The effect of awareness on networked SIS epidemics

We study an SIS epidemic model over an arbitrary fixed network topology where the n agents, or nodes of the network, have partial information about the epidemic state. The agents react by distancing themselves from their neighbors when they believe the epidemic is currently prevalent. An agent's awareness is weighted from three sources of information: the fraction of infected neighbors in their contact network, their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time 2ⁿ-state Markov chains. Through a coupling technique, we establish monotonicity properties between the benchmark and awareness models. Particularly, we show that the expectation of any increasing random variable on the space of sample paths, e.g. eradication time or total infections, is lower for the awareness model. In addition, we give a characterization for this difference of expectations in terms of the coupling distribution. In simulations, we evaluate how different sources of information affect the spread of an epidemic.