ADAPTIVE SIS EPIDEMIC MODELS ON HETEROGENEOUS NETWORKS WITH DEMOGRAPHICS AND RISK PERCEPTION

Abstract

In the context of epidemic spreading on networks, there are at least three concerns that should be considered. Firstly, the demographic process can change the underlying network structure and thus affect the disease spreading; secondly, the attachment probability of newcomers (namely, newborn or immigrated nodes) to other nodes depends on the degrees and states of existing nodes in the network; and thirdly, newcomers may remove some dangerous contacts once they perceive the risk of disease. In view of these facts, we propose two high-dimensional susceptible-infectious-susceptible (SIS) epidemic models on heterogeneous networks with demographics and risk perception — one that neglects both the degree and state correlations among nodes and the other that reserves the state correlation. Then the log-normal moment closure is adopted to reduce the dimensions of models. The basic reproduction numbers of the two corresponding low-dimensional models are derived. It is found that the basic reproduction numbers of the two models are different. In spite of this, both of them show that increasing recruitment will help to inhibit the disease spreading. In addition, numerical results demonstrate that the extent to which newcomers avoid contacting with infectious nodes can affect both the epidemic threshold and the equilibrium prevalence. Finally, comparisons between numerical and stochastic simulations indicate that the model with state correlation is more accurate.