Optimal control of the treatment and the vaccination in an epidemic switched system using polynomial approach

We study the problem of optimal switching on a treatment-vaccination model with four switches. These switches provide a more realistic approach when dealing with the control of an epidemic. We have used a relatively new approach to investigate optimal switching. The main idea behind this approach is to convert the switched system, a nonlinear, nonconvex optimal control problem, into an equivalent optimal control problem with a linear and convex structure. This allows us to obtain an equivalent convex formulation better suited to being solved by high-performance numerical computing. Toward the end, we perform some numerical simulations and draw the conclusion that the presence of treatment is essential, whereas vaccination control can be used at intervals with progressively larger gaps between the intervals.