Competing control scenarios in probabilistic SIR epidemics on social-contact networks.

A probabilistic approach to the epidemic evolution on realistic social-contact networks allows for characteristic differences among subjects, including the individual number and structure of social contacts, and the heterogeneity of the infection and recovery rates according to age or medical preconditions. Within our probabilistic Susceptible-Infectious-Removed (SIR) model on social-contact networks, we evaluate the infection load or activation margin of various control scenarios; by confinement, by vaccination, and by their combination. We compare the epidemic burden for subpopulations that apply competing or cooperative control strategies. The simulation experiments are conducted on randomized social-contact graphs that are designed to exhibit realistic person-person contact characteristics and which follow near homogeneous or block-localized subpopulation spreading. The scalarization method is used for the multi-objective optimization problem in which both the infection load is minimized and the extent to which each subpopulation's control strategy preference ranking is adhered to is maximized. We obtain the compounded payoff matrices for two subpopulations that impose contrasting control strategies, each according to their proper ranked control strategy preferences. The Nash equilibria, according to each subpopulation's compounded objective, and according to their proper ranking intensity, are discussed. Finally, the interaction effects of the control strategies are discussed and related to the type of spreading of the two subpopulations.