How demography-driven evolving networks impact epidemic transmission between communities

In this paper, we develop a complex network susceptible-infected-susceptible (SIS) model to investigate the impact of demographic factors on disease spreads. We carefully capture the transmission by short-time travelers, by assuming the susceptibles randomly travel to another community, stay for a daily time scale, and return. We calculate the basic reproductive number R0 and analyze the relevant stability of the equilibria (disease-free equilibrium and endemic equilibrium) of the model by applying limiting system theory and comparison principle. The results reveal that the disease-free equilibrium is globally asymptotically stable given R0<1, whereas the condition R0>1 leads to a globally asymptotically stable endemic equilibrium. Our numerical simulations show that demographic factors, such as birth, immigration, and short-time travels, play important roles in epidemic propagation from one community to another. Moreover, we quantitatively demonstrate how the distribution of individual's network degree would affect the result of disease transmission.