Propagation Dynamics of a Periodic Epidemic Model on Weighted Interconnected Networks

Many real-world networks are comprised of several networks interconnected with each other and they may have different topologies and epidemic dynamics. The dynamical behaviors of various epidemic models on coupled networks have attracted great attentions. For instance, many people adhere to the statutory working and rest days, which results in a periodic fluctuation of disease transmission in the population, and the strength of connections between two individuals cannot be ignored either. In this paper, we explore the disease transmission on weighted interconnected networks by establishing a model that includes contact strengths and periodic incidence rates. The weights on the links indicate the familiarity or intimacy of the interactive individuals. Here, we analyze the stability of the disease-free periodic solution and the unique positive periodic solution (i.e., disease-free equilibrium and endemic equilibrium) of the model, and an explicit expression for the basic reproduction number in some special cases of the periodic model is derived. We also perform numerical simulations to validate and supplement the theoretical results. It is found that the weight exponent promotes the epidemic transmission by enlarging the basic reproduction number, and the influence of internal infectious rate on epidemic prevalence is larger than that of cross infectious rate for different network structures. It is expected that this work can deepen the understanding of transmission dynamics on weighted interconnected networks.