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tom mcandrew
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outbreak_science/chap2.ipynb

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" 4. There are 0 infectors and $\\mathcal{R}_{0}=2.00$\n",
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"\n",
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"\n",
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"9. \n",
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"When we computed conditions for when an the number of expected infectors would increase (i.e. when an outbreak will take place) we used several assumptions: (1) the number of susceptibles is close to $N$, (2) the probability of infection is small. Lets investigate how the conditions for an outbreak would change if we removed assumptions (1) and (2).<br><br> If we remove assumptions (1) and (2) then we can state that our new condition for an outbreak is when the expected number of infectors at time $1$ is larger than the expected number of infectors at time zero, or \n",
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"9. When we computed conditions for when an the number of expected infectors would increase (i.e. when an outbreak will take place) we used several assumptions: (1) the number of susceptibles is close to $N$, (2) the probability of infection is small. Lets investigate how the conditions for an outbreak would change if we removed assumptions (1) and (2).<br><br> If we remove assumptions (1) and (2) then we can state that our new condition for an outbreak is when the expected number of infectors at time $1$ is larger than the expected number of infectors at time zero, or \n",
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"\\begin{align}\n",
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" \\mathbb{E}(I_{1}) = S_{0} \\left[ 1- (1-p)^{i_{0}}\\right] > i_{0}\n",
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"\\end{align}\n",

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