Interior Point Methods for a Two-Group Discrete Time Influenza Model

We formulate a discrete time model to identify and evaluate the role of optimal control strategies on influenza transmission. We divide the population in two subgroups defined according to the contact activity or susceptibility levels. The individuals are identified as susceptible, infectious, treated, and recovered. The potential effect of antiviral treatment considering unlimited and limited resources is evaluated, where an isoperimetric constraint is incorporated in the presence of limited resources. The optimal control problem is solved by using the primal-dual interior-point method that enforces epidemiological constraints explicitly. Our goal is to determine how treatment doses should be distributed in each group when the objective is to minimize the number of infected and the cost of treatment.