Competition between awareness and epidemic spreading in homogeneous networks with demography

Although a major effort has been made in the study of the coupled dynamics of disease and awareness spreading on multiplex networks, the full understanding of their dynamical interactions is still lacking. To address this issue, in this paper we investigate a simple model for the competition between disease and awareness processes in a homogeneous network with natural birth and death processes. We show that the natural death process has no impact on the competiting dynamics between the epidemic and awareness spreading processes, while the birth process exerts siginificant impacts on the model dynamical behavior. In particular, there exists a threshold value of the population birth rate that distinguishes the model dynamics from a simple susceptible-infected-susceptible (SIS) dynamics to a nontrivial, intriguing competing dynamics between awareness and epidemic spreading. When the population birth rate is above the birth threshold, the pahse diagram of our model resembles that of the standard SIS model. That is, the system is always awareness-free, stabilizing at either a fully susceptible state (where neither epidemic nor awareness existes) or an awareness-free epidemic state (where awareness vanishes). However, when the population birth rate is below the birth thrshold, there emerges a tricritical point defined as a critical value of the awareness efficacy. When the awareness efficacy is below the tricritical point, there are two contiuous phase transitions, segregating an epidemic-free aware state (where epidemic vanishes) from an awareness-free epidemic state, with an intermediate hybrid state (where susceptible,infected, and aware individuals coexist in the population) interpolating between them. As the awareness efficacy reaches the tricritical point, the two continuous transitions disappear while a discontinuous transition emerges from the epidemic-free aware state to the awareness-free epidemic state. When the awareness efficacy exceeds the tricritical point, the discontinuous transition split into two discontinuous ones, leading to a bistability regime where both the epidemic-free aware state and the awareness-free epidemic state are stable. The rich dynamics in our model highlights the intriguing competition between the awareness and epidemic spreading processes as well as its dependence on demographic changes. Our analytical results are supported by extensive stochastic simulations of the model on homogeneous random networks.