Spatial epidemiology of networked metapopulation: An overview

Lin WANG; Xiang Li

Assuming that a population of individuals is mixed homogeneously, this model organizes the persons into different compartments (states), according to their health status, e.g., susceptible (denoted by S, those healthy ones who may acquire the infection), infectious (I, those infected ones who are contagious), and recovered (R, those who are recovered from the disease). Within each compartment, all individuals are identical. The transitions between different compartments depend on the specific transition rates. For example, the transmission rate β represents the infection probability for a susceptible individual that encounters an infectious person, and the recovery rate µ represents the probability with which an infectious individual is recovered. If the disease could not endow recovered persons with a long lasting immunity but infect them again, e.g., seasonal flu, asthma, gonorrhoea, the related epidemic reactions are well described by the so called SIS model; otherwise, if recovered people become immune permanently to the disease, e.g., pandemic influenza, pertussis, smallpox, the epidemic dynamics can be characterized by the SIR model properly. Figures 1(a) -(b) illustrate the relevant compartment transitions in the SIS and SIR models, respectively. The dynamical evolution of these models can be simply delineated by ordinary differential equations [3] .