77fC3bK5ueW1wI0blEy31JcRtgdXU1gLQACLGXjhyay/VHDmRk9zR62M3xDkcIEYNouS8pCoCqqioA0tPT4xyJEF3XpZMK4h2CEKIVouW+pLgEUFMTvoUpNTU1zpEIkRgWbSznj51ya6AQnVm03JcUBUB9fT2A3AUgRBv4cnUJpz/3C1e/vRx/QKbYFqKzipb7kqIAqKurA8BqtcY5EiG6vgn9M+lpN7O+tI6Xf9oa73CEEM2IlvuSogAoLy8HICMjI86RCNH1GXUabj96CAD/ml/Itgq5K0CIziha7kuKAqCsrAyAzMzMOEciRGI4YkgOx4zIw+ULcMv7vxMKyQBBQnQ20XJfUhQATqcTs9mMWp0UmytEh5hz3FDSzDp+2FDO+8t2xjscIcRfRMt9SZERKysrZQwAIdpYptXAbX9eCnji6w0yTLAQnUy03JcU4wBUVFSQlZUV7zCESDh/G5VPeZ2Hk/bvjlqtinc4QogGouW+pCgASktL5fq/EO1ArVZx0aH94h2GEKIJ0XJfUlwCKCsrIzs7O95hCJHQvP4g360ri3cYQog/Rct9SVEA1NbWYrPZ4h2GEAnLFwhyzOPfc9aLv7K22BHvcIQQRM99SVEA1NXVSQEgRDvSadSM75dJKAT3fLpGbgsUohOIlvsSvgDw+Xw4nU65C0CIdnbF5P6kGLV8v76cbwpL4x2OEEktltyX8AWAzAQoRMewW/RcMbk/AHd/sgavX+YJECJeYsl9CV8ARJsPWQjRdmaN603fTAubyut5edGWeIcjRNKKJfclfAHgcIQ7JKWkpMQ5EiESn16r5vZj/xwc6JsNONy+OEckRHKKJfcl/DgA0gIgRMc6bEAWJ4zKZ3y/DCz6hD/ECNEpxZL7Ev6vUwoAITqWSqXikVP2i3cYQiQ1uQTA7mYQuQ1QiPio8/jjHYIQSSeW3JfwBUBNTQ0AqampcY5EiOQSCoX41/xCDrr3KzaV1cU7HCGSSiy5L+ELAOkEKER8qFQqyus81Hn8PPC/wniHI0RSiSX3JXwBUFtbi8lkQqPRxDsUIZLO1VMGYNCq+d+qYlbuqI53OEIkjVhyX1IUAHL2L0R85KQYOXt8bwDu/99aGSJYiA4SS+5LigJAOgAKET8XH9aPFKOWHzdUsLBQZgsUoiPEkvs6vADYunUrZ511FkOGDOH4449n6dKlLS5fW1vL/fffz6xZs7jttttwOp2t+jyXy4XRaNyXkIUQ+yDNrOfyw8NDBN/72Rr8ARkiWIj2Fkvu69ACYPny5QwZMoSlS5cyc+ZM3G43Y8eOZeHChU0uX1VVxahRo3j11Vcxm818/PHHHHvssa0qArxeL3q9vo22QAixN2aN70VPu5luaSYcbrktUIj2Fkvu69CBgC677DIOOOAA5s+frwR24okncscdd/Ddd9/tsfyLL76I0+nkjz/+wGg0Ul5eTlZWFt9++y1HHXVUTJ8pBYAQ8WfQanjvkvFkWPSoVKp4hyNEwutUBUBRURE//vgjX375ZaOgzj77bI477jhKS0vJzs5u9J4tW7aQlZWlLK9SqVCpVMr9jQ2tWbOGtWvXolarMRgMpKWlcdBBB+H3+9FqE37AQyE6vUyrId4hCJE0Ysl9HZYZf/rpJwDGjx/f6Pk+ffoA4b4Bfy0ATj/9dB5//HGOP/54pk6dytNPP01BQQFTp07dY/3z5s1jzpw5jZ4LhUKEQiHU6oTv6yhEl7FiezX//W4Td88YRrpFWueEaA+x5L4OKwDq6+vR6/V7dEowmUxAuLnir8aMGcPUqVP55JNP+OKLL/B6vVx77bVN3toQCATaJ3AhRJv61xeFfL++nPx0E7dMHxzvcIRIWh12apyZmYnX692jA19lZSUAGRkZe7zn5Zdf5vvvv+fVV1/F4XDw9NNP88gjjzB37tw9lh08eDDHH388xxxzDFOmTGHMmDHKa3LvsRCdxw1HDgLg5UVbKK5xxzkaIRJXtNzXYS0AvXv3BmDt2rXsv//+yvNLlizBZrMxYMCAPd7zyCOPcOmll3LGGWcAcOGFF7Jo0SLmzZvHXXfd1WjZmTNnMnPmzD3WodFo8PlkTnIhOovh3VOZPjyXz34v5vGv13PPCcPjHZIQcfHTrp/4uehntjm2Ue2p5u4Jd5NlykKv2fdLY7Hkvg4rAAYNGkTfvn154403lALA7/fzyiuvMG7cuCavVZSWlpKbm9vouZSUFOrqYp9YRK/XK2MiCyE6h2umDOB/fxTz9m/buWBiX3plWOIdkhBtIhAMsKNuB0X1RZTUl7Crfhc7a3eyq34XxfXFzB0/l7G5Y4FwAfDiqheV905/bzp3H3w3x/Y7dp/jiCX3dVgBoFKpuPbaa7n88suBcGfAp59+mp9//pkvv/wSCDdXvPfeexx33HHodDomT57Mo48+yujRoxk0aBDLli3jzTffbPJMvzk6nU5aAIToZAqybZw4ujvvLNnBQ1+s47GZo+IdkhAtKqkvYUfdDspd5VS4Kqjx1FDjraHSXUk3Szeu2v8qAGq8NRzz/jHNrqe4vlj5+dAeh2LSmehp60mvlF7kWfLIMO15OXxvxJL7OvT+uIsvvhi73c4NN9zAww8/zH777cenn37K4YcfDsDnn3/OSSedxJNPPskll1zCQw89xMUXX8zkyZMJhULo9XpmzZrFvffeG/NnGgwGPB5Pe22SEGIvXTVlAB8u38VXa0qorPdilzsCRAdz+V0UVhZS7CympL6Eclc5RfVFlDnLqPJU8e/D/k3ftL4APLbsMT7a+FGT6xlkH6QUAOmGdPqk9sFutJNjziHXkkt3W3fyrfnkWnLJt+Yr79s/Z3/2z9m/yXXuq1hyX4cWACqVilNPPZVTTz2VQCCwxyxFU6ZM4e677+b0008HIC8vjw8++AC3201FRQU5OTmtvqffaDTidktHIyE6m/w0E/86eSRje6dL8hdtyhvwsrNuJ6XOUqo91VS7q9lZt5NttdsYljmM84efD8DO2p2c+fmZza6nwl1BX8IFQEFaASOyRpBlyiLTlEmKPoVUQyp2o508S57yHpVKxUczmi4UOlIsuS9uI+Q0NUWhTqfj1ltv3eN5o9FIfn7+Hs/HQqfT4ffL0KNCdEbHjewW7xBEFxUKhdhWu41N1ZvYWLORmYNmYtGF+5Jc9OVF/Fb8W5Pvq/fVKwVAujGdYRnDyLGEz9QzTZnkWnLJNmVjN9rpbuuuvO+cYedwzrBz2n/D2kgsuS/hh8gzGo24XK54hyGEaIE/EOSTlUVMH56HXisDd4k91XnrWFq6lDUVa/i9/HdWlq2kylOlvH5Y98MoSC8AoG9qX4rqisix5JBuSCfFkEK+NZ8eth4MSN99x1mGKYM3j3mzw7elI8SS+xK+ALBara26a0AI0fEue2MZ/1tVTFmth9kT+8Y7HNEJFNcXU+muZEjGEAB21e/i0q8ubbRMhjGDQRmD6GXrhVVvVZ6/9cBbk37OiVhyX8IXADabDY/Hg8/nQ6fTxTscIUQTTh7bnf+tKubpbzcy88CeWA0Jf2gSfxEIBlhWuoyvtn3FT7t+YmPNRkZlj+KVo14BoF9qPw7OP5g+KX0YljmMEVkj6G7t3mSiT/bkD7HlvoT/K7PZbADU1dWRnp4e52iEEE2ZNDCb0T3TWLqtmv98s4Ebpg2Kd0iigxRWFvJ/6/6PL7d9SbmrXHneorOQacokFAqhUqnQqDU8fcTTcYy0a4kl9yV8AWC1hpuFpAAQovNSqVTcfswQTvjPIp77YTNnje9NToox+htFlxRJ6gBrKtfwVuFbAORb85naayoTu09kZNZIdBpptd1bseS+hC8AIlVQbW1tnCMRQrRkVM90jhqWy+d/FPPCD5u5WSYKSjiFlYW8tOolMk2ZXDvmWgAm95zMpupNHNnnSIbYh0jzfRuJJfclfHfbyE6Q4YCF6PwuOrQfAK//so0al4zgmSiWlizlgi8u4KSPT+KTTZ/w/ob38QXC/782vY1rxlzD0IyhkvzbUCy5L+FbAMxmM8AesxAKITqfkT3S+Pv+3RnRPRWD3A7Y5RVWFvLwkodZtGsRACatib/1/xtnDD5DmvfbWSy5L+ELAIslPDBEfX19nCMRQsTiwb+PjHcIog2sq1rH3z/+OyFCWHVWzhhyBmcMPoNUQ2q8Q0sKseS+NikA/H4/arW6yRn94k0KACG6rmAwhFotzcJdRSAYQKMOj/I6IH0AE7tPpIetBxeOuJA0Y1p8g0syseS+VmXsxYsXM3v2bKZOncphhx3G+PHj6dGjB3q9nssuu2zfom0nkZ0glwCE6DrcvgD3/28t0x/7Hl8gGO9wRBTBUJDPNn3GMe8fQ2FlofL8Y4c/xo0H3CjJPw5iyX0xtwC4XC6OOuoosrOzOeKIIwgEAgBMnTqVXr16MXny5H0Mt33Y7XYAKioq4hyJECJWeo2aBatL2FBaxwfLdvL3MT3iHZJoxsbqjcz9aS7LSpcBMK9wHrePux0AtarztQoni1hyX8wFQCAQoKamhn/84x9cfPHF+x5dB7HZbFitVnbt2hXvUIQQMVKrVVx8aD+ufWcFT327kRNHd5dLAZ2My+/i2ZXP8uKqF/EH/WQYM7h81OXMKJgR79AEseW+mMszq9XK7bffzs0338xXX33VJgF2lIyMDCorK+MdhhCiFY7brxv5aSY2ldXz5ZqSeIcjGlhftZ6TPz6ZZ39/Fn/Qz0kDTuLDGR9y4oATlT4AIv6i5b6YWwCcTicajQatVssRRxzBYYcdxtFHH01WVhZ1dXUceeSRFBQUtEnQbc1ut1NeXh59QSFEp6HTqDl3Qh/u+mQ1z36/ialDc+MdkviTWWemxFlCQVoBd467k/2y94t3SKIJ0XJfzAVAUVERb7/9Nj179qRbt25s2rSJf/zjHzidTlJTU7FYLJ22AMjNzaW4uDjeYQghWumUsT3495fr+G1LFX/srGFYvtxCFi+76naRZ8lDpVKRb83n6SOeZkjGEIxaGbK5s4qW+2IuAPr168eKFSvaJKiOlpuby7Jly+IdhhCilawGLX/fvwcv/LiZr9aUSgEQB6FQiHfWvcODvz3ItWOu5dRBpwIwOmd0nCMT0UTLfa0eB8Dr9fLtt9+ydetW7HY748ePJze3czfN5eXlUVpaSjAY7JRjFQghmnfOwb05anguY3rJZF4dzelzcseiO5i/ZT4AhVWFUd4hOpNoua9VBcDKlSs56qijKCoqomfPntTV1VFXV8fNN9/MnXfe2WZBt7Xc3FyCwSClpaWdvlgRQjTWw26mh90c7zCSznbHdq5eeDWFVYWYtWbuGHcHR/c9Ot5hiVaIlvtadTp89dVXk56ezvLly9myZQtlZWX897//Zc6cOZ36zoC8vDwASktL4xyJEGJfbCqrwy8DA7W7b7d/y8mfnExhVSG9Unrx1jFvSfLvgqLlvlYVANu2bWPKlCmMGDECCM/hPWvWLAYPHsxHH320j6G2n4yMDEAGAxKiK7vl/d85/KFv+WqtFPLtKRAM8MTyJ6jz1TG552TeOPoN+qT2iXdYYi9Ey32tKgBmzJjBSy+9xMqVK5XnCgsL2bp1K/369duHMNtXamq445BMCSxE19U3Mzy06eu/bItzJIlNo9bw8GEPc+3+1/LIYY+Qok+Jd0hiL0XLfa0qAG6++Wb69u3LyJEj2W+//TjkkEMYOXIkAwcOZPbs2fsebTuJTIsoEwIJ0XWdtH939Fo1368vY3ulzO3Rltx+N/MK5xEKhQDoYevB2cPORqWS0Re7smi5r1UFgN1u59dff+X//u//mDx5MoMHD+aFF15g0aJFmEymfY+2nciEQEJ0fWlmPdOH5RIKwTuLt8c7nIRR5a7ivC/O466f7+LFVS/GOxzRhqLlvlbfBqjRaDjxxBM58cQT9y2yDiRTAguRGE4e24MPlu/i/5bs4MojBqCR+QH2SZmzjPO/OJ9NNZvIs+QxMX9ivEMSbSha7muxAAgEAthsNh599FFmz57Nq6++ypIlS7DZbKSkpKDRaPB6vahUKi677DLlwzobuQQgRGI4qE8GPewmtle6+HlTBQcXZMY7pC5ru2M7sxfMZmfdTgrSCnhmyjNkm7PjHZZoQ9FyX4sFgEqlYvjw4QwZMgSAdevW8fPPP+NwOKitrSUQCKDX67FYLJxyyimdtgAwGAyoVCpcLle8QxFC7AO1WsUJ++Xz9Heb2FReLwXAXtpUvYnzvzifMlcZQzOG8tQRT5FulIGWEk203NdiAaBWq/nll1+U3++66y7uuuuuto2wA6hUKkwmk/QBECIBnHNwH86b0JdUsy7eoXRZ9/xyD2WuMsbkjOGJyU9g0XXOkzexb6LlvlZ1Anz11VcpKema03JaLBa5BCBEAki36CX576P7J97PKQNP4T9H/EeSf4JrKffFXAD4/X5mzZrFggUL2iywjmS1Wqmrq4t3GEKINuILBFm9S8b2iFW5q1y5zS/TlMltB92GSdt5794SbaOl3BfTXQDbt2/H4XCg1+tZtWoVP/74I263W3loNBqOOOIIrFZrmwbelsxms/QBECJBONw+Dn3gG1y+AEtum4LF0OobmpLKpppNnPO/c5jeZzo3jL1B7u9PIi3lvqh/NQsXLmTSpEnK7/fddx/33XffHstde+21/Otf/9qHMNuXyWSSAkCIBJFi1NE708KybdV8u66M6cPz4h1Sp7WlZgvnzT+PSnclm2o24Q/60WnkEkqyaCn3Rb0EcPDBB/PDDz/w66+/YjabueWWW9i6dSulpaXU1tbi8Xioq6vj/vvvb/PA25Jer8fj8cQ7DCFEGzlqWHh2s89+L4pzJJ3X9trtnDf/PMpd5RyQewD/nvRvSf5JpqXcF7UFQKfTcfDBBxMMBnG73QwfPpyePXvu8QGdnVqtJhiUWcSESBRHDcvj3s/W8vXaUty+AEadJt4hdSrlrnIuXHAhpa5S9s/Zn8cPf1yu+SehlnJfzJ0A1Wo1S5cu5YQTTtjjtVAo1OmTq1qtVjrACCG6vh52MyO6p+L0Bvh+fXm8w+lUar21XPzlxWyv3c6QjCE8OflJzDpzvMMScdBS7mtVz5m0tDQefPBBCgoKMJvNBAIB1q5dy+uvv8706dN54IEH2iTg9hAKhVCrW3XXoxCikztyaC4rd9Tw+R9FTBmSE+9wOg23340/6KdXSi/+M1lu9UtmLeW+VhUA119/PZ999pnSocBut2MymSgpKeHqq6/e90jbUTAYRKuVnsJCJJKjhuXy4PxC1hbVEgqFpHf7n7LMWbw07SWcPicZpox4hyPiqKXc16pT4u+++44XXngBn8+H3++nrKyMdevWkZeXx2+//dYmwbYXOTgIkXj6Zln56tpD+fSKCUn/9x0Khfh2+7dKc2+qIZU8q9wdkexayn2tKgDy8vJYsWIFarVaWaHRaOTAAw/k+++/3/dI21EgEECjkU5CQiSaflnWpE/+AE+veJrLvr6Mu3++O96hiE6kpdzXqgLgoosu4sEHH+TVV19Vqszt27fz448/0rdv332PtB15PB4MBkO8wxBCtJNd1S78gc7dGbm9zCucx39W/Ae1Ss34buPjHY7oRFrKfa0qAGbPns3ZZ5/NrFmzyMzMZMCAAfTt2xe9Xs+pp57aJsG2F7fbjdFojHcYQoh2cO28FYy/72t+2lQR71A63Fdbv+KeX+4B4PaDbmdyr8lxjkh0Ji3lvlb1ilOr1fz3v//l6quv5v3338fv99O/f39OOOGETp9cfT4fOp0MgCFEIspPCx9/5q8q5pD+WXGOpuP8XvY7N3x3A8FQkItHXsxJA06Kd0iik2kp97VYAASDQbxeLxqNBq1Wq1xnGzx4MIMHD277SNuR1+vtEgMWCSFab9KgbB77egMLC8uSpsNvcX0xV35zJd6gl5MGnMTFIy+Od0iiE2op97V4CeDEE0/EZDKh1+tRq9XodDqMRiM2m42srCx69OhBQUEBI0eOZP78+e0SfFuRFgAhEtfI7mlk2QzsqHKxuig5ZgjUqrVkmjIZkzOGWw64JSmKHtF6e90CcO+99zJr1iz8fr9y618gECAQCOB2u6mvr8fpdOL3++nVq1e7BN9WXC4XJpMMgylEIlKrVRw+MJu3F2/ny9WlDO2WGu+Q2l2mKZOXpr2EL+iT8f1Fs1rKfS0WAF2xqb8pwWAQh8NBWlpavEMRQrSTo4bn8vbi7Xy0YidXTC5I2DPiRTsXcVC3g1Cr1DK8b4KIDKcfDAYJBALKz5Hn/X5/o9cjy+j1esxmMykpKU1+36Plvpg7AQaDQa644gpcLhc2mw2j0UgoFCIUCuH1ehk3bhynnHJKTOv64osv+Prrr8nLy+O8887DarVGfc+qVatYtGgRs2fPjjVkRV1dHaFQiNTUxD8rECJZHVyQSZpZx+byenbVuMlPS7wWv482fsStP9zKUb2P4v6J9ydskdMWQqEQdXV1+P1+1Go1arUajUaDSqVSHpExbRqObdPcuiL/NvVomKz/mrz/+nwgEGiU0CPLNIwx8rNKpUKj0SjPabVa9Ho9Wq0WtVqNx+OhoqICj8dDdnb2HnFHy32tugvA7Xazbt066uvrlcEFvF4vq1atIicn+jjcXq+XU045hQ8++IDRo0ezdetW/vnPf/LFF18wYsSIZt+3YsUKJk2axFFHHbVXBUB1dTWAFABCJDCdRs0r5x5A70wLKcbEaxIvrCzkrp/uAmBM7hhJ/i0IhULs3LkTn8+H0WhslHybS9wtTRYXKRga/vzXQqJhwv5rgaHT6Rotp9Vq90j0e/P/abFYSE1NZcuWLRgMhj1yXLTcF3MBoFaree655/Z43uv1kpKSElMfgPvvv58vv/yS7777jkMOOYS6ujpOOOEErrjiChYuXNjkezZt2sSRRx7J+PHjef7552MNt5Hy8vBMYRkZMia2EIlsRPe0eIfQLipcFVz5zZW4A25mFMzg5IEnxzukTq2iooJgMEivXr0SfhI4jUZDTk4O5eXleyT6aLlvn/eMXq8nLy+PNWvWtLhcKBTi2Wef5aqrruKQQw4BwGq1ctNNN/Htt9+yfv36Jt938803M2zYMN577729HmugqqoKkAJAiGThCwSp9/jjHUab8AV9XLPwGnbW7WRoxlBuPfDWeIfU6Xk8HlJTUxM++UcYjUa8Xu8ez0fLfa26BLBo0SIl4YdCIWpqali3bh27du0iNze3xfdu2LCB7du3c8IJJzR6fr/99gOgsLCQ/v37N3pt/fr1vP/++7z77rs8++yzZGVlMX369Cb7DKxZs4a1a9eiVqsxGAykpaVhNpsZOHCgUgXZ7fbWbK4Qogt6Z/F27v1sDRcd2o8LD+0X73D22f2/3s/S0qVkm7J5YvITGLWde9C1zsDv9yfV7K8qlarJSxjRcl/Me8jtdjNlyhScTucer02dOpUzzzyzxfcXFRUB4QmFGkpPTwegsrJyj/c88sgj+Hw+jjvuOPR6PV6vF7vdzldffaUUDhHz5s1jzpw5e6zj9ddfp7a2ttFnCSESl1mvpcrpY/6q4i5fALj9btZUrEGn1vHIpEfINGXGO6QuIdkmf2uuAIj0AWgu98VcABiNRkpKSti0aRPV1dUYDAbS09Pp0aNHTPfXR65N1NXVNXo+kpybOqv/7bffmDhxIs8//zz9+vVj3bp1HH/88dx11128++67jZYNBAJNfq7VaqWkpAQId5gQQiS2SYOyMOrULN1WTanDTXZK1z1jNmqNvDTtJX4v/50RWc13lBaNJUILwObNm1m3bh1ZWVmMHDmyxYKmuQIgcsLeXO5r1QUSq9XKkCFDAFi3bh0rVqygtLQ0pvdGLhHs2LGj0fPr1q0DaPIugKqqKo466igKCsL39A4cOJDzzz+fH374YY9lBw8ezPHHH88xxxzDlClTGDNmDIMGDSIvL4+SkhJ0Oh0pKSmt2VwhRBdk1muZUBA+U56/uiTO0ewdX8BHMBSe2VCn0TE6Z3ScI+o6Ir36u2oLwNq1a5kyZQp9+/Zl2rRp7L///vTr12+Pk+dYRMt9rSqRfv/9d4466ih27tyJwWDA7/ejUqm4/fbbueOOO1p8b05ODoMHD+aTTz5h0qRJyvMff/wxdrudfv32bKrLzc1l+/btjZ5zuVxNVjMzZ85k5syZTX72f/7zH7Kzs5OmQ4gQye7Iobl8uaaU//1RxJkHde5RSpty76/3Uuos5d4J95JqkNuXWyMQCES9r7+zKi0tZcKECYwdO5bff/+dQYMGUVRUxI4dO/aqBbukpKTF3NeqjHj99deTlZXF+vXrcblcOJ1O5syZw5133skff/wR9f3nnHMOTz/9NO+//z4+n4833niDf/3rX5x11llN/mdNnjyZd999l4qK8BSfNTU1vPrqqxx77LGtCZuioqKonRSFEIljypAcdBoVP22soMThjnc4rTJ/y3z+b93/8fOunymuL453OF1OV27+/89//kNVVRXvvPMOw4YNQ6vV0qNHD8aNG7dXBU203NeqAqC4uJiJEycqTfJ6vZ6bbroJvV7Pd999F/X9V111Feeddx4nnngier2e008/nWOPPZa7774bCHcE1Gg0yu+XXXYZZrOZwYMHc9JJJzF06FCCwSA333xza8KmtLR0j86HQojElWbWc/igbIIhWNCFLgOU1Jcw96e5AFw39joG2gfGOaKupysXAN27dycYDHL55Zczb948fv75Z1wu116vL1rua9VeOuaYY3jppZeYM2eO0qvQ4XAovfOj0el0PPbYY1x66aWsXbuW/v37K30KAEwmE4MHD1aey8rKYvXq1bzyyits3LiR448/nr///e+tHg+grKyMkSNHtuo9Qoiu7aojBnDZpP4My+8afX/8QT83fn8jtd5aJnafyKkDT413SF1SMBhsssl7wK2fo9WoSDHqSDPrsBi02IxajFoNMw/syaEDsgDYUFrLsm3VpJn1mPUajDo1eo0GnVaFSaehp92snI37A8HwCH8qCIYgEAzhDwbxBUKkmlo/GuU555xDRUUFb775Ju+88w719fXo9XruuOMObrml+Rkfm5sCO1rui7kAWLduHT/++CM7d+5kxIgRpKSk4Ha7lV6G11xzDbfeeisqlQqz2cxXX31FVlZWk+saOHAgAwfuWdmaTKY9LiUYjUYuuOCCWMPcQygUorS0tMlxkoUQiWtwXtdI/BHP//48S0qWkGXKYu74uV3yGnZn0FQB4A8E8QaCeAPg9AYo/stlocMH784PizZWcMeHq5pct0oFm+6drvw+/bHvWVfSdOe8Lfcd3erYNRoNN954IzfeeCOhUIht27bx8MMPc9ttt9G/f39OPjn2ESBjyX0xFwDp6ekUFBTQs2dP0tPTlQmBGva0jPS+bGpM4nipqanB6/VKASBEEqt1+7B14vkB1lSs4ekVTwNwz4R75H7/fdDUGABajZr19xyFxx+k2unF4fJT5/FT5/Hh9gUZnr87X/XNtPK3UfnUuHw4vQFcvgBefxBfIIhG3XjMfhWNizSNWoVWrUKvURMMhlCr976IU6lU9OrVi3//+9988803LFiwoFUFQCy5L+YCICsri2effTbmD+8sIrcpxjJZkRAisVQ7vVzwyhI2V9Sz6KbD0Wk6551AfdP6cubQMwkGg4zrNi7e4XRpzQ0CpNOo0WnUWA1aaGFMuAn9M5nQP7YCbP7VE/c2zD0sWbKEr7/+muuuu65RkVFaWsqOHTtaTP5NXQKIJfe1uqfEl19+yWuvvcbWrVvJyMjg8MMP59xzz93rcfrbm8PhAGQmQCGSUapJR0W9h7JaDwsLy5gypHOeCBg0Bq7Z/5oWZ6QTsQkEAuh0nbe1pzlFRUXccMMNbN26lZkzZ6LX61m8eDGPPPIINpuNK6+8stn3NlUAxJL7WlUOP//880yZMoUVK1Ywbtw48vPzmTt3LgcccMA+9VRsTzU1NYAUAEIkI5VKxcljegDw9m/b4hzNnrY6tlLn3X0NWa7777uuOgzwMcccw5NPPsmCBQuYMGECBxxwALfffjtHH300v/zyCzabrdn3NlUAxJL7WlUA/Otf/+Lkk09myZIl3HvvvTz66KMsXbqUTZs2NTlVcGcQqYJa2nlCiMT1t9Hd0apVfL22lKKaznOiEpnl77gPjqOwsjDe4SSM5u4C6AouueQSCgsLqa2tpbq6mvLych555JGo49iEQqE9tjmW3NeqvRQZiajhB+Xn59OzZ082b97cmlV1mMhOkGGAhUhOWTYDRw7NJRiCt37dHv0NHeTlVS+zrmodeo2eXildb7TCzqqrtgA0ZLVaW9VqHQwGm70E0FLua1UBcNVVVzFv3jxuvvlmVq9ezbZt27jvvvtYs2YNU6dObc2qOkykGSQtLS2+gQgh4ub0g3oC8NZv2/AFgnGOJtz0H+n1f8dBd8gUv22oK7cA7K2WLgG0lPta1Qnw9NNPp7i4mHvvvZf77rsPCLcK/OMf/2DatGmtDLljRHaCtAAIkbzG9c2gX5aFXdVuCotrGZYfvz5BoVCIe36+B0/Aw7F9j2V8/vi4xZKImhsUJ5E1VfTEkvtaVQCoVCquu+46Lr74YgoLC3E4HOy///6d+vp6XV0der2+S/YKFUK0DZVKxWMzR9E9zUyqOb7HggVbF/BT0U+k6FO4fuz1cY0lEUkBEBZL7mv1bYDFxcV8/PHHbN26Vbn177DDDmvtajqMz+eT5C+EYGi3+N8J5PK7uP/X+wG4cvSVpBtbuCFd7JVkLACa6vcQS+5rVQHwzTffMH36dNRqNQUFBbhcLm6//XZOP/10Xn311U650z0eT6cdo0AI0fE8/gDLt1VzYN+MDv9so8bInePv5PPNn3Ni/xM7/POTQTIWAE21AMSS+1rVU+L2229n/PjxlJeXs2LFCtatW8fbb7/N66+/zqJFi1ofdQeor6/HbDbHOwwhRCfg9gU49IGFzHz2Z3ZWd/wtgSqViondJ/LPQ/6JRt21e6p3VslYADTVAhBL7mtVAeD1eunfvz8mk0l57u9//zt6vZ7ly5e3ZlUdxu12SwuAEAIAo07DAX3sBEPw/Pcde+tycX1xh35eskrGAqCpFoBYcl+rCoCZM2fy1ltvsWXLFkKhEH6/n+3btysTDvj9fgKBQKcaztLtdjcqWIQQye3CQ/sC8Oav26io83TIZ/5R/gfT3p3GPT/f0yGfJ5JLcwVAtNwXcwGwfPlyHn/8cWpqahgwYAA6nQ6dTkevXuEBLE4++WR0Oh1arRaTycSuXbv2YjPantPplAJACKEY2i2Vwwdl4/IFeP6H9m8FCIVCPLT4IQKhACadHItE22vqEkAsuS/mToADBgzgkksuwev1xjQdcLShCzuK3AUghPiryw4v4Ou1pby8aAvnTuhDptXQbp/1/c7vWVyymDRDGucPP7/dPkd0bQsWLOC3337D7/djMBhIS0ujR48ejBo1iry8vBbf2+53AZjNZq677rpYF+9Ukm1UKCFEy0b3TGfSwCy+KSzj6YUbue2YIe3yOcFQkEeXPgrA+cPPJ0UvA5KJpj388MP88MMPhEIh6uvrlef3339/Fi9e3OJ7mxv+OFruS/jM2Jn6IwghOo9rpw6kb5aFET3S2u0zFmxdwLqqdWSbszl10Knt9jmi6/v888+pra3l7rvvJi0tjbq6OlavXs2HH34Y9b1N9QGIJfe1eiAgIYRIBMPyU/ny6kNRq9unx3gwFFTG+79g+AUYNO13mUHsplKpuvSdAFVVVaSmpmKxWBg8eHBM7/H7/Wi1rU/nCV8AqFQqAoFAvMMQQnRC7ZX8AZw+JwPSB+D0OTmh/wnt9jmisUgB0FXV1ta2auyaUCjUZMETS+5L+AJArVYTDMZ/9i8hROdUXOPmv99toluakfMP6dtm67Xqrdw/8X5cfhd6jb7N1ita1mwBcFcWqHVgTAVTOhisYEgBnRH2PxsKjggvV1YIOxaHl9GbQWsCrR40etCZIL0PRJJtwB/+WaWGUBCCAQj6IOADU9pexe/1elvVcT0UCqFWq/coAGLJfS0WAA8//DDdunXj1FPD167eeecdunXrxsEHHxxzcPEmBYAQoiUby+p44cfN2C16Zh7QE4uhbc+LTFq59a8jNXnMD/gh4A0/fPVQ+5fb1Ac0mM1283fwWXMd3lVwZ9XuX5+eAGVrml50Tk2rY4fW56xAINBkZ799LgC+/vprdDqdUgA89thjjBs3rksVAFqtFr/fH+8whBCd1Ph+GezXI43l26t54YfNXD65/z6v81+//YsD8g5gQv4E1KqE72vdqTSZ+DRauL0c/G5wVYG7Bjy14YfPBd1G7V42owBGnAruavDWh18PeMJn9Wrt7rN/aPwzgEoDGl24tSAYhL24A81ms+HxxD5AVXN3AMSS+1osAI444giuvvpqrr76ai677DL0ej21tbUxB9YZSAEghGiJSqXihmkDOe3ZX3j6242cPLYHOSl7P3z48tLlvLz6Zd5d/y4LTlqAVW9tw2hFNM1eAtDowg9DlOnr+00KP2JxyU+tDzAKjUbTqj4MTd0BALHlvhbLk4suuoiLLrqIp59+moKCAr7++mueeeYZbDYbdrsdm82GwWDAarUycOBA1q5dG3PQHUUKACFENOP7ZTJ1SA713gAPf7Fun9b1wh8vADBz0ExJ/nHQVS/7/vbbb9x77718+umnFBcXc/TRRzNt2jRee+21Ft/Xbi0ARqORp556iscee4y1a9dyxx13sHr1au68804gvKPVajUul4vy8vJOM/pfQzqdDp/PF+8whBCd3E1HDeKrtaW8s2Q7s8b3Ymi31FavY1P1JhZuX4hOreO0wae1fZAiKpVK1SULgJdffpk33niD7t27c9BBB6FSqTAajRgMLd8+2lwLQCy5L6beLjqdjuHDh3PooYdSVVXFaad1nS+20WjE7XbHOwwhRCfXN8vKrHG9ePHHLSwsLNurAuDFVS8SIsSMghlkmjLbIUoRjVqt7pK3AT7xxBM88cQTrX5fc2MexJL7WtXd9fLLL+eCCy5oXXRxZjAYWtWhQgiRvK46YgDThuZyYN+MVr+33FXOp5s+RYWKs4ee3fbBiZh01UsAeysYDDZZAMSS+1pVAGg0Gnbt2sW8efPYunUrdrudyZMnM3ny5E476pJer8fr9cY7DCFEF5Bq0u1V8gf4v3X/hy/oY1KPSfRM6dnGkYlYJVsBEBkH4K9iyX2tKgA+/fRTZsyYQXp6OhMnTmTbtm08/PDDTJkyhQ8//LDJjgjxZjabcblc8Q5DCNHF/LalkhqnjyOG5MS0/N8H/B2DxsB+2fu1b2CiRV31EsDeaq4TYCy5r1UFwO23385hhx3Ge++9h80WvpVi2bJlHHjggbzxxhuceeaZrVldh4jshOY6SgghxF/9urmSk5/5iQyLnoV9D8NmjD4yW4Ypg3OGndMB0YmWqNXqpLrzKxgMNjkPQCy5r1UZ0ev10rt3byX5A4waNYr+/fuzZMmSVobdMSJjKktHQCFErMb2Tmf/XulU1Ht59vvN8Q5HtIJWq02q+V+aS/Cx5L5WFQDnn38+L730Ei+88AJut5tgMMi7777L2rVrOeCAA1oZdseIFCtdbQAjIUT8qFQqbjpqEADPf7+JirrmO1PVemuZ8cEMnlj2RFI1PXdWyTb2S3NDAceS+1pVAFxyySWcc845zJ49G4vFgsVi4aSTTuL0009XhgvubKzW8EAcdXV1cY5ECNGVjO1t57CBWdR7Azz5zcZml/ty65dsrNnIstJlnbYzdDLRaDRJVQA01wkwltzXqgJAr9fz3//+l/Xr1/P666/z6KOPsnbtWl555ZVOe33daAwP6SkdAYUQrXX9kQNRqeDVn7ewo8rZ5DLvrX8PgKP7Ht2RoYlm6HS6pCoAmusEGEvu26tpr/r27Uvfvm03bWZ7MpnCM3FJASCEaK2h3VI5dkQ3Plqxi6cWbuSeE4Y3en2rYyvLy5Zj0VmY1ntaM2sRHUmj0RAIBJodICfRNFcAxJL72nbey05ICgAhxL64esoAMq0GLp3Ub4/XPtjwAQCTe07GrDN3cGSiKSqVSikCmuodnyykAAAsFgsA9fX1cY5ECNEV9cm0cMexQ/Z43hf0KQXA3/r/rYOjEi3pigXAqlWruPTSS7FYLPTu3ZvjjjuOqVOnRm3FaK6lI5bc1zkv3LehlJQUQO4CEELsO68/SFFN+Ixq0c5FlLvK6Zval9HZo+McmWioK3YEXLhwId999x2BQIAPPviAadOmcdxxx0XtwN5cARBL7mt1eRQKhXA4HHi9Xnw+H9u3b2fLli0MHz6cIUP2rJLjTVoAhBBtYU2RgwtfXUKWzcD/XTSOCfkTeGbKM/iD/qS41tyVdMWxANLT0wmFQnz44Yfo9Xo+/vhjzjvvPC644AJef/31Zr9jHdYC8MADD2C320lLSyM7O5v8/HwOOuggTj31VF588cXWrKrDRG6FkAJACLEvuqebqPf4WbK1ii9Wl6BRaxjfbTwTu0+Md2jiL7rifACRa/ZOpxOVSsVxxx3HJ598wptvvsnHH3/c7PuaKwBiyX0xtwBUVVVx0003cf755zNr1iyll2VmZia9evVqNDpgZ5KWloZaraa0tDTeoQghujCbUcflhxcwf3UJz32/jsmDstFqEv4qapfUFQuA6upqVCqV0nQPsN9++2GxWNi4sflxKJobfCqW3BdzAWC1WunRowcGg4EJEybE+ra402q1ZGZmSgEghNhnpx3Yi+NGduPsL0/mki/f5r5D78JutMc7LPEXTRUAo18djVatxaa3kWpIxaK1YNVbMWqMnDTgJA7OPxiATdWbWFm+klR9KiadCaPGiE6jQ6fWYdKY6G7rrpxx+4N+VKhQq9QEQ0GCoSC+oA9/yE+KPmWPuFpSXFxMbm4uGo0Gn8/Hb7/9xpw5cwgEAkyb1vItpk21AMSS+2IuAHQ6HS+++CJHH300Pp+POXPmkJubG+vb48pqtUonQCHEPtNr1exwFbK5ZhN13lpSdK07yIuO8dcCwB/04wv68AV9uPwuSp2Nk2LDyzi/FP/Cvb/c2+R6VahYMWuF8vvfP/47G6o3NLns72f93qqYy8vLKS4uxmazKR3/+vbty6effsrgwYNbta6IaLkv5gJg69atXH/99ajVap555hmee+45xowZQ1ZWFnV1dVx11VUcf/zxexVke7NYLNIHQAjRJj7a+BEAR/Y+ko1lLgbmds7Ln8lMpVI1ahrXqrUsPXMp3oCXGk8Ntd5a6nx11PvqcfvdDM0cqizbO6U3x/Y9FofXgcvvwu134w168QV8aNSaFjt8alQatGotOrWOYCiIWhX7JSK/3096ejo9evRgxYoV2Gw2nn76aQ4//PCYtrcp0XJfzAVAWloaM2bMQKvV4vP5qKmpoaqqCpfLRX5+Pt26dYt1VR3OYrHgdDY9jKcQQsTK7Xfz2ebPAJhRMIOqam+cIxJN0Wg0eDyNJ3DSqcPN+BadpcX3jus2jnHdxsX0Oe8f//5ex/hXJpOJrKwsli9fzjfffMNll13G1KlTufDCC3niiSf2akyDaLkv5jWmpqZy++23tzqApjgcDv744w9ycnLo12/P0bWas2vXLioqKhg+fHj0hRuw2WxyCUAIsc8WbF1ArbeWYRnDGJA+AJVdbv/rjNRqdZebmdFsNitT906aNInly5fzyCOPcPPNN1NeXs4777zT6lsBo+W+Vndh/fbbb7ngggs48sgjmTlzJs8++yxeb+xV8Isvvki/fv04+OCDKSgoYObMmTgcjqjvW79+PUOHDmXixNbfcpOamkpNTU2r3yeEEA3NK5wHwIkDTpR7/zuxrngXQEFBAX369FF+1+l03HDDDXz00Ud7vS3Rcl+rCoCXX36Zww47jEWLFjFixAjS09O55ZZbOOigg5TKpSUfffQR5557Lueddx47d+5kwYIFLFq0iOuuu67F9wUCAc466yz8fv9eDe6QkpIiBYAQYp/srNvJyvKVWHVWpveZDkCN08c/P1vDXZ+sjnN0oqGuWACcdtppfPPNN3s8f/TRR/Pee+/tVcEZLfe1qgC4//77OfHEE1mxYgUPPvgg//nPf1iyZAmFhYW88MILUd9/1113ceqpp3LffffRrVs3jjjiCP7xj3/w8ssvU1ZW1uz7HnzwQVatWsWNN97YmnAV6enpVFdX79V7hRACIN+azxcnfsFDhz6kTPxTVufm2e838dKiLWwsa3nIVtFx1Gp1lxsJcG/9tcNjQ9FyX6t6FZhMJnQ6XaOpB3v27EmvXr3YsKHpWyEiysrKWLx4Mffdd1+j56dMmYLX62XlypVMnjx5j/etWLGCO+64g8ceewyDwdDs+tesWcPatWtRq9UYDAbS0tIwm80MHjwYq9WK0+kkGAyiVsvAHUKIvZNjySHHkqP8XpBt4+QxPXjrt+3c9clqXjrngDhGJyJaSoqJpqX+DtFyX6sKgCuuuIKzzz6b/v37c+aZZ2Kz2Xj99ddZs2YNDz74YIvvLSwsBGDAgAGNns/KygLCHfz+yuPxMGvWLMaPH88FF1zAyy+/3Oz6582bx5w5c/Z4/rPPPsNoNALgdrsxm2XKTiFE65S7yrEb7U3e1nXdkQP5dGURCwvL+HZdGYcOyIpDhKKhZCoAVCoVwWCw0Yl5RLTc16oC4Mwzz2Tnzp3cf//93HXXXcoH3HHHHRx99NEtvlev1wPscV3G5/MB4Q4Pf3X99dezfv16li5dGvX6R3PNPU6ns9GYyFIACCFa68pvrqTSVcm/J/2bgfaBjV7LtBq47PAC/vn5Wv752RomFGSiUUsHwXhKpgKgpf4O0XJfqwoAtVrNLbfcwmWXXcbq1atxOBwccMABpKWlRX1vdnY2EL4U0KtXL+X5yJl/QUFBo+UXL17M448/DqCMghTZ0KysLF588UWOOeYYZfnBgwdz/PHHEwgE8Hg8VFVVUVdXh8PhICMjQ/nsSIuDEELE4o/yP1hZthKb3kYPW48mlzlrfG9eXrSFtcW1vL9sJyft372DoxQNdcVOgHurpWInWu6LWgB8//33jB49WplaEMI9Cw866KBWBdm9e3cyMzP59ttvGTNmjPL8N998g16vZ8SIEY2WHzVqFD///DM1NTX4fD48Hg9ffPEFL730Eg888AAHHND4WtvMmTOZOXNmk5/9xRdfAOEJjYQQojVeX/M6AH8r+JvS+e+vjDoN1x05kGvmrWDJ1iopAESHiaUAaC73tVgA+Hw+Jk6cyK233srdd9/NOeecw4IFC7DZbNhsNjQaDV6vF7VazbvvvkvPnj2bXZdWq+Vvf/sbTz/9NGeeeSbZ2dls3bqV+++/nylTpiiXCCI0Gg0HHnhgo+dqamp44403OOecc1oKew+RZpDI+MpCCBGLMmcZ/9vyP9QqNTMHN32CETFjv3y6p5s5oI9MDhRvkY5xfr9/r0bQ6yoi29jcJfBoua/FPaPT6XjzzTeZOnUqALNmzWLYsGE4HA5qa2sJBALo9XosFgvp6elRg50zZw4LFy5k0KBBHHTQQfz8889otVoeeughINzp78ADD+Qf//gHxx133B7v39smnchUxTIaoBCiNV5f8zr+oJ8pvaaQb81vcVm1WiXJv5NQqVTY7XY2btyIWq2mX79+XeoOsGAwSDAYJBAI4Pf7lSQfCoUIBALKay6XC6PR2Gzftmi5L2ppdOqppyo/T5o0iUmTJu3N9gCQl5fHypUrefLJJ1m9ejU33XQTF198sRJkVVUVK1euZOHChU0WAMcee+we4zvHwm4P/1GWl5fvdexCiORS561TRv6bNWRWq977+44avlhdzLVTB0ZfWLSL7OxssrKy2LhxI+vWrUOtVqPRaJR/VSoVarV6j+cjP6vValQqlfKI/B4pJP7aMT0UCilN8ZEEHgqFGv0cSd4Nfw4Gg0qS9/v9yuuRWLRaLVqttlHMer0ejUaD3W7HaDQ220k+Wu6LuW0kFAoxY8YMbr311j2uv7eGwWDgmmuuafK13Nxc/H5/s5VadnY2l1xySas/M9L5oaXBhoQQoqGtjq1Y9VYG2AewX/Z+Mb+vzuPntGd/ptbj58A+GUzon9l+QYoWqVQq+vXrpyTihkm34SPyvM/na7RMJKlH3t/w979ed48UCkCjAqLhz5HiIvKzVqtFrVYrST7ye8N17YtouS/mAiAQCPDRRx9x0kkn7VMBEE17NNPo9XqsViuVlZVtvm4hRGIamjmUT//2KVXu1nUethq0XHRYPx6cX8jcj1fxv6smym2BcdTwDD6R+wM0JVrui7o36uvrefbZZ6murkan0/Hyyy+zZMkS3G638tBoNFx88cVMmDChzTegrVitVukEKIRoFZ1aR7Y5u9XvO/+QPrz56zbWl9Yxb/F2Zh7QfAdpIdpTS7kv6un2ihUruP/++3nppZcIBAKsXr2an376ibVr11JSUoLL5aKqqopNmza1eeBtSa/Xt2rWQiFEcvIFfTz/+/NUuve+xdCg1XDDtEEA3Pf5Wkod0SdLE6I9tJT7orYAjB8/nqKiIkKhEGazmVtvvZVLL720zYNsb0ajMaYZC4UQye1/m//Hv5f+m/9t+R/vHPvOXq/n2BF5/N+SHXy3row5H6/iP6fv34ZRChGblnJfzBfcQ6EQvXr12mPAnq5CCgAhRDT+oJ9nVj4DwGmDTtundalUKv75t+GY9Rq+W1dOUY2rLUIUolVayn0x94hQq9WsXbu2yde6wix7cglACBHNhxs+ZKtjKz1tPTmm3zHR3xBFfpqJJ08bzdBuKWSnGNsgQiFap6Xc16qs/dZbbzUafx/g448/ZvDgwTidzr2PsANotVr8fn+8wxBCdFJuv5v/LP8PAJfudyk69Z4TlO2NSYOyJfmLuGkp97WqALjtttsYN25co+cOO+wwysvLee211/Y+wg6g0WiaHS5RCCHeLnybUlcpg+2DmdZnWpuv3x8I8tz3m/h+vYxHIjpOS7kv5gLA5XKxcePGPcYAsNlsHHzwwSxdunTfomxnGo0maWaHEkK0jtPn5L8r/wvAZaMuQ61q+0ua/7dkB3d/uobr3llBtVMuR4qO0VLui/lbbjQaOeigg7j33nupqKhQnvf5fPzxxx/07t17nwMVQoh4MGlN/HvSvzlryFkckn9Iu3zGSft3Z/9e6ZQ4PMz5aFW7fIYQrRFzAaBSqXj99dcpKiqioKCAK6+8kieffJKjjz6ampoazjvvvPaMc58Fg8E2GVpRCJF4VCoVY3PHct3Y69rtOKHVqHno7yMx6tR8sHwX/7dkR7t8jhANtZT7WtXO1bdvX1auXMlDDz3E+vXrefLJJ8nMzOS7775TxhzurAKBABqNJt5hCCE6mZ11Ozvss3pnWrjz2KEA3Pr+76zaVdNhny2SU0u5r9UXuvR6Peeeey6fffYZq1ev5o033qBPnz7U1HTuL7IUAEKIvyp1lnL8B8dzw7c3EAh2TCfhmQf05NSxPfD4g1z+5jJq3b4O+VyRnFrKfa2aGWH58uU8+uij9OvXD7PZTCAQYO3atbz33nvMnj2bBx54oE0Cbg9dYawCIUTHeuGPF/AEPPhDfjTqjjtBuPPYoSzdVkWaWY8vEIr+BiH2Uku5r1UFwE033cTatWv5/vvvlbmINRoNTqeTm2++uU2CbS8+nw+drm3u6xVCdH3bHdt5u/BtVKi4cMSFHfrZJr2G1847kDSzHr1WTkxE+2kp97Xqm7ds2TL+9a9/sWHDBgoLC/npp5/47rvvKCgo4NNPP22TYNuLFABCiIYeX/44/qCfY/sdy0D7wA7//OwUo5L8/YEgi7fIdOWi7bVZAdC/f3++/vrrxitQqxkyZAjLly/f6wA7gt/vlwJACAHAirIVfL75cwwaA5fuF9/JzXyBIOe+vJhT//sz362TQYJE22op97WqALjqqqt46qmnmDNnDlVVVQSDQX788Ue++uorRo4c2SbBtheXy4XRKMNxCiHgiWVPAHDmkDPpZu0W11h0GjVD8lLwB0Nc/NoS/tjZuTtUi66lpdzXqgLgpJNO4v777+eBBx7Abrej1+uZMGECw4YN48QTT2yTYNuLy+XCZDLFOwwhRJz5g356pfQizZDG2UPPjnc4ANxw5ECOG9mNem+AWS/8SmFxbbxDEgmipdynCoVCre6CWlNTw/z58/H7/fTv358xY8Z0+kF2UlNTOfvss3n00UfjHYoQohNw+pyYdeZ4h6Hw+oNc8OpiFhaWkWk18M5F4+iTaYl3WKKLayn3teougLlz5/LZZ59RUFDAa6+91umTfkQoFKK+vh6r1RrvUIQQnURnSv4Aeq2ap8/Yn/Ne/o0fN1Rw2rM/8/4lB5ObKpcuxd6JlvtivgQQCoW499576dmzJ5MnT+4yyR/CTSCBQACbzRbvUIQQcRIKhbjl+1v43+b/ddigP61l1Gl4dtYYDuhtpyDbit2ij3dIoguLlvtibgFQqVSMHz+evn37cu6557ZZgB3B4XAAkJKSEudIhBDx8t2O7/h408cs2rWIQ3scikndOfsEmfVaXjhnLCpQbhMMhUJd6qRLdA7Rcl+rOgHefPPNPPXUU/zyyy/7HlkHqq6uBiAtLS2ucQgh4iMQDPDYsscAOHfYuZi0nTP5R1gNWiyG8PmZ1x/kvJcX88nKXXGOSnQ10XJfq/oALFy4EJ/Px/jx4xk/fjwajYZQKEQoFOLss8/utC0DkXkKUlNT4xyJECIePt/yOeuq1pFnyeOUQafEO5xW+fT3XXy9tpSv15aytqiWq6cMQKOW1gARXbTc16oCYPTo0Vx//fX4/f49XisoKNiL8DpGpBlECgAhko8v6OOp5U8BcPHIizFoDHGOqHVm7JdPRZ2Xez9bwxPfbGDlzhoePWU/0qV/gIgiWu6LWgCsX7+egoICVCoVJ510EieddFLbRtgB6uvrAbBY5JYaIZLN++vfZ1vtNnql9OLYfsfGO5xWU6lUnH9IXwbnpXD5m8v4bl0Zxz7xA0+eNpqRPdLiHZ7oxKLlvhb7AGzdupWBAwdSWFgIhKcVfPbZZ3E6nW0cZvuqqKgAID09Pc6RCCE62ocbPgTg8lGXo1W3qtGzUzm4IJOPL5/AiO6p7KhyceJTi/h9h4waKJoXLfe1WADMnz8fo9GoNO+vWrWKCy64gKVLl7ZxmO2rtLQUgJycnDhHIoToaM8f+Txzx89lSq8p8Q5ln+WnmZh34TjOPbgPE/pnMixf7mwSzYuW+1oshzdv3kx2djZabXix8vJyoOv1pq+ursZgMMhQwEIkIaPWyN/6/y3eYbQZo07DHccOwR8IKrcGbiit5bPfi7lgYl+MOk2cIxSdRbTc12ILQKSHf8PfATSarvUFczgcMgaAEEnmj/I/qPPWxTuMdqPV7B4j4I4PV/HwgnVMeeRbFqwuiXNkorOIlvtaLADy8vIoKioiEAiPmhW5FLB69eo2DLH9lZeXY7fb4x2GEKKDuP1uLv/6cqb+31S2ObbFO5x2pVKpuPzw/gzMsbG90sXsVxYz64VfWbqtKt6hiTiLlvtavATQo0cPfD4fxx9/PEajEZVKhUql4q677uLjjz9Go9Gg0WjQarUMGjSIK664os03oC1UVlaSkZER7zCEEB3kgw0fUO4qZ7B9MD1sPeIdTrsb1y+DT6+YwCs/beWRBev4bl0Z360r4/BB2cw9big97J1r3gPRMaLlvhYLgP79+3PssceiUqnw+/0Eg0GmT5+Oz+dj27ZtBAIBfD4foVAIl8vV5sG3lfr6erkEIESS8AV9vPDHCwCcP/z8pBlCV6tRc+6EPhy/Xzee/2EzLy3awo8bypXhhEXyiZb7WiwAhg8fzkcffdTmQXW0uro6unXrFu8whBAd4JONn1BUX0Tf1L4c0euIeIfT4TKsBm6YNohzJ/Rh8ZYqclLCswn6A0HOfXkxRw/P5YRR3aUwSALRcl/XvSm2FSoqKqQPgBBJIBAMKGf/5w0/D7UqeZNcptXAtGG5yu9frC5RLg088L9CjhmRx8ljezC0m4yQmqii5b6k+Ouorq6WAkCIJPD19q/Z4thCN0s3jupzVLzD6VSmDMnhkVNGMijXRkW9l5d/2srRj/3ACf/5kXmLtze640skhmi5L+FbAHw+H263u9n5kIUQiSNVn8rIrJFM7zMdnVoX73A6FZ1GzQmjujNjv3xW7XLwf0t28O7SHSzbVo3TE+DkMbs7S9a6fdiMsv+6slhyX8IXADIToBDJ44C8A3gt7zWCoWC8Q+m0VCoVw/JTGZafyg3TBvLxil1o1Lsbg7dW1DP5oW85oI+dwwdlc0j/LAbkWJOmM2WiiCX3JXwBIBMBCZF8kvnaf2uY9VpOGduz0XMrd9QQAhZtrGDRxgpgDXmpRg4flM2EgkymDs2V6Yi7gFhyX8IXAG63GwCj0RjnSIQQ7WV77Xae+/05Zg6aySD7oHiH06UdO7Ibh/TP5Nt1ZXyztpQfN1ZQVOPm9V+28eHyXY06Fr756zYyrQYG59nITzNJK0EnEkvukwJACNHlvb7mdd5b/x7+oJ97JtwT73C6vDSznuP3y+f4/fIJBkP8sauGb9aWUe3yKkne6w9y50er8PqDf75Hx7BuqYzumcbYPnZG9kgjRfoRxI0UAEgfACESXY2nhvfWvwfArCGz4hxN4lGrVYzonsaI7mmNnnf5Apw1rhdrimpZXeSgst7LDxvK+WFDeNK4R04ZyQmjugOwvqSWKqePEd1TZbKiDiJ9AAjfBgFdbwZDIURs3lr7Fi6/i3F54xhoHxjvcJJGqknHrUcPAcITEhU73KzYXsPiLZUs3lrFsAbjC7z281Ze/mkrWrWK/jk2hnZLYWT3VMb0tjMgxyZ9CtpBLLkv4QsA6QQoROJy+928vuZ1IDzwj4gPlUpFXqqJvFRToz4CEXlpJgbl2lhXUsuaIgdrisK3IQKM65vBmxccBIRHK9xa6aR3hkWKgn0knQDZ3QwiLQBCJJ5PNn1ClaeKoRlDOSD3gHiHI5px0aH9uOjQfji9flbvcrBql4Nl26r4bUsVA3N336e+oayOaf/+HrNew8juaQztlsKY3uns38tOls0Qxy3oemLJfQlfANTW1gLIQEBCJJhQKKSc/Z8x5Azpgd4FmPVaxvS2M6a3nbPG9wbCZ/0RVfU+uqUa2VXj5qdNFfy0qYLnftgMQLpZx0eXTVBmNqz3+DHrNfL/3oxYcl+HFwCbNm3ixhtv5OuvvyYvL49bb72VU089tdn/RIfDwYMPPsiCBQuw2WycccYZzJo1K+b/dIfDgVqtxmyW6TCFSCQqlYqHDnuI99e/z5G9jox3OGIvaTW7x2wY1y+DRTdPprzOw7Jt1azaVcOvmytZuaMGpzdAXuruHu3nvvQbK3fU0NNupofdRPd0M70yzBRkWxmcl0KmNblbDGLJfR1aAKxbt44xY8bQt29f7rnnHlavXs2sWbOoqKjgsssu22P5zZs3c+SRR1JbW8vpp5/Oli1bOPvss6murubKK6+M6TMrKytJS0tDrZaBQYRINH1T+3LtmGvjHYZoY5lWA1OG5DBlSA4Qbu2pqPcqxUIwGGJbpROXL0BhSS2FJbWN3n/hxL7cPH0wAGuLHTz3/WaybQaybQZyU010SzOSbTOSYdWj03R8bnD7Aji9AdSq8C2XEN7G8jpvm13qiCX3dWgBcNNNN9G/f39++ukn9PrwRqenp3PPPfcwe/ZsDIbGG/7bb78xYsQInn76aTIzMwE4+uijeffdd2MuAJxOp5z9C5Fg3H43Bo1Bmn+ThEqlanRGr1ar+OnmydS4fGyvdLKjysn2ShebyuvZUFpLQbZVWbZhh8OmLLt9CumWcD567Kv17KhyYjFoMes1mPVaDFo1WrWKATk2xheE81BprZsPlu1EhQq1WkUgGMTjC+L0Bahx+bhsUgHd0kwA/GfhBj5dWYTHH6Te46ey3ovnz7ETRnRP5aPLJgDgD4YYe8+X3H/i8D1GZ9wbseS+DisA3G43n3/+Oc8//7yS/AFmzpzJP/7xD5YuXcq4ceMavefkk0/m5JNPVn73+XysW7eOsWPH7rH+NWvWsHbtWtRqNQaDgbS0NEaPHo3P50Onk8EohEgk//z1n6ytXMvtB93OsMxh8Q5HxEmqSUfqn/MaNGdUj3T++bfhlDo8lNa6Ka5xU1TjprTWg8PlI9W0Oz8sWF3C7ztrmlzPyWO67y4AHB7u/Wxts5958pgeSgGwo8rFql2ORq/rNCrMem2jgZI2ltUxfXhum7UAxJL7OqwA+P3333G73RxwQOOeuj17hiudrVu37lEANORyubjwwgvZtGkTL7/88h6vz5s3jzlz5jR6rri4WAoAIRJMUV0RH238iEAwgE0vnXtFy3pnWuid2fStcMFgCHWD2w2vmTKAYoebeo8flzeA0xfA7QvgD4QY3StNWS7bZmD2IX0IhiAYCqFWqTDq1Jh0GlJNOvL/TP4Qvhwxc2xPDDo1Zr0Gu0WPSbdn58VBuSn85/T922y7O1UB4PF4APZokogEGAw2P3vX77//zsyZM9m2bRvz5s1j/PjxeywTCAT2eE6r1eL3+9FqE/5mByGSxvN/PI8/6OeoPkfRK6VXvMMRXZj6L2MNTBqUHdP7slOMyiBI0fTKiM8YNLHkvg7LjNnZ4R1bWVlJt27dlOcrKioavf5X8+bNY9asWUyYMIFPP/2UXr2a/oMfPHgwxx9/PIFAAI/HQ1VVFQaDQVoAhEggpc5S3lv/HipUXDjiwniHI0Sn1alaAPLz89Hr9axYsYJhw3Zfs/v1118BGDNmzB7v2blzJ2eccQbnnXceTz75ZIu9GWfOnMnMmTP3eN7r9TbqcyCE6LreWvsWvqCPI3oeQb+0fvEOR4hOK5bc12H3P1gsFo444gheeeUVQqEQEG62f+qppxgxYkSToxV9+OGH6HQ6Hn744b2+jU8uAQiRGHwBH++ufxeAM4ecGedohOjcOtUlAAjfBnjYYYcxffp0jjvuON59912++uor3n//fWWZJ554glNPPZXMzEyKiorQaDSceuqplJWVUV9fj0ql4rTTTuOGG26I6TMDgQAajcw+JURXt6lmE8FQkIK0AkZlj4p3OEJ0arHkvg4tAA455BAWL17MNddcw5w5cxgwYABffPEFU6ZMAcJ3Alx++eUUFhby+OOPc/zxx1NYWIjVaqWgoACr1YrH41EmOYhFKBSSQYCESAAD7QOZf+J8dtXtkvv/hYgiltynCkXa4zuJDz74gMMOO6zNJu857LDDAFi4cGGbrE8IIYTo7GLJfZ3u1HjGjBltPnNfJ6txhBCtEAqF+L91/4fT54x3KEJ0KdFyX6crANqDFABCdF2LSxYz96e5nPH5GfK3LEQrJH0BoNFomhwkSAjRNbzwxwsATOk5Ra79CxGjWHJfwhcAWq1WCgAhuqiN1Rv5YecPGDQGTh10arzDEaLLiCX3JXwBoNfrlWGIhRBdy/O/Pw/AjIIZpBvT4xyNEF1HLLkv4UfIMZlMuFyueIchhGilwspCPt38KRqVhnOGndN2K/bWg77B+Ozzb4VtP4efD/rCrxlTwZoD+fvDQRe33WcL0UFiyX0JXwBYLJZWjRsghOgcHlr8EMFQkJmDZpJvzd+3lZWuhbUfw7r5sHMpXL0KUvLCr9UWwc7FTb/PXbO7APC54O0zoWAyDDoa0vZ9znYh2kssuS/hCwCz2SwtAEJ0QbOGzsLpd3LJyEv2bgXuGljxNix5EUpX735epYGytbsLgENvhAMuBIMV1Frw1IG7GupKwJK1+307l8KGBeHH/26CvJEwciaMPBVMcnlCdC6x5L6ELwB0Oh1erzfeYQghWmlC/gQm5E/Yuze7quGRYeCtDf9uSoeBR8Og6dBnIhhsu5fNGhjbOnOGwN+ehbWfwPovoWhF+PHlXBh+Iky7r/F6hYijWHJfwhcAer1eCgAhupA6bx1WvbX1bwyFIHKboCkNeo0HnxPGnh9ustfs47TgpnQYcXL44XPDuv/Bkpdg0zfhPgS6+Mz7LkRTYsl9SVMAhEIhuYdYiE6u2l3NjA9nMLH7RG458BaMWmNsb9z2M3x6HRz9EPQ8MPzcKa+C1tA+geqMMHRG+FGxMdyPIDLuuqMIPr0GJt0CucPb5/OFiCKW3JfwtwEaDAZCoRB+vz/eoQghorj/t/upcFews24nBk0MydvvgS/nwAvToOR3+PHR3a+1V/L/q4x+0LvBpYqfnoDCz+CZifDxVeCs7Jg4hGggltyX8AWAzRa+JudwOOIciRCiJYuLF/PJpk8waAzcOe7O6C125evhucnwwyPh3ydcAyc93/6BRjPhGjjwIkAV7oD4+Gj46clwsSJEB4kl9yV8AZCRkQFAVVVVnCMRQjTHF/Bxzy/3AHDusHPpmRLlFruV78Azh0Lx75DeG86dD0fcCTpT+wcbjSUDjrofLvkJ+hwKriqYfws8PQF2LIl3dCJJxJL7Er4ASE8P355TWSnNcEJ0Vi+vfpkN1RvoaevJecPPa3nh+vLwNXZfPQz/O1z4/e7r/p1J1kCY9SGcNg8yCsItFkFfvKMSSSKW3JfwnQBTU1MBqKmpiXMkQoimbKrZxNMrngbg1oNujX7t35IJJz4HNTtgzLm7e/53RioVDDgy3BKwaSH0PGj3ayWrw7cWCtEOYsl9CV8AWCzhW3NkNEAhOqcsUxZTek1BrVIzvtv4pheqLYHtv8CQ48K/Dziy4wJsCzojDJy2+/eN38CrM2DI8XDUA2DLjVtoIjHFkvsSvgCQFgAhOjeb3sY/D/kn/mAzvZWLVsCbp0FdMZz1cfj+/q6uZkd43IDVH8LGhTBlLux/duduzRBdSiy5L+H7AEQ6QpSXl8c5EiFEQ2sq1uD2u5XfteomzkfWfBK+xc+xIzwxT0b/DoywHY0+Ey77FfpPBU8NfHIVvPY3qC2Od2QiQcSS+xK+AEhNTcVoNFJUVBTvUIQQf9pVt4sLFlzAzE9nUuGq2HOBUAi++xe8fXp4NL+RM8Nn/9asPZftqlK7hzsInvg8mOyw8Wt48gDYuijekYkEEEvuS/gCQKVSkZeXR3GxVNZCdAYuv4urvrmKak81uZZc0o1/mUjH54Z3z4Ov7wJUcMQcmPFUxw3s05FUKhh+Ely8CAqmhC8LZA2Kd1QiAcSS+xK+DwCEb4eorq6OdxhCJL1gKMjtP97Omso19LD14L5D7kOt+st5SF0xbPgK9Db423/DE/gkupQ8OP2d8JDCZnv4Ob8XNn4FA6ZJ3wCxV6LlvqQoAFJSUqQToBCdwBPLnmD+lvlYdBYem/QYqYbUPRdK7w2nvBZOhDlDOzzGuFGpIKXb7t+/mhseVrhgChzzMKRFGRxJiL+IlvsS/hIAhHdCbW1tvMMQIqm9v/59nv39WTQqDQ8d+hAF6QW7X1zxFvz89O7f+xySXMm/KVkDwZgKGxbAkwfCr89CMBjvqEQXEi33JUUBkJGRQWlpabzDECKpralcA8DNB9zMwfkHh5/0ueGTq+H9C2H+zVBWGMcIO5nRs+DSX2HoCeGOkJ9dBy8fA5Wb4x2Z6CKi5b6kKAByc3MpLS0lFArFOxQhktbNB9zMC0e+wCmDTgk/UbkZXpgKi18AjR6OeSR81it2s+XC31+Cv78MlmzY+iM8NR7KN8Q7MtEFRMt9SVEA5OTkEAgEqKho4nYjIUS7WVqylFJn+AxEpVIxNnds+IXVH4Un8ylaAWm94LwvwgPhiKYNnQGX/gLDToQ+E8NTEAsRRbTclzQFAEBZWVmcIxEieSzcvpDZX8zmwgUXUuttcB3y12dh3pnhAXAGHQMXfgfdRsUtzi7DbIeTXoCTX9l9V0DJKvj02vCMg0L8RbTclxQFgNVqBaCuri7OkQiRHN5f/z5XfXMV3qCX0dmjMWvNu18cOB2sOXDkP8O9/U1pcYuzS2o4HsLnN8Jvz8HjY2DJSxBoZjhlkZSi5b6kKABSUlIAcDgccY5EiMQWDAV5dOmj3LHoDgKhALOHz+a2A29Fs37B7h7sqflwxXIYd4nc376vjnoAeh0MznL4+Ep4alx4fgHp7ySInvukABBCtIlaby2XfnUpz/3+HBqVhtsPup0rRl6E6r3Z8OYp8NPjuxfWm5tfkYhdzhA4+9PwpYG0XlC+DubNgmcmQvEf8Y5OxFm03JcUAwGZzeGDjUwJLET7+XLrl/yw8wfSDGk8MPEBxpnz4ZHh4ZH9TOlgl45r7UKlCncOHHQsLH05PIdC+XqwZsc7MhFn0XJfUhQAkSpIBgMSov3MKJhBmauMo/seTf6Gb+HD6RAKwsCjwyPZyZz37UurhwNmw6gzYOfS3QVAwAcvHxvucDnqDOlzkUSi5b6kuARgs9kAKQCEaEs1nhrmLJrDhqrwPekqlYoLbEPIf/9y+ODicEe/k1+BU1+X5N+RdCboffDu39fNh20/wRe3wkOD4P2LwgWCSHjRcl9SFAAmkwkAp9MZ50iESAzf7/ieEz48gXfXv8udi+7YPdBIr/Hgd8OEa+CyxTDkeOnoF28Dj4JT34Q+h4LfBSvehGcnwbOT4bfn5c6BBBYt9yXFJQC1Wo3RaJQ+AELso3JXOQ8tfohPNn0CwH5Z+zF3/FxUzgqwZIJaDWd9Ev5XdA5qTXhGxUHToXJTOOkvfRV2LgZ3DYw5d/eyAT9okiItJIVouS9p/qfNZjMulyveYQjRJfkCPt5Y+wbPrHiGWl8terWeS0ddylm9jkLz2fVg6wbTHwgvLMm/87L3hSPvgUm3wpqPQaPb3UJTtSU8OuPAo2DwcdBvUvhygujSWsp9SVMAWK1WGQhIiL3k8Dp4asVT1PvqOST/EG458Ba6b/0VXj0Rxp4X7lwmug69GUae0vi5DV+Buzp8iWDFm6CzwIAjYfhJ0G8y6IxxCVXsm5ZyX9IUABaLRQoAIWIUCoX4tfhX9sveD4PGQIYpg5t6HI29z6EcYsxD9cVc6HkQzP5KzhITxdjzwvMMrP4w3DpQtBxWvRd+WHPg2sLdrQXBoLT0dBEt5b6kKQB0Oh0+ny/eYQjRqYVCIRbtWsRzvz/H4pLF3Dz8Qk4bfRkAM/odC+sXgL0PzPhPuPlYJJbM/jDxuvCjaguseh/+eA9S8ncnf58LHhkG3ceE53DIHQ49x4XnKhCdTku5L2kKAL1ej9frjXcYQnRKLr+LzzZ9xmtrXmNDdfi2vhR9CtqGY/h32w/yRkqv/mSR3hsmXB1+BBokkF3LwkMPr/tf+BGR1hPyx8CkW8KFhOgUWsp9SVMASAuAEE17t/Ad/r3sMao91QBkmbI4ffDpnFxwArbKzeGDf+RsX5J/cmrY2tNrPFy9Grb+CMW/hwuCHb9B9bbwY8rc3cv++Gj4ToPuB0D+aBmdMA6kBQDQaDQEAoF4hyFE3JU6S/EGvHS3dQfAVL2dak81wzKGcdrg05iWfxi6+lLQWSF//zhHKzql1HwYcXL4AeHbB8sLoWhFuCUgYsXbULpq9++2buGWpG6joeBw+X51gJZyX9IUAGq1evdgJUIkmeL6YuZvmc8XW75gZflKjs+bwN1TnwJg8tDTeS3/IEZkDEWl1oDBCkZbnCMWXYpGCzlDw4+Gjrgz3FKwY3G4OKjdBYW7oPAz8NXvLgDK18Oaj8KXmLqNlv4Ebail3Jc0BUAwGESrTZrNFYK15auZv20B3+34jnVV65TnDRoDKoMtPGWsSoXBmsNIa04cIxUJa8CR4QeE7xyo2BC+u2Dn0vCthRGbv4Wv/rH79/Q+4WIgbwTkjggvK3cd7JWWcl/SZMRAIIDBYIh3GEK0i2AoyLqqddhVerLT+wLw1e8v8dy2zwEwaU1MyJ/AtN7TmNBtPGa1Tq7ni46lVkPWgPAjcukgImc4HHgR7Foebimo2hx+rP4gPJPkDZt3L/vTk+HbErOHQEZBeBIk0ayWcl/SFAB+v19aAETCcHgdrCpfxcqylfxR8QdLS5bi8Dq4us8JnDsxfCZ1RP5E6iwZHNL9EPbPHoVBbZCzKNE59Tww/IBwf4KyNVC0MlwMqFS7i1W/BxbcAcE/5y9QayFrcLilIGdoeBRDe9/4bEMn1VLu6/CMGAwGee211/j666/Jy8vjyiuvJDe3+ZnCgsEgb731FgsWLCA7O5srrriC/Pz8Vn+ux+ORFgDRJTm99Zj1FuX3cz47k8Vly/dYLteSi9aYovw+cMAx3MgxHRGiEG1How2PLZA7HEad3vi1yERTxb+Hi4SqrVDye/gBkNJtdwGw7gvY8n34lsTsIZA5ABr8fSSLlnJfhxYA9fX1TJ06lcWLF3PEEUfwww8/8PjjjzN//nwOPvjgPZZ3uVxMnz6dH374gSlTprBo0SIef/xxPv30UyZNmtSqz3a73RiNMpSl6JyCwQClrjI21WxiZ91OdtXtYkPVBtZXr2dX3S6+n/Epqak9AEhHg16tZ5B9EMOzhjMscxgjs0bS3ZKPSs7wRSIzpsLht+7+3VsfLgaKf4eSPyBvv92vFX4GS15s/H5LdrhvQe+Dw+MbRCTwyIYt5b4OLQDmzp1LYWEhy5YtY8iQIfj9fk455RSuuuoqfv31V1R/uSb5z3/+k+XLl7NkyRJGjBhBIBDgzDPP5Morr2TFihV7LN8Sp9OJ2WyOvqAQ7SQQ8FPhqaS4vpji+mLSg0HG9p0GwOI173De4nuafJ9OrWNL8RJG/lkA3DbuDu63dUcn1z5FstNbwkNS9zxoz9eGnhAewbC8EErXhDsg1pfChgV/tiT8WQB46+G+nuGBj+z9IL0XpPYI386Y1jPccmCwduhmtaWWcl+HFQChUIhXXnmF6667jiFDhoQ/XKvl6quv5pBDDmH16tUMHTp0j+WvvPJKRowYAYTvZ7zmmmsYO3YsS5cuZf/9d99DumbNGtauXYtarcZgMJCWlobZbKZXr16kpqZKARCD6tpdbHGVUuOpweV34Q168QV8+II+vAEvZww6DfWfU4W+vORxNnsqCNH49hIVKoab8jhx1IXhdVZv5eVNH6BVa9GoNFh0FlINqZi0Jiw6C0NtvUm1dQPA63OCWotOrWtVcdcZhIJBKjyV7KzbydC0gWj/nDjluSX/5teK1eyq38XOup34g7vnXp+Stb9SAPTOGo7daKd3Sm96pvSkm6UbfVL70D+9Pz1tPdBpdid7e7pc4xQiqr6Hhh8RwSBUbw33K2g4f4WjKNynoGJD+PFXp83bfSfDkpfDox+a7WDODHdQNKWFWyasOeFBkpT17gr3UVBr/5x1Ud3godk97bLfC67KcP8GY2p4fW2oUxQAa9asoaSkhOnTpzd6PpL0N2zY0KgA2Lx5M1u3bm1x+YYFwLx585gzZ84enzt69GiWLFmC1+tFr2+7M6adRct4v/hHjFojaYY0LDoLVp0Vi86CQWugwNoDg6Fjrzf5Aj4cXgc+n4vclPAgL6FgkOdXvYDD66DOW0edr44aTw3F9cVUuau4tOdRnDL+ZgC+W/0Wt659sdn1n9RrGuY/R/L6Zud3LKla2+RyrpwDOJFwAVBVu53nfn+u2XU+P+YWDhg6E4BHvr2Z13Z+jQoVJq0Jo9aIUWNEr9EzwNaTh454UnnfY78+SECjxaw1Y9PbsJvsmDQm9Bo9fY3Z5Nj7hfeJ10lIE1tREQoGCRDEH/TjCXhw+924/C6cfiepITX5mYMA2F60jHd2fqM01Ze5yqhwVyjJ/Yupr5CXNwqA1SXL+alsifIZdqOdHHMOuZZcRqYNUJ7PzhrCtycvlJ75QrQXtTo8j4W9T+PnMwvg1uJw8q/aEu5XULMj/HPNjsYDG+1aGr600JTsIXDJT7t///fw3Z0V/+rYx2D/s8I/L38dPrkq/POQGTDiFBg0ven37YWWcl+HFQDl5eUAZGc3HgoyJSWcJGtqamJa3mQyodPp9li+uZGOIp0f2roT4Pby1Tyz8plmX/940jP07hmuBm+bfxE/1azHqrdi0powaAzoNDq0ai3DLD24bFz4mpazrpRHVz2PWhW+FhUihD/oxxf04Q/6OTP/cAb1Cd87+9YvD/JW0Y+4A25qvbU4/U4lAeWZsvni5K8AUKnVvPzHS1R7a/4aIgDlfw7/CpBn686IzBGkGFIwa83oNXp0al34odEBu5PTmYNOZ3rIi1qlRtXg+SBBemh2d1hLs3bn8lGX4w/68Qf91PvqqfHW4PK5qPfVk/nnaHR/BotWpcUf8uP0O3H6ncpL+gYDWQT8Xl5Y+zqBUNP/5zcVnMzpB98OwKdLn+L2wpcAUKvU6NV6NGqNEvOiU39Urpuf8uEM1jg2N7nOU7sdyq1TngCg0rGVF1ftWSjZ9DZ62HrgCbgb7KfTmDHiXLpZupFvy8ekbWbmPEn8QsSPzrS742FLDro0PCaBsyI8H4KrOjyFsrsmfLkhIhgES1Z4GO2AL1wIhIK7H8EGQ/PqTOFltUYoWxtuVWhDnaITYHp6eKNqamoa9fp3OBwApKamNrt8Qy6XC5/Pt8fygwcP5vjjjycQCODxeKiqqqKurg673Y7f78fn87XpJYD8zEFcPPJi3AE3Ve4qnD4ndb46nD4n7oCblAYDq1T6ail1lVLqKt1jPeqMkbu3zVPDG2vfaPYzDzf3UAoAh7uKjTUbG72uUWmw6W3Y/tLyMHvQaXi1eqWFIs2QRrY5mwxTBqm63de2xg45mdeH/OX+3GZMHjAjpuXS03tzQfoFMS174+RHuBEIBAO4/C7cATduvxtPwIPfU6ssFwz4uG7Mdbj84SKizldHpbsSt9+NO+Cmh62Xsqw35Eer1uIP+gmGgrgDbmhmROhIMaNT6zBoDBi1RgwaAxadhQzz7kK0d84oLh91OXmWPHrYepBlziLTlIlBs+cf2ai+U2PadiFEFxAZxyAatRqubbqFdA8jTw0/2kG03KcKddD4uOXl5WRlZTF//nymTt19UPzxxx+ZMGECW7ZsoVev3Qfu2tpaUlJS+PDDDznuuOOU55csWcKYMWNYu3YtAwcOjOmza2pqSEtL41//+hfXXntt221UjNzeeqq8Dup99bj8LjwBD96gF3/QT2oQRvacCIDTWcF7Wz4nEAqgQoVKpUKj0oRbC1RaDkgpID8nXKGWV22hCh9GjRGrPpzYdSqt9AJvRigUIhAK4A14G7UcWLUWZZ8FgwHUak28QhRCiDYVLfd1WAtAZmYmo0aN4oMPPmhUALz//vvk5OTQs2fPRsvbbDbGjRvHBx980KgAeP/990lLS6N//9inm6ysrAR2typ0NKPeQl6D+7ibYzZncMaQM2JaZ2Z6bzL3NbAkolKp0Kq0aNXNf+Ul+QshEkm03NehtwHOnj2bK6+8kuHDh3Pcccfx9ttv8+9//5tbb71V6aBVW1uL1WpFpVIxe/ZsZs+ezX777ceJJ57Ie++9xwMPPMDVV1+NuhVnupGdkJkpKVMIIURyiJb7OrQAuPDCC6mqquKaa67hkksuQafTcemll3LbbbcBUFpaSk5ODldccQWPPvooZ599NuXl5dx0001ceeWVaLVaZs+ezT/+8Y8on9RYpJ9BpMOhEEIIkeii5b4OLQDUajW33HIL559/Pps3b6Z3797k5OzuLJeens7UqVM54YQTgHCz7fXXX88555zDxo0b6dmzJ3l5ea3+3EhHwr92HBRCCCESVbTcF5fZcbKzs/e4vQ9Ap9Mxf/78PZ7PzMzcp+b7qqoqIH59AIQQQoiOFi33JUWX8bq6OgCs1q47nKMQQgjRGtFyX1IUAC6XCwgPIiSEEEIkg2i5LykKgJqaGjQajcwFIIQQImlEy31JUQDU1tZis9m63AQzQgghxN6KlvuSogCIjIYkhBBCJAuv19voTru/6rChgOMtEAig0XTNkd5CoRA1NTVUVFRQU1NDfX09NTU1VFVVUVFRQW1tLR6PB6/Xi9frxefz4XQ6qa+vx+Vy4fV68fv9e0yYpFKp0Gg0aLVa9Ho9Op0OrVaLTqdDp9NhNpux2+2kpKRgs9lITU3FYrGQlpZGamoqRqMRo9GIxWIhNTUVnU4Xpz3Uvvx+P9XV1dTV1VFfX4/D4VD2rcvlwu12U1dXR21tLU6nU3l4vV48Hg9utxufz4ff71cewWCQYDBI5M8vUqFH9nvDfWswGNDpdFitVlJTU0lNTSUlJYWUlBTl5+zsbFJTU7tsK1dtbS2VlZXU19crD6fTSW1tLbW1tcr+jfwc2adutxuPx4PP58Pr9Tb6jqtUKuW7rdfrMZlM2Gw25dFw/6WlpZGWlqb8nJ6enhDfZ4/Hw65du6iqqqKyspKSkhLl++t2u5XvqsfjUb7Tke9q5N+G+1StVqPT6dDr9cq+NRgMaLVaTCYTVqsVi8WifH8j+zKyvzMyMsjNzW3Tidk6m1AohNfrVb7DZWVlFBUVUVZWRnl5OWVlZdTU1OBwOKirq1OOz36/XzkeNNzPkX+tVqtyLI58X81mM1arFbvdrjyXk5MT80B5SVEAXHnllfzxxx+YTCbS0tKw2+1KQot8adPT05WDgd1ux263Y7FY0Grb5k7JYDCIy+WitrYWh8OB0+nE4XAoX4KSkhJKSkooLi6moqJCea2qqoqioiLcbneL61epVMqBLnKws1gsmEwmDAYDGo0GjUaDShWeYyAUChEMBgkEAvj9fqVwiPzhR4qI6upqgsFgTNsY+YPPyMhQDgR2u53MzEzlwJqdnU1GRgYWi0U5AEcOvCaTqc0TmNfrpaysjMrKSiV5VFRUUFFRoSSSuro6qqqqcDgc1NTUUFtbqyShuro6ysvLY94HEO5wYzKZlIOj0WhUiqvIQ61WK4+IYDCIz+drVFg4nU4l2Xm93hY/V6/Xk52dTVZWFtnZ2eTl5ZGTk0NOTg5ms5m0tDQyMzNJT08nMzOTtLQ0rFZrq0bVbEkoFMLj8SjFZ+QAGClei4qKKC4uVv4tLi6msrJS+b+IhcFgwGq1YjKZ0Gq1GI1GpUDS6/XKdxzC+zPy3fZ6vbjdbuXvL9I5qiWRg6vNZlP2aUZGBna7HbPZTFZWFpmZmcp3PTU1lfT0dOVA3Bb7NZJMnE4ndXV1OBwOysrKlMnOHA6Hsk2Rk4JIsiktLaWsrKzF9UeuDxsMBuV40fBEQKvVotFoUKvVStEa+S5G9q3H48Hv9+Nyuaivr8fj8UTdrsj/Y8MCwW63k5OToxyDMzIyGh2zI/s5Uky0dYEWCoUaFfRlZWXKd9PlclFZWUlVVZVSNNXU1CgnZBUVFVRWVuJyuaipqWlxH+h0OtLS0rDZbFitVqWYihwXIHzCGtnPkX8j/9/19fUtbodWq1W+oxaLhfHjx/Pf//63yWWTpgBYvHgxbrebyspKqqurqa2tbXYK4YZ0Oh0GgwG9Xo/ZbFbOziJVb8M/jr/+p0USSOQgHo1Go1HGSIgUKGlpaeTm5pKXl0dmZqZyFp6amordbic9PZ2UlBS0Wm27nP0Fg0HlTKy6upr6+nqqq6upqanB7XbjdruVFonIWVxlZaVythz5w3A4HFEPDBqNBovFohQwkYN8pEVCrVYrhUzDP5SGRUwkpsgfTCyJJZIcI2fXNptN+eOx2WzK/4nFYlGeixwsI49IojAajW2WUP/K5/PhcDiorq5WDvyRg1BJSQmlpaWUlpZSXl6uJNnS0lJ8Pl+z61SpVErx1fCMI/IdjyRUtVqNSqVSkoDX68XlcimJKXL2GO1wolaryc7Oplu3buTm5pKZmYndbqdbt25kZGQo+91isWA2m5UzHqvVitVqbbODfiAQaFTwVVdXK/u1urqaqqoq5ThRW1ur7NeysjKqq6txOp0trj+yXy0Wi7JfI8eRhok1EkvkO+zxePB4PLhcLqXVKZZDtFarVY4XOTk5yr7Nz88nPz9fKfxycnJITU1VjmM6na7Njxt+v1/5O2y4Xx0OB+Xl5UorRKTwjhQzkf3rcDha/M5GmEwmZTusVquyPZFjReQ7CyitbZECJvKIxBkpDmP53EguiJzUWCwW0tPTlYIlchyJfI8j3++srCyysrJISUnZp30eDAaVk8NIsR1pHa6oqGDHjh1KMVJfX8/AgQO59957m1xXUhQATQmFQjidTlwul/JFjDTLlJeXU1VVpZzBRJrXI5VfpNkx0jwWCoWU5vSGB9HIQStyNm42m5Xmx8gZcEpKClarlaysLDIyMuLehOvz+ejXrx86nY6UlBSWLVvWZut2Op2UlpYq+zaSvBomtEiTWKQSb/jHGimyIvscUIqCSHNkpOkx0mRmt9uVM7VIIklPTycrK0tpqmyvhB0PoVCI+vp65b7fyMGivr5eaQaOtIA03P+Rpt9I8Rr5jkf2deQRKQYMBkOj4ify/Y581yO/R77nGRkZSiG1t/vb7/czYcIE5Tuybt26ttx1rRIMBikvL1fOEBtelquurlZONOrr6xslm4YtbZFWpYbfYYPBgMFgUIrSSGKLHDsi+zJyRhwpkNqj9awtBQIBnnjiCbKyssjNzeXwww9vdtlQKKQkOJfL1agYi5xURY7VDY/hDY8XkUI1ItLyGWlajzwixwuj0ai0SEYKiszMTLKyspRjeKQloqlW4VAoxPbt23G5XDgcDsaOHdsu+7GtJW0BsC+CwSAej0ep5BNJVVUVdrsdAIvFEnPTbFfhcrm4/vrrKS0txe/3895778U7pDYV+f+z2Wz07t2blStXxjukNpPo381IX59IC0Dv3r3jHVKbSfT/u666fYlz6tOB/vjjD8xmMzqdjsGDB8c7nDa1fft25ecePXrEMZL2sX79ep588kneeecd1qxZE+9w2lzk/y/W5syuJNG/m7///jvp6enk5uZy1FFHxTucNpXo/3dddfukANgLDa//Jdrwwom8bSDb15Ul8rZBYm9fIm8bdN3tkwJgL1RXVys/J9oEQ4m8bSDb15Ul8rZBYm9fIm8bdN3tkwJgLzTszZ5o97Mm8raBbF9XlsjbBom9fYm8bdB1t08KgL3QsHdpVx1cqDmJvG0g29eVJfK2QWJvXyJvG3Td7UusLuwdZNCgQcydO5dAIMCgQYPiHU6bSuRtA9m+riyRtw0Se/sSedug626f3AYohBBCJCG5BCCEEEIkISkAhBBCiCQkfQBayePx8Pjjj/POO+9gNpu54oormDFjRqcehrMpLpeLCy+8EEAZAlaj0VBbW8sDDzzA8OHDgfCAMvfffz/z588nIyODG2+8kUmTJsUz9Ba53W6uu+46cnNzue2225TnA4EAL774Ii+88AIqlYrZs2dz5plnNuqws23bNu68805WrlzJ4MGDueOOOxgwYEA8NqNZy5cv54orruD555+nf//+ADzxxBP89NNPqFQqPB4PoVAIv9/PpEmTuPLKK4HwKHMffvghjz76KE6nk5NPPplLL70Uo9EYz81R+P1+XnnlFRYsWIDVauWMM87g0EMPbbTMTz/9xN13301JSQmTJ0/mpptuanTLlcvl4uGHH+bDDz8kJSWFa665hqOOOqpT/G1u3bqVp556io0bNzJkyBAuvfRSsrOzAfjxxx954okn0Gq1ylDBkaGB33jjDSX+1atXM2fOHDZu3MiYMWO4/fbb6d69ezw3CwgfE19//XV++eUXcnJyOO200/a4Dt7wb2vQoEHceeedjf62QqEQ8+bN48knn8Tr9XL66adz4YUXotfrO3pz9rBx40ZeeuklKioqGDlyJGeeeSZmsxmAsrIyrrrqKjQaTaP/u7q6Op5++ml69uwJQEVFBXfddRc//PAD+fn53HbbbZ1iuGBpAWgFl8vFIYccwty5cxk3bhw9e/bk73//O3Pnzo13aK1mNBr5/PPP+fXXX/H7/RgMBlQqFYMGDVLmj66oqGDUqFE888wzTJo0CavVyuGHH87zzz8f5+ibVlRUxMSJE3nyyScpKSlRng8Gg8yYMYNLL72UESNGMHz4cC6++GKlAAL47bffGDRoEIsXL2batGls3LiRkSNHtulcCPvqnXfe4eCDD+b7779vNDPghg0b+OCDD3C5XMrkSTabjf32209Z5sorr+Rvf/sb+fn5jB8/nrvvvpvp06e3apbD9lJRUcGkSZO47LLL8Hq9LFu2jMMOO4w33nhDWeapp55i/PjxhEIhpkyZwltvvcXYsWNxOBwA1NXVcdBBB/Hggw/+f3t3HxXFdf4B/Lu7vBNAlPASFA+kJoqIZbNRwfdQPTFbUNHg0apEwVQbS15qoolJDjGkrTXGqNVYE2qP6wuiUl/haMSjghtjNBpfQEERI8FVXBCCwCo7398f/HaadVE3trKbw/38553Z4T7euTPPzty7F4MHD0ZgYCASEhLw8ccfOyos2a5duxAVFYXc3FyoVCosX74carVarntzczOys7NhMBgAtPZNlUqFuLg4+ea/e/duREdH48qVK3j++eeh1+sRHR2Ny5cvOywuoLVvDRw4ELNnz0ZFRQW2bt2K3r17Y//+/fI+d/et8vJyREdHW/Wt1NRUTJo0CREREejfvz/mz5+PpKQkuxZCepQOHjyIyMhIbNy4EeXl5Zg7dy4GDBiAlpYWAICPjw+ys7Nx6tQpSJIkX0f79u2LTp06AWhN/iIjI5Gbm4sRI0bg9u3b6NevH3bu3OnAyP4fBbstXLiQPj4+LCsrk8tWrVpFT09P3rhxw4E1ezgBAQFcunTpPbfPnj2boaGhvHbtmlw2f/58hoSE0GQytUcVf5YFCxawT58+DA8P5+9//3u5fMOGDVSpVDxy5IhctmvXLgLguXPnSJIxMTEcOXKkHJckSRw+fDgTExPbN4h7kCSJ3bp1Y0JCAgHw5MmT8rbXXnuNGo3mnp89cuQIATAnJ0cuKy4uJgDm5+c/0nrb44svvqBarWZpaSlJ0mw2c9iwYRw6dChJ8tq1a/T09GRGRgYlSSJJ1tbW0t/fn4sXLyZJvv/+++zcuTMvX74sH3fx4sX09fVlfX19+wZ0l9jYWP7pT3/inTt3SJIlJSUEwOzsbJJkQUEBAdBgMLT5eZPJxNDQUKakpNBsNstlvXr14h/+8If2CeIeJEni0qVL5f93SZI4YcIEjhkzRt7nQX3LEv/u3bvlz3zzzTcEwEOHDrVjNLbKysq4evVque2qqqro7u7OPXv2kCTv3LlDANy0adM9jzF+/Hj27t3b6jxMTU1l79695fPZUUQC8DNoNBqmp6dblTU0NNDV1ZX/+te/HFSrh3Pnzh0qFAp+9NFHnDlzJuPj4/m73/2OZ86cIdnaSYODg7lo0SKrz5WXlxMACwoKHFHt+5IkiWazmWq1mrNmzZLLx44dy6SkJKt9zWYzg4ODmZmZyQsXLhAA9Xq91T46nY4KhYKNjY3tUv8HMZvNPHr0KAHw1KlTcvmkSZM4cuRI/vnPf2ZCQgJHjBjBdevWyReXOXPmsG/fvjYXm7i4OE6bNq1dY7CHJEmMjo6W2+yf//wn/fz8eOvWLav90tLS2L9/f5Jkr169+Pbbb1ttr6mpIQBu2bKlfSpuJ71eTwDcu3cvSXLjxo10c3NjdnY2J0yYwGHDhvH9999nXV0dSfLgwYNUKBS8dOmS1XH+8pe/MCAgoL2rf1+SJHHy5Mnyzd2evjVz5kzGxcXZHCs6Opp//OMf26Xe9rIko5bEuaqqigC4bNkyTp8+ncOHD2dqaiovXrxIkmxsbKS7uzt1Op3VcSznwNmzZ9s9hp8SrwDs1NTUhOPHj2PIkCFW5d7e3ggODkZFRYVjKvaQrl+/DpKYP38+jh07hsjISJw7dw4DBgxAZWUlysvLYTAYbOINCwuDUql0yngty33+dGUuACgqKrKJQ6lUIjw8HBUVFTh8+DDc3NzQv39/q30iIiJAEt9//3271P9BlEolampqAMAqPoPBgL179+KTTz6R14GfPHkyVq5cCeA/8d/9LjwiIsLp2lGSJLz77rs4deoUpk+fDqC1/hqNRn7vamGpv9FoRElJic2YAX9/f/j7+ztVjJWVlZgxYwbCw8Pl+hoMBvm9t2Ue+cqVK5GcnAygNf7u3bvbrA4YERGBGzduOMXKc6WlpZg7dy40Gg1ycnIwb948ALCrbxUVFdm0nWUfZ2m7nJwcTJkyBZGRkfj1r3+NESNGAGh97QgA6enpKCsrQ1RUFPR6PWJjY1FfX49vv/0WJpPJ5voTEREBAA6PTwwCtFNTUxNIyu91fsrLywvNzc3tX6n/QnV1NQAgLS0N//jHP6BUKtHU1ISnnnoKWVlZGDNmDADYxKtSqeDh4eHU8RqNRnkcA9D6fvh+7fbjjz/C19fXZp16yw3HmWI1Go0AgMcff1wuq66uRnh4OAoLCxEaGgoACAoKwqeffopXXnnlgfE7i6tXryIlJQX79+/HkiVLoNVqATy4/W7dugUA8PPzu+c+zmD79u2YPn06OnXqhPz8fHmAW3V1NVxcXLBt2zY55hdffBHx8fEoKSm5b/xA6yA8Ry9AU1BQgKysLBiNRowaNQqRkZEAWtvuQX2roaHhnm1nuU45ktlsxsqVK3H48GEArddMy+BhS/3eeecdZGZmQqFQoLa2FmFhYdi4caOctN3dfs5ybRFPAOzk5+cnf7u8W01NDbp06eKAWj08y6CUVatWyZ3T09MTcXFxOHv2rBzP3fGaTCY0NjY6bbwtLS2or6+3SgC6dOly33YLCAhAbW2tzYAjy7dtZ4q1pqYG/v7+VqOj//73v1vd/AHgueeew4ULF2AymR4YvzMoLCxEdHQ0Kisrodfr8dprr8nbHlT/e52rJFFbW+vwGM1mM9544w2MGTMGL774Ik6ePImnn35a3p6WloZDhw7JN38AGDp0KJRKJYqLi+8bv4uLC3x9fdsljvuZNWsWqqurkZeXh8LCQqSlpQH4T9vdr29Z+t/dnOX8VKlUOHDgAIxGI1JTU5GamoqCggIAwKBBg7B9+3b55g+0PnlSq9X3vY46y7VFJAB2UqlU6Nq1K86dO2dVXllZierqamg0GgfV7OG4urpi7NixNr9bXV9fD5IIDAyEu7u7TbyWkbvOGm9TUxMA6yU5w8LCbOJobm5GcXExNBoNwsLCYDabcfHiRat9Tpw4gaCgIKsbq6M1NTXZfNsbMmSITR0tI8xJthk/0BqfM7Sj0WiEVqvFwIEDcfz4cfTr189qe1hYGM6fP29zE7HU39vbG126dLGJsbS0FI2NjXjmmWceeQz389lnn+HTTz/F1q1bsWrVKvj4+FhtDw8PR2xsrFVZQ0MDJEmS26+qqkpuU4sTJ06gb9++cHV1feQx2EOhUGDUqFF4/fXXkZ+fL9f9QX2rrfOTpNOcnxa+vr5YsWIFgoKCkJ+fD6D1FXBiYqLN6zXLdbRbt24A0OZ1VKFQICYmpn0qfw8iAfgZtFotcnJyrKZO6XQ6uLq6Ovwi83OZzWaUlpZalVVWVuLQoUOIj4+Hm5ubPN3qp9auXYvAwED5HZaz8fT0hEKhsFqfW6vVytPkLLZs2QKTyYTY2Fg8++yzCAgIsIq1paUFGzZsQGxsrFPMI7fw9va2ig1onQZ4584dq7KNGzciLi4OHh4e0Gq1OHDggDzNDAD0ej0uXrxoc+NxhO3bt8NkMmHNmjXw9PS02a7VavHDDz+gqKhILquqqsK+ffvk+mu1WmzatMkqSdDpdPDy8kJ0dPSjD+I+1q5diylTpiApKanN7UajEdevX7cqy87OhkqlwpAhQ+T3zbm5ufL2xsZGbNmyxeHtV1ZWhk8++cSqzNvbG15eXlAoFHb1La1Wi71798rfigFg3759uHbtmsPjW7NmDY4ePSr/W6FQwMvLS36Ef/v2bZvk5syZMzh9+jTi4+MRFBQEjUZjFT9J6HQ6REVFOf7pTfuPO/zlOnPmDF1dXZmQkMC8vDzOnz+fCoWCr776qqOr9rPp9XoqFAouW7aMFRUV3LNnD3v16sWgoCDW1NSQJPft20cAnDZtGvPz8zlr1iwC4Mcff+zg2rft/PnzXLhwId3c3JiYmMidO3eSbB2p6+fnx8GDB3PHjh1ctGgR3dzcOG7cOPmzCxYsoLu7OxcsWMDdu3fzueeeo1KpZFFRkaPCsZGTk8Pk5GQqlUpmZGSwqqqKJBkREcHExEQWFxfz5MmTTE1NtZr2d+vWLT755JPs3bs3N2/ezNWrV9PPz49qtVqeVuZI7733Hv39/Zmens5JkyYxMTGRo0eP5vr160m2jiz/zW9+w5CQEGZlZTEnJ4fdu3dnYGCgfK4eO3aMSqWS48ePZ15eHt98800C4DvvvOPI0Ei2TrcdPnw4Z8yYwfHjx1Or1fKll15ieXk5SfLVV19lWFgYDxw4wAsXLnD58uX08PDg1KlT5WO8/PLL9PX15ZIlS7hjxw7GxMTQ09OT58+fd1RYJMmvvvqKADhnzhwWFRXx888/p6+vr9WMjAf1rbq6Onbt2pUxMTHMzc3lihUr+Nhjj3HQoEEOnyaXkpLCJ554gtnZ2Tx48CBTUlLo6uoqTwXPzc2lm5sb165dy4qKCm7bto3dunVjjx492NzcTJJcv369fJ/Iy8vjxIkTCYDr1q1zZGgkxTTAn+3rr7+mWq0mAPr5+fHDDz90yjnxDyJJEv/617/S19eXAAiAQ4cO5enTp63227NnD3v06EEADAoK4vLly53iptGWzz77jGq1mjExMYyJieG8efPkbSUlJRw2bBgB0MPDg3PmzJGnWZFkS0sLV6xYwU6dOhEA+/Tp4xRz5C0kSeKIESPk+NRqNY8ePUqSPHz4MPv06SO3Y2hoKFevXm31+R9++IHjxo2jQqGgSqXitGnT5ATC0b788ktqNBoOHz6cSUlJnDJlCidMmMDp06fL+9TX1zM9PZ0uLi4EQK1Wy+LiYqvjFBYWMioqigDYuXNnLly4UJ6/7UivvPIKn3nmGWq1WiYnJ3PatGmMj4+X571XV1dz3Lhxcvt5enpy1qxZVtNPTSYTMzMz6enpSQCMjY3l4cOHHRWSlaysLIaEhBAAvby8mJ6eLt/8yLb7Vl5entUxKioq+Nvf/pYA6OLiwpkzZ/L69evtHYqN2tpaTpw4UT7vnn76afmLBdk6NXfu3LlyuwDg888/bzVlU5Ikbt68maGhoQTA7t27c+3atQ6IxpZYDfAhNTU1wd3d3WZ06y9NXV0dysrKEBAQYDPN6KcaGxvlx+u/ZM3NzXB1db3nmt0k0dTUZDPlzNlJkoSzZ8/CbDYjKioKLi5tT/AxmUzyz8z+ErW0tMBsNsPd3f2e+/xSz9Xvv/8e165dQ48ePdoc9Q+0trPJZGrzVYkjSZIEo9GIxx577J51s6dvOev5aTKZcPPmTQQGBrZ5XhmNRpSXlyMkJOSeP89sid+Zzk2RAAiCIAhCB/TL/voqCIIgCMJDEQmAIAiCIHRAIgEQBEEQhA5IJACCIAiC0AGJBEAQBEEQOiCRAAiCIAhCByQSAEEQ7LJkyRIkJSXhq6++cnRVBEH4HxAJgCAIdtm0aRP+/e9/Iy4uDoMHD8auXbus1sUQBOGXRSQAgiDYRaVSISUlBTqdDnV1dUhISMALL7xgtYjL/5L4jTJBeLREAiAIgl0sy85OnjwZJ0+exPr163H06FHExsbixo0bVvtKkoTCwkLs2rVLXgv93LlzuHnzptV+JKHX6+WbfXNzM7Zt24aXXnoJ/v7+WLZs2aMPTBA6KJEACIJgFxcXF5jNZgCAUqnEpEmToNfrceXKFbz99tvyft988w169uyJoUOHYvLkyejWrRsOHjyIqVOn4uWXX7Y6ZnZ2NgYOHAiDwYArV67gqaeewtixY1FSUoLHH3/cailWQRD+t0QCIAiCXVQqlZwAWPTs2RMZGRnQ6XS4fv06amtrMWrUKHTv3h0GgwGXL1/GrVu3UFdXhzfeeAObN29Gfn4+AMBsNiMjIwMvvPACQkJCkJGRgZaWFnz33Xf4+uuv8cUXX2Dq1KmOCFUQOgSRAAiCYBez2dzmKm3JyckwmUz47rvvoNPpcPv2bWRnZyMwMFB+5B8cHIzk5GT07dsX8+bNgyRJ2LlzJ0pLS/HWW28BANzc3NDQ0IAPPvgAn3/+OZ599lmMHDmyPUMUhA5FJACCINjFsgT23X788UcAgI+PD7799luo1Wp06dIFAODt7Q2gdfyAUqlEZmYmTp06hR07dmD58uXo168fhgwZAgD429/+hnfffRf19fWYPXs2NBoNmpqa2ik6Qeh4RAIgCIJdGhsb4eHhYVO+Zs0a+Pv7IyYmBv7+/mhsbJS3de7cGS4uLmhoaAAAaLVaDBgwAK+//jr279+PuXPnymuj+/j44K233sKXX36J48eP49KlS9iwYUP7BCcIHZBIAARBsEtzczOuXr2K5uZmAK3f/BctWoSlS5fivffeg7u7OwYNGoRjx45hx44duHnzJtatWwcAOHDgAABAoVAgMzMTFRUV6NGjB0aPHg0AuHTpEuLj47F161acOHECp0+fBknxOwOC8AgpKCbbCoJghxkzZiArKwsqlQo+Pj6ora2Fq6sr3nzzTXz44YdQKpUwm82YMWMGdDodWlpa8OSTT6Jnz564dOkSzp49CwC4evUqunbtihUrVmDmzJkAgIaGBowePRr79++X/96oUaOQm5vb5lMHQRD+eyIBEATBbhcvXkRBQQEaGhrwxBNPYNiwYQgODrbZr7a2FjU1NYiIiABJlJeX41e/+hUA4IMPPsCyZctw5coVeHl5WX3OYDDAYDAgJCQEQUFB7RKTIHRUIgEQBKHdtLS0ICwsDBMnTsTixYsdXR1B6NDEGABBENrNkSNHcPXqVTG/XxCcgEgABEFoNx4eHkhLS0N0dLSjqyIIHZ54BSAIgiAIHZB4AiAIgiAIHZBIAARBEAShAxIJgCAIgiB0QCIBEARBEIQOSCQAgiAIgtABiQRAEARBEDqg/wO1ZHboLF4nSwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Close previously interactive figures\n", "plt.close()\n", "newparams[\"figure.figsize\"] = (8, 6)\n", "plt.rcParams.update(newparams)\n", "plt.plot(ts, ys, \"--\")\n", "plt.legend([\"S\", \"I\", \"R\"])\n", "plt.xlabel(\"Days\")\n", "plt.ylabel(\"Fraction of population\")" ] }, { "cell_type": "code", "execution_count": 14, "id": "recent-freedom", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "# Fehlberg method\n", "a = np.array(\n", " [\n", " [0.0, 0, 0, 0, 0],\n", " [1 / 2, 0, 0, 0, 0],\n", " [0, 1 / 2, 0, 0, 0],\n", " [0, 0, 1, 0, 0],\n", " [1 / 6, 1 / 3, 1 / 3, 1 / 6, 0],\n", " ]\n", ")\n", "b = np.array([1 / 6, 1 / 3, 1 / 3, 0, 1 / 6])\n", "bhat = np.array([1 / 6, 1 / 3, 1 / 3, 1 / 6, 0])\n", "c = np.array([0.0, 1 / 2, 1 / 2, 1, 1])\n", "p = 3\n", "fehlberg = EmbeddedExplicitRungeKutta(a, b, c, bhat, p)" ] }, { "cell_type": "code", "execution_count": 15, "id": "induced-comment", "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Finishing time-stepping reaching t = 365.0 with final time T = 365\n", "Used 42 steps out of 10000 with 3 being rejected\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, 'Fraction of population')" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Nmax = 10000\n", "tol = 1.0e-5\n", "ts, ys = fehlberg(y0, t0, T, sir, Nmax, tol)\n", "plt.close()\n", "plt.plot(ts, ys, \"-o\", markersize=3)\n", "plt.legend([\"S\", \"I\", \"R\"])\n", "plt.xlabel(\"Days\")\n", "plt.ylabel(\"Fraction of population\")" ] }, { "cell_type": "markdown", "id": "painful-apparel", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Final mentimeter if time permits\n", "\n", "* For $R_0=2$, can you find the turning, i.e. when $I(t)$ starts to decrease? What is percentage of the population that got infected after a year?\n", "* For $R_0=3$, can you find the turning? What is percentage of the population that got infected after a year?" ] }, { "cell_type": "code", "execution_count": 16, "id": "instructional-lightweight", "metadata": {}, "outputs": [], "source": [ "# Close all interactive figures\n", "plt.close(\"all\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 5 }