Optimal control of SIR epidemic model with state dependent switching cost index

The problem of epidemic control has to face with the resources allocation; a change in the strategy should be advisable during the epidemic spread in view of a rational use of the limited resources. The SIR epidemic model, which describes the dynamics of Susceptible, Infected and Removed subjects, is considered and an optimal vaccination strategy is proposed by introducing a cost index that weights differently the control depending on the severity of the disease. The introduced weight is a step-wise one and the switching instants are not known in advance. The meaningfulness of this approach has been tested and compared with the case of a constant weight for the control, showing a more efficient resource allocation in the proposed approach.