Epidemic spread over networks with agent awareness and social distancing

We study an SIS epidemic model over an arbitrary connected network topology when the agents receive personalized information about the current epidemic state. The agents utilize their available information to either reduce interactions with their neighbors (social distancing) when they believe the epidemic is currently prevalent or resume normal interactions when they believe there is low risk of becoming infected. The information is a weighted combination of three sources: 1) the average states of nodes in contact neighborhoods 2) the average states of nodes in an information network 3) a global broadcast of the average epidemic state of the network. A 2n-state Markov Chain is first considered to model the disease dynamics with awareness, from which a mean-field discrete-time n-state dynamical system is derived, where each state corresponds to an agent's probability of being infected. The nonlinear model is a lower bound of its linearized version about the origin. Hence, global stability of the origin (the diseasefree equilibrium) in the linear model implies global stability in the nonlinear model. When the origin is not stable, we show the existence of a nontrivial fixed point in the awareness model, which obeys a strict partial order in relation to the nontrivial fixed point of the dynamics without distancing. In simulations, we define two performance metrics to understand the effectiveness agent awareness has in reducing the spread of an epidemic.