Discrete-Time Sequential Persuasive Game for Containing SIS Epidemic Propagation

Containing the spread of infectious diseases is a challenging problem, both for central authorities as well as individuals, especially when the infected individuals are asymptomatic, and the decisions need to be made under incomplete information and strategic uncertainty. In this paper, we consider the susceptible-infected-susceptible (SIS) epidemic model, where a large population of individuals decide whether to adopt partially effective protection without being aware of their exact infection status. Instead, they receive noisy signals from a strategic sender that convey incomplete information regarding their infection state in the form of action recommendations. These recommendation signals are strategically designed so that it is optimal for the receivers to follow their recommended actions, and the infected proportion at the next time-step is minimized. When the sender has accurate information about the receivers' states, we obtain analytical (closed-form) solutions of the optimal signals under suitable assumptions by exploiting the monotonicity of the cost function in the action recommendations. Finally, we consider the case when the sender is not omniscient, and show that there may not exist any action recommendation that strategic followers are guaranteed to follow. We validate the proposed framework via numerical simulations, and illustrate that disclosing true infection status to the receivers is not always the optimal choice, instead, strategic action recommendations can lead to a smaller infection prevalence. We also show that when the sender is not omniscient, the infected proportion and the strategies adopted by the receivers may not converge to a steady-state.