# Influenza

Our influenza mathematical models explicitly addresses the issue that stockpiles are of finite size and asks: “If there are not enough drugs to treat every patient, what is the best strategy for distribution?” Drugs may shorten the duration of symptoms, and hence the infectious period in individuals. Widespread use of antiviral drugs could therefore slow or reduce infection spread in the community. Figure 1 is an example of a simple model to describe this effect, assuming that only some infected people (a proportion α) receive treatment, to recover more quickly than those who do not. The model has 5 groups of people: S, susceptible; IT, infected and receiving treatment; IN, infected but not receiving treatment; RT, recovered after receiving treatment; RN, recovered having not received treatment. The model has three parameters: b, the transmission rate, gT the recovery rate for treated patients and  gN, the recovery rate for un-treated patients.

The graph in figure 2 shows epidemic curves, predicted by this model, when only 30% of infected people receive drugs (blue curve) and when 70% receive drugs (red curve). Although the latter policy exhausts the stockpile prematurely, fewer people are still infected overall.

Figure 1. A mathematical model of the use of drugs to reduce the impact of influenza epidemic.

Figure 2. Samples time courses from this model showing how aggressive treatment can exhaust the stockpile but still lead to a smaller number of cases overall.