EFFECTS OF DISPERSAL ASYMMETRY ON DISEASE SPREAD

Human movement is a leading cause of the rapid global spread of infectious diseases. Factors such as emerging pathogens and outbreaks, large-scale events, bilateral or multilateral agreements, resource allocation, and urban planning can lead to unsynchronized changes in population movement among regions. In this paper, based on a two-patch susceptible-infected-susceptible model, we investigate the dependence of disease persistence (measured by the basic reproduction number) and disease prevalence (proportion of people being infected) of both patches and each patch on dispersal asymmetry, respectively. It is shown that their dependencies are completely consistent, i.e., strictly increasing, strictly decreasing, or constant. Biologically speaking, an increase in migration from the high-risk patch (where the patch reproduction number is larger) to the low-risk patch (where the patch reproduction number is smaller) will reduce both infection risk and size. In addition, the basic reproduction number and the global and local disease prevalences at zero and infinite dispersal asymmetry are given. Numerical simulations suggest that there are some substantial differences between the two-patch case and the three or more patches case, such as the appearance of Simpson’s paradox on disease prevalence in the three-patch case.