Optimal Control for a Discrete Time Influenza Model

We formulated a discrete time model in order to study optimal control strategies for single influenza outbreak. In our model, we divided the population into four classes: susceptible, infectious, treated, and recovered individuals. The total population was divided into subgroups according to activity or susceptibility levels. The goal was to determine how treatment doses should be distributed in each group in order to reduce the final epidemic size. The case of limited resources is considered by including an isoperimetric constraint. We found that the use of antiviral treatment resulted in reductions in the cumulative number of infected individuals. We proposed to solve the problem by using the primal-dual interior-point method that enforces epidemiological constraints explicitly.