Epidemic models in well-mixed multiplex networks with distributed time delay

Abstract

In this paper, we consider an epidemic model in well-mixed multiplex networks with distributed time delay. Specifically, the model consists of two layers of well-mixed networks in the physical and virtual worlds, respectively, where two diffusive processes interact and influence each other within the same individual. We assume that there is a distributed time delay for an individual to become infected, but no delay for an individual to transition from unawareness to awareness. Our main results are as follows: Let R0P and R0V represent the basic reproduction numbers in the physical and virtual worlds, respectively. First, we demonstrate that the disease will die out for any delay time, provided that R0P≤1 or 1<R0P≤R0V. The latter condition emphasizes the significance of effective information spreading in eradicating the disease. Secondly, in the case of R0P>max⁡{1,R0V}, we establish that the model exhibits an endemic and information saturated equilibrium, denoted as E3. Additionally, we show that the model is uniformly persistent, indicating the sustained outbreak of the disease.