James Moore-Stanley edited section_Theory_of_the_SIR__.tex  almost 8 years ago

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\item Every individual that is infected has equal probability of encountering an individual that is susceptible per unit time.   \end{enumerate}  These assumptions will obviously limit the practical usages of the model, as the model's outcomes would not represent results in a real world environment. However, the model may be adapted in order to incorporate dimensions from a real world scenario, such as that of Yellow Fever in Angola. In order to adapt the model to fit the situation, understand of the underlying, or basic model is required. This will be explained below. As stated above, individuals may be in one of three categories. The equations below show the number of people in each of the three categories as a function of time. As to be discovered, it is easier to assign fractions of the population to each of the classes, not the real values. This means that all values for $S$, $I$ and $R$ as functions of time are divided by $N$, the value of the total population.   \begin{gather} \begin{gather*}  S = \frac{S(t)}{N} \\  I = \frac{I(t)}{N} \\  R = \frac{R(t)}{N} \\  \end{gather} \end{gather*}