DEMOGRAPHICS INDUCE EXTINCTION OF DISEASE IN AN SIS MODEL BASED ON CONDITIONAL MARKOV CHAIN

Abstract

Demographics have significant effects on disease spread in populations and the topological evolution of the underlying networks that represent the populations. In the context of network-based epidemic modeling, Markov chain-based approach and pairwise approximation are two powerful tools — the former can capture stochastic effects of disease transmission dynamics and the latter can characterize the dynamical correlations in each pair of connected individuals. However, to our best knowledge, the study on epidemic spreading in networks relying on these two techniques is still lacking. To fill this gap, in this paper, a deterministic pairwise susceptible–infected–susceptible (SIS) epidemic model with demographics on complex networks with arbitrary degree distributions is studied based on a continuous time conditional Markov chain. This deterministic model is rigorously derived — using the moment generating function — from the Kolmogorov differential equations for the evolution of individuals and pairs. It is found that demographics will induce the extinction of the disease by reducing the basic reproduction number or lowering the epidemic prevalence after the disease prevails. Moreover, due to the demographical effects, the resulting network tends to a homogeneous network with a degree distribution similar to Poisson distribution, irrespective of the initial network structure. Additionally, we find excellent agreement between numerical solutions and individual-based stochastic simulations using both Erdös–Renyi (ER) random and Barabási–Albert (BA) scale-free initial networks. Our results may provide new insights on the understanding of the influence of demographics on epidemic dynamics and network evolution.