{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "The story of rabbits in Australia, and the resulting eradication efforts, provides a cautionary tale about viruses and immunity. This post will explore the growth of that population and the government's response to it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Captive rabbits were first introduced into Australia in 1788 by the first European settlement - the penal colony at Botany Bay. The early settlers brought only five rabbits with them to Australia. The rabbits were kept for food and bred but never released into the wild. More rabbits subsequently arrived as settlements dotted the Australian landscape. They spread around Tasmania (then known as Van Diemen’s Land) but were mostly controlled on the mainland and didn’t spread into the wild.\n", "The settlers were able to keep the rabbit population in captivity and under control for over half a century, until one thing happened - they got bored. They wanted to hunt rabbits like they did in England and so, in 1859, they released 24 rabbits into the wild. From there the population grew, like, well, rabbits.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To simulate the population, we'll need an equation for population growth. The population will change by the growth factor, which is the difference in the birth and death rates, times the population size. Mathematically, this would be written as:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\dfrac{\\mathrm{d}P}{\\mathrm{d}t} = P*(b-d)$$\n", "\n", "where\n", "\n", "* $\\dfrac{\\mathrm{d}P}{\\mathrm{d}t}$ - change in population\n", "* $P$ - population\n", "* $b$ - birth rate\n", "* $d$ - death rate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The birth and death rates are usually combined into a single factor, the growth rate $r$, where $r=b-d$. We can plug this in and integrate the differential equation to give us the standard equation for exponential population growth:\n", "\n", "$$P(t) = Pe^{rt}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This equation works well enough in the beginning, but it misses an important component - carrying capacity. Carrying capacity refers to the maximum population that the land can contain. There are limited amounts of food and shelter for the rabbits to survive, so at some point they must reach capacity. We have to add a \"carrying capacity factor\" to the differential equation.\n", "\n", "However, this doesn't allow us enough precision. For example, rabbits don't reach sexual maturity until 17 weeks - how do we factor that in? We'll have to distinguish the sexually mature population from the rest." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\dfrac{\\mathrm{d}P}{\\mathrm{d}t} =P_m * (b-d) * (1 - P_{tot}/K)$$\n", "\n", "where\n", "\n", "* $\\dfrac{\\mathrm{d}P}{\\mathrm{d}t}$ - change in population\n", "* $P_m$ - sexually mature population\n", "* $b$ - birth rate\n", "* $d$ - death rate\n", "* $P_{tot}$ - total population\n", "* $K$ - carrying capacity" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Now we have to start pluggin in the numbers. Rabbits have a gestation period of about four weeks, and each new litter of rabbits contains four baby bunnies. And there's no relaxing, right after giving birth they can start the process again. So if it takes two rabbits four weeks to make four baby rabbits, that’s a growth rate of about .5 rabbits per week for each rabbit. Rabbits in the wild live an average of roughly a year, so we'll give them a death rate of .02.\n", "\n", "Let's simulate the population growth for the first year." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "import math\n", "from IPython.core.debugger import set_trace" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Rabbit facts\n", "time_to_sexual_maturity = 17 #weeks\n", "birth_rate = .5 # the growth rate is 4 babys /2 parents /4 weeks = .5\n", "death_rate =.02 # lifespan is about a year, so we'll say 50 weeks\n", "# birth_rate contains those with immunity, death rate doesn't" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Build a function to spread the disease\n", "def spread_myxo(infected, immune, total, infection_rate): #infected is the number of infected rabbits, total is the total population\n", " \"\"\"This function return the number of newly infected rabbits\"\"\"\n", " susceptible = total - immune - infected\n", " percent_infected = infected / total\n", " new_infections = round(susceptible * (2/(1+math.exp(-infection_rate*percent_infected)) - 1))\n", " return new_infections" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def project_population(num_weeks, week_myxo_released=float(\"inf\"), rabbit_population=None, infected=None, \\\n", " immune=None, carrying_capacity=600000000, num_myxo_released = 5000, chance_of_mutation_immunity=0, \\\n", " myxo_inhereted_immunity = 0, infection_rate=.5, inf_capacity_factor=0, resist_capacity_factor=0, \\\n", " extermination_week=float(\"inf\"), extermination_number=0):\n", " \"\"\"This function shows the population change over time. It functions with and without the viral or immunity information\"\"\"\n", " \n", " # If no initial values are given, initiate them as empty\n", " if rabbit_population == None:\n", " rabbit_population = np.zeros(num_weeks)\n", " rabbit_population[0] = 24\n", " if infected == None:\n", " infected = np.zeros(num_weeks)\n", " if immune == None:\n", " immune = np.zeros(num_weeks)\n", " # Initialize other values to 0\n", " new_infections = 0\n", " newly_infected = np.zeros(num_weeks)\n", " infected_1_week_ago_remaining = np.zeros(num_weeks)\n", " infected_2_week_ago_remaining = np.zeros(num_weeks)\n", " deaths_from_infection = 0\n", "\n", " # The death rate will affect many things, so we'll need to find the fraction that remain\n", " assert (0 <= death_rate <= 1), \"Death rate should be between 0 and 1\"\n", " percent_remaining = 1 - death_rate\n", " \n", " # Iterate over each week, starting at 1\n", " for x in range(1, num_weeks):\n", " \n", " # Check that the rabbit population is still viable\n", " if rabbit_population[x-1] < 2:\n", " print(\"Rabbits have been removed\")\n", " #set_trace()\n", " break\n", " \n", " # Determine the number of sexually mature rabbits in the given week\n", " if x < 17:\n", " sexually_mature_population = 24\n", " else:\n", " # The sexually mature population is at most the population of 17 weeks ago, but could be less\n", " # This gives us reasonable value for growing, shrinking, and changing population\n", " sexually_mature_population = rabbit_population[x-1] * min(rabbit_population[x-17:x]) / max(rabbit_population[x-17:x])\n", " \n", " new_births = round(sexually_mature_population * birth_rate)\n", " \n", " percent_immune = immune[x-1]/rabbit_population[x-1]\n", " \n", " # if either parent has immunity, the newborn might inherit immunity\n", " inhereted_immunity = round(new_births * percent_immune * myxo_inhereted_immunity)\n", " \n", " # Rabbits without immune parents may have it through mutation, much less likely though\n", " mutation_immunity = round(new_births * (1 - percent_immune) * chance_of_mutation_immunity)\n", " \n", " # Then factor in normal death rate\n", " # We'll also need to factor in deaths into the infect and immune populations\n", " draft_population = round(rabbit_population[x-1] * percent_remaining + new_births)\n", " draft_infected = round(infected[x-1] * percent_remaining)\n", " draft_immune = round(immune[x-1] * percent_remaining + inhereted_immunity + mutation_immunity)\n", " \n", " # Now let's see how the infection spreads\n", " # Check if the myxo virus has been released\n", " if x == week_myxo_released:\n", " newly_infected[x] = num_myxo_released\n", " elif x > week_myxo_released:\n", " \n", " # Advance each stage of myxo by one week\n", " deaths_from_infection = round(infected_2_week_ago_remaining[x-1] * percent_remaining)\n", " draft_infected_2_week_ago_remaining = round(infected_1_week_ago_remaining[x-1] * percent_remaining)\n", " draft_infected_1_week_ago_remaining = round(newly_infected[x-1] * percent_remaining)\n", " infected_remaining = round(infected[x-1] * percent_remaining)\n", " # Check that there aren't more infected than total (can happen due to rounding)\n", " if infected_remaining > draft_population:\n", " infected_remaining = draft_population\n", " \n", " # We'll assume those about to die can still spread infection\n", " new_infections = round(spread_myxo(infected_remaining, draft_immune, draft_population, \\\n", " infection_rate)) \n", " \n", " # Now remove those dying from the population\n", " if draft_population > deaths_from_infection:\n", " second_draft_population = draft_population - deaths_from_infection\n", " else:\n", " second_draft_population = 1 # To avoid div by zero\n", " \n", " # Now we see how many die due to being near carrying capacity \n", " overcapacity_deaths = round(second_draft_population * (second_draft_population/carrying_capacity) * \\\n", " (birth_rate-death_rate))\n", " \n", " # Calculate the percentage of the population remaining\n", " # e.g. if 20% of the population died, the overcapacity_deaths_factor is .8\n", " overcapacity_deaths_remaining = 1 - overcapacity_deaths / second_draft_population\n", "\n", " # We'll subtract the overcapacity deaths from each field\n", " # In the population case, this is equal to rabbit_population[x] = draft_rabbit_population - overcapacity_deaths\n", " rabbit_population[x] = round(second_draft_population * overcapacity_deaths_remaining)\n", " if x > week_myxo_released:\n", " infected_2_week_ago_remaining[x] = round(draft_infected_2_week_ago_remaining * overcapacity_deaths_remaining)\n", " infected_1_week_ago_remaining[x] = round(draft_infected_1_week_ago_remaining * overcapacity_deaths_remaining)\n", " newly_infected[x] = round(new_infections * overcapacity_deaths_remaining)\n", " immune[x] = round(draft_immune * overcapacity_deaths_remaining)\n", " \n", " infected[x] = newly_infected[x] + infected_1_week_ago_remaining[x] + infected_2_week_ago_remaining[x]\n", " \n", " # Check for human-cause extermination\n", " if x == extermination_week:\n", " rabbit_population[x] -= extermination_number\n", " \n", " # Check for errors or incorrect values\n", " \n", " if new_infections < 0:\n", " set_trace()\n", " \n", " if rabbit_population[x] <= 0:\n", " #set_trace()\n", " print(\"Rabbit population less than or equal to 0\")\n", " rabbit_population[x] = 1 # To avoid div by zero\n", " \n", " if immune[x] > rabbit_population[x]:\n", " print(\"too many immune\")\n", " set_trace()\n", " immune[x] = rabbit_population[x]\n", " infected_1_week_ago_remaining = 0\n", " newly_infected[x]=0\n", " if immune[x] < 0:\n", " print(\"immune less than zero\")\n", " set_trace()\n", " immune[x] = 0\n", " \n", " if newly_infected[x] < 0:\n", " set_trace()\n", " newly_infected[x] = 0\n", "\n", " if newly_infected[x] > rabbit_population[x] - immune[x]:\n", " set_trace()\n", " newly_infected[x] = rabbit_population[x] - immune[x]\n", " \n", " return rabbit_population, infected, immune" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_rabbits(rabbit_population, infected = None, immune = None, title=\"Rabbit growth in Australia\"):\n", " \"\"\"This function plots the rabbit population. It will also plot the infected and immune populations\"\"\"\n", " x = np.arange(len(rabbit_population))\n", " fig, ax = plt.subplots()\n", " fig.set_size_inches(10,10)\n", " matplotlib.rcParams.update({'font.size': 18})\n", " ax.fill_between(x, 0, rabbit_population, color='g')\n", " #ax.fill_between(x, 0, infected, color='r')\n", " if immune is not None:\n", " ax.fill_between(x, 0, immune, color='b')\n", " if infected is not None:\n", " ax.fill_between(x, 0, infected, color='r')\n", " ax.set_title(title)\n", " ax.set_xlabel(\"Weeks after first rabbits introduced\")\n", " ax.set_ylabel(\"Number of rabbits\")\n", " if infected is not None and immune is not None:\n", " ax.legend((\"Total rabbits\", \"Immune rabbits\", \"Infected rabbits\"), loc='upper left')\n", " elif infected is not None:\n", " ax.legend((\"Total rabbits\", \"Infected rabbits\"), loc='upper left')\n", " else:\n", " ax.legend((\"Total rabbits\",), loc='upper left') # Trailing comma request to print entire label.\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rabbit_population, infected, immune = project_population(52)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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rZAQ3AABQ0MYtG6eORR2jLiMlBDcAAFDQRpaOzOkLyycjuAEAgII2YtEIuTzq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\nP/i81tavVWemM7zWWnQ2aD7Ix1whACQbwQ3AjKX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rabbits(rabbit_population)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5000 rabbits. That’s a lot, but it’s manageable. But herein lies the problem with exponential growth. You may have a manageable number after a year, but after a second year you have:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rabbit_population, infected, immune = project_population(104)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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BdwP3lBI5gJTSSuAKYE/g4LJTPgQE8NNOTf0KWA2cWKNtS5Ik9Vp7RztLm5cW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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rabbits(rabbit_population)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Half a million rabbits! It’s a classic example of unintended consequences. And given the expanse of the Australian landscape, the limit to the number of rabbits is huge. Based on population estimates, the maximum population for rabbits in a huge country like Australia is in the hundreds of millions (remember, the human population is only 24 million). Based on the exponential growth of rabbits, they would near this number in only four years. Due to the additional time it would take to spread proportionally throughout the country, it probably took a bit longer than that. Either way, it was the fastest spread ever recorded of any mammal anywhere in the world." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rabbit_population, infected, immune = project_population(520)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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OvGhsbGT48OHrDVIpLS1lzz335Mknn8y4fyWa1o5WZiyZwetVrzOtYhpvLXmL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\nQd2OaAPH5DVRRHwDOA64ALgYOAL4IDAXeElKabjE8NpWRCR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ULL+K/Lcwh9zLd0tKaWPN\n8kXkD/bpo/Sy1bqfnED92Tjq1vpJEcePgQsj4rX1pzJTnobiiuJBceXfDeTB5q/dxbpfSv7v/59S\nSmfULohxXCFZG8Io5bu7z6Upen5+VjyIPNnuN4B/Zscpu702xUjN6bgfpJTeV7fsFbt46RHkXqda\nTy6e63vCjmiw3UeRL/Bo1GtWa5f7mlJaT+5tPqPowfsqeTLq1wAXjLHuPbW77bAYODoiHpSKCxZq\nPJl88dDGmrpzImL/2t68iNiH3CO4enswKQ1FxGYa9zbW95jeT/7MeeYYsU7kM2Y1+TPs8AbLntyg\nTB2sJf9zlPamlFIfOdF7DvlL6dr0wHnVFpB7Vf6dBvPjpZTuB34D/H1EHFm//sgOLuoOku/I8PyI\n+LtG8UTEn48S55nkHqWjgF/XjCFklNOyt5MH+Y91amukx+QBvSMR8UryMRmvkS+/B2xvT/a5DKMc\nyz8Wz7X7tpWJnTbcldHa4FDylc+j+UjtaeSIeDT5CtrbUkr1VyM/JSJeU1c2MnH0L8aIr2HbRp4u\n5IDaspRSYsfpx711fMaKbXeGFPyC/M/bx2oLI+JvgKcBvyz2BfKV1tOBD9et4wPkz4R6dwMvKJLA\nkfUeSL4Ty3bFP2Znk8c0vp06I6e8d+Mz5tfA8+KBUyAF+TNM2s6ePHWKK8jJ0/PJU2hsl1JKETGX\nPPh6pG69fyGfYrs68nxUN5P/fh5bvO508hWRkMd8PR/4eUScC8wjjwF7DPmU1zzy6a6dpJTOiYgB\n8hfDxRHxqqJn4YdFonQZsIx8Je5bi+ex7sjwe/K4nq8XpylXkqeHeBs5wd2pB2gU84rnr0bEWeQE\nc35K6fY92ecS3F209/XkKVIOAd5D3p9za+rNA94eEf9JnrJjmJwYTPhikZTSpoi4vFhfH3AT+UrZ\nfyUPrJ89yktnkueuO5s8tuu95HkfP9Sg7nzg7Ij4XrHOF5PnHrycosdyF66nuLq0SCa2sWPA/70R\ncSE5sVtD7q16L/mK4MmYsmMe8IqI+Gbx8xD5quex7kZzOnnql09HxOPIQxaeRL6S9j52zPsIeQqX\nd5OHPzyefLHWc8jHr9GYvG+Rp5T5XUScSU5C31PUrf+HZmQKpx8WvbZ/IHewjMzB947ieSKfMZ8i\nX4hxcXFcVpJ78w8c45io05R9ea8PH5PxII87G5lm4kUNlh9fLBsEDhhlHQeTr+K7m5wQbCR/sZ4M\nHF5Xdz9yMrmAfGplC3lg/PeAI2vqNZy6gjznVR95fq0Hkedeu4g8rUcf+cv2CuB149z/Z5DHzI1c\neHEF+dT0T4HBurq7mirlk+QvsgF2nhpjj/Z5HPsw0SlURpt241PkL/y15OlqlpPHyz2zrt7DgfOL\ndh4e7ZjU1N9pupAG758fkBOMnuK9865Gx6OmDQ4nT4NyP3nIwTzgxXXr3T6lB3mc4fXF+leTT0Hv\nV1d/tPfcO8mD+ftr1jeTfIXuDeTe7pELEU4DHj+ONtvVFCo7HadG7z3y6eYfFu/5kXZ44VjtXPPa\n/y5i7i+O44+pmbqlpu5BxXY2kJPc35ETsUbvryD/Y3Nvsd7byb14ox3bh5DHq95D/vtdR/7n6w17\n8BnzDPJt6LqLmM8gT4vkFCo+tj8ipb027ESSJEktwjF5kiRJFWSSJ0mSVEEmeZIkSRVkkidJklRB\nJnmSJEkVZJInSZJUQSZ5kiRJFWSSJ0mSVEEmeZIkSRVkkidJklRB/x+Qmf8ReXEWcgAAAABJRU5E\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rabbits(rabbit_population, title=\"A Decade of Rabbits in Australia\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously, hundreds of millions additional animals competing with native wildlife for food and water has a devastating impact. The vast amount of plant life they consume not only decimates the native plant life, but that in turn causes erosion, which leads to nutrient-poor soil, thus increasing the damage. It wasn’t long before the Australian government determined that rabbits were causing significant economic damage. In 1887, the government of New South Wales started soliciting methods for removing them.\n", "\n", "The most obvious method - hunt them, isn’t actually very effective. There were efforts to shoot, trap, and poison them. The efforts were expensive, but ultimately had little impact against the robust rabbit population. To get an idea of the futility, imagine launching a tremendous rabbit hunting, trapping, and poisoning campaign that is so incredible effective that it causes the death of 50 million rabbits in a single week. But the moment that expensive campaign is stopped, which would come eventually, the population just regrows. Here’s a simulation of 50 million rabbits being killed in week 250. As you can see, within a year the population has recovered." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rabbit_population, infected, immune = project_population(302, extermination_week=250, extermination_number=50000000)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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wuVRiJT3qc9bbLNq4iBMfOpHNDZuJe3H1R1SSJyIikmFT10zlz2//mecXPk+p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\n101PXw9dfV1093UfTLa6ervo7O2kraeNtq422rrb2N+9n7b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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rabbits(rabbit_population)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But in the 1950’s, after decades and decades of ineffective techniques, the Australian Government tried something different - biological warfare. Viruses are incredibly effective at population control because after the target is infected, it finds new victims automatically, and the virus spreads by itself. The trouble is, how can you find a virus that’s safe to release in the wild but will not wreak havoc on the ecosystem?\n", "\n", "The myxoma virus seemed like a perfect candidate. It causes myxomatosis, a deadly disease specifically targeted towards rabbits. Although myxoma infects several mammals, from rabbits and mice to humans, it can only replicate in the cells of rabbits. Without the ability to replicate in the cells, as in the case of humans, it never causes myxomatosis and is harmless. On top of that, myxoma virus spreads easily and kills rabbits within two weeks (depending on the species).\n", "\n", "After some initial trials, the technique was approved and released into the rabbit population. The rabbit population quickly cut in half, then in half again. The disease continued to spread and kill more and more rabbits. Based on the deadly efficacy of myxomatosis, the rabbit population should have been completely wiped out.\n", "\n", "Assuming each rabbits spreads the disease to two others, this is the simulation for how it should have gone after releasing myxoma in week 250." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rabbits have been removed\n" ] } ], "source": [ "rabbit_population, infected, immune = project_population(350, week_myxo_released=250, infection_rate=2)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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lhQlpEyeerPQsenTuwaeXfsqAnQY0vIP4xsxmOOcOb2g7leQlgBIqEZHEW75l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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rabbits(rabbit_population, infected)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But that's not what happened. The problem is, in any large population, there’s likely to be some members that, through chance genetic mutation, have a natural resistance. This is true for nearly all diseases. Some people were naturally immune to the Black Death that killed half of all Europeans in the 14th century. Even HIV has a rival in people born with a mutation known as Delta32.\n", "\n", "Myxoma was terribly effective on rabbits, but even if we assume efficacy against 99.99% of the population, there are still some with immunity. And once all the susceptible rabbits die, those with immunity breed and pass on their immunity to their progeny. Here's a simulation with the same virality as before, but giving 0.01% of the population immunity, and assuming that immunity passes on to the next generation 99% of the time." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rabbit_population, infected, immune = project_population(1800, week_myxo_released=400, infection_rate=2, chance_of_mutation_immunity=0.0001, \\\n", " myxo_inhereted_immunity = .99)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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IWq+LLroIgEmTJnHjjTeSmJhI9+7dSU9P5/rrr2fIkCF07tyZ0047jd9++405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OulIpN2dmV8r20ea2jjcG5OuEZGEpiSZ/DyJy/bTF7CrNwMtX0UaTs1DMN2PRsG+Fm46j4u1zZR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\n09Wzx0k6s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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rabbits(rabbit_population, infected, immune)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Although the virus has a large impact initially, every time the virus starts to take hold the immune rabbits, with no more competition from all those who died, spread across the land and themselves number in over 100 million. And so, the myoma virus experiment ended, leaving Australia with a large population of mutant, disease-resistant rabbits." ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }