197 lines
148 KiB
Plaintext
197 lines
148 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"import matplotlib.pyplot as plt\n",
|
|
"import numpy as np\n",
|
|
"\n",
|
|
"from random import random\n",
|
|
"from math import log"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"eta = 1\n",
|
|
"beta = 10 #Try beta=50 also.\n",
|
|
"delta = 1 \n",
|
|
"dt = .005\n",
|
|
"\n",
|
|
"t = np.linspace(0,100,int(100 / dt))\n",
|
|
"B = np.zeros_like(t)\n",
|
|
"P = np.zeros_like(t)\n",
|
|
"\n",
|
|
"B[0] = .01\n",
|
|
"P[0] = .000001\n",
|
|
"for i in range (0, int(100 / dt) - 1):\n",
|
|
" B[i+1] = B[i] + dt * (B[i] * (1 - B[i]) - eta * B[i] * P[i])\n",
|
|
" P[i+1] = P[i] + dt * (beta * eta * B[i] * P[i] - delta * P[i])\n",
|
|
"\n",
|
|
"plt.title(\"Without resistant\")\n",
|
|
"plt.plot(t, B, label=\"Bacteria\")\n",
|
|
"plt.plot(t, P, label=\"Phage\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"eta = 1\n",
|
|
"beta = 10 #Try beta=50 also.\n",
|
|
"delta = 1 \n",
|
|
"dt = .005\n",
|
|
"g = 0.8\n",
|
|
"alpha = 0.2\n",
|
|
"\n",
|
|
"t = np.linspace(0,1000,int(1000 / dt))\n",
|
|
"B = np.zeros_like(t)\n",
|
|
"P = np.zeros_like(t)\n",
|
|
"R = np.zeros_like(t)\n",
|
|
"\n",
|
|
"B[0] = .01\n",
|
|
"P[0] = .000001\n",
|
|
"R[0] = .01\n",
|
|
"\n",
|
|
"for i in range (0, int(1000 / dt) - 1):\n",
|
|
" B[i+1] = B[i] + dt * (B[i] * (1 - (B[i] + R[i])) - alpha * B[i] - B[i] * eta * P[i])\n",
|
|
" R[i+1] = R[i] + dt * (g * R[i] * (1 - (B[i] + R[i])) - alpha * R[i])\n",
|
|
" P[i+1] = P[i] + dt * (beta * B[i] * eta * P[i] - delta * P[i])\n",
|
|
"\n",
|
|
"\n",
|
|
"plt.title(\"With resistant\")\n",
|
|
"plt.plot(t, B, label=\"Bacteria\")\n",
|
|
"plt.plot(t, R, label=\"Resistant Bacteria\")\n",
|
|
"plt.plot(t, P, label=\"Phage\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 115,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# 12.3.3\n",
|
|
"\n",
|
|
"Omega = 2\n",
|
|
"omega = 1e-3 \n",
|
|
"p = .1\n",
|
|
"x1 = .01\n",
|
|
"x2 = .9\n",
|
|
"xstar = p * Omega / (Omega - 1) - (1-p) * omega / (omega - 1)\n",
|
|
"if xstar > 1:\n",
|
|
" xstar = 1\n",
|
|
"elif xstar < 0:\n",
|
|
" xstar = 0\n",
|
|
"\n",
|
|
"steps = 500\n",
|
|
"\n",
|
|
"Lambda1 = np.zeros(steps)\n",
|
|
"Lambda2 = np.zeros(steps)\n",
|
|
"Lambdastar = np.zeros(steps)\n",
|
|
"\n",
|
|
"\n",
|
|
"for i in range (0, steps - 1):\n",
|
|
" if random() < p:\n",
|
|
" Lambda1[i+1] = Lambda1[i] + log(omega * (1-x1) + x1)\n",
|
|
" Lambda2[i+1] = Lambda2[i] + log(omega * (1-x2) + x2)\n",
|
|
" Lambdastar[i+1] = Lambdastar[i] + log(omega * (1-xstar) + xstar)\n",
|
|
"\n",
|
|
" else:\n",
|
|
" Lambda1[i+1] = Lambda1[i] + log(Omega * (1-x1) + x1)\n",
|
|
" Lambda2[i+1] = Lambda2[i] + log(Omega * (1-x2) + x2) \n",
|
|
" Lambdastar[i+1] = Lambdastar[i] + log(Omega * (1-xstar) + xstar)\n",
|
|
"\n",
|
|
"\n",
|
|
"plt.title(\"Bet Hedging\")\n",
|
|
"plt.plot(Lambda1, label=\"x = 0.01\")\n",
|
|
"plt.plot(Lambda2, label=\"x = 0.9\")\n",
|
|
"plt.plot(Lambdastar, label=f\"x* = {round(xstar,2)}\")\n",
|
|
"plt.ylabel(\"log(Population)\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "venv",
|
|
"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": "3.8.10"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|