Epidemical dynamics of SIS pair approximation models on regular and random networks

One useful method to characterize the spread of infectious diseases on networks is using the pair approximation models. However, there is no theoretical study in view of dynamical behaviors of these models. As a result, we systematically investigate the global stability of an susceptible-infected-susceptible (SIS) model using pair approximation on regular and random networks, which is based on the assumption that the number of infected neighbors of individuals is multinomially distributed. The basic reproductive number R0 is analyzed and we prove that the disease-free equilibrium is globally asymptotically stable when R0<1; otherwise, there exists a unique endemic equilibrium, which is globally asymptotically stable. Furthermore, numerical simulations are performed to verify the theoretical analysis results. The obtained results well enrich the findings in epidemical models on networks.