Low-Dimensional SIR Epidemic Models with Demographics on Heterogeneous Networks

To investigate the impacts of demographics on the spread of infectious diseases, a susceptible-infectious-recovered (SIR) pairwise model on heterogeneous networks is established. This model is reduced by using the probability generating function and moment closure approximations. The basic reproduction number of the low-dimensional model is derived to rely on the recruitment and death rate, the first and second moments of newcomers’ degree distribution. Sensitivity analysis for the basic reproduction number is performed, which indicates that a larger variance of newcomers’ degrees can lead to an epidemic outbreak with a smaller transmission rate, and contribute to a slight decrease of the final density of infectious nodes with a larger transmission rate. Besides, stochastic simulations indicate that the low-dimensional model based on the log-normal moment closure assumption can well capture important properties of an epidemic. And the authors discover that a larger recruitment rate can inhibit the spread of disease.