Year of Graduation
Optimal Control Problems for the Stochastic Model of Virus Spread in Networks
We study the stochastic continuous-time model for spreading of virus that belongs to the class of SIS (Susceptible-Infected- Susceptible) models. We assume that all infection and curing rates are equal. It is investigated a problem where damages of virus and costs of “cure” must be minimized. The optimal controller is considered as curing rate of infected node. It is assumed that optimal controller is bounded. Using Pontryagin’s maximum principle, the optimal conditions are derived. It is shown that optimal controller outputs only boundary values (bang-bang control). This result is studied on networks with different topology (“Cycle”, “Star”, and bipartite graph). Based on the analysis of numerical result it is shown that the optimal controller contains singular arcs.