Optimal control and differential game solutions for social distancing in response to epidemics of infectious diseases on networks.

In this paper, the problem of social distancing in the spread of infectious diseases in the human network is extended by optimal control and differential game approaches. Hear, SEAIR model on simulation network is used. Total costs for both approaches are formulated as objective functions. SEAIR dynamics for group that contacts with individuals including susceptible, exposed, asymptomatically infected, symptomatically infected and improved or safe individuals is modeled. A novel random model including the concept of social distancing and relative risk of infection using Markov process is proposed. For each group, an aggregate investment is derived and computed using adjoint equations and maximum principle. Results show that for each group, investments in the differential game are less than investments in an optimal control approach. Although individuals' participation in investment for social distancing causes to reduce the epidemic cost, the epidemic cost according to the second approach is too much less than the first approach.