The analysis of discrete-time epidemic model on networks with protective measures on game theory

Protective measures such as wearing mask, quarantine, hand washing and so on can prevent and control the spread of infectious diseases. In this paper, a discrete-time model on networks combines infectious diseases and protective measures is proposed. Protective measures include voluntary protective measures of susceptible individuals and compulsory protective measures of infected individuals. The epidemic threshold is obtained and the time series of optimal control probability of infected individuals are analyzed by optimal control theory. The results of optimal control are compared with other constant control and the influences of protective measures on infectious diseases are analyzed by simulations. The optimal control results indicate that the greater the control proportion of infected individuals, the greater the average social payoff. It is shown that increasing the effectiveness of protective measures could effectively control the spread of infectious diseases.