Chaos induced by breakup of waves in a spatial epidemic model with nonlinear incidencerate

Abstract

Spatial epidemiology is the study of spatial variation in disease risk or incidence, includingthe spatial patterns of the population. The spread of diseases in human populations canexhibit large scale patterns, underlining the need for spatially explicit approaches. In thispaper, the spatiotemporal complexity of a spatial epidemic model with nonlinear incidencerate, which includes the behavioral changes and crowding effect of the infective individuals,is investigated. Based on both theoretical analysis and computer simulations, we find outwhen, under the parameters which can guarantee a stable limit cycle in the non-spatialmodel, spiral and target waves can emerge. Moreover, two different kinds of breakup ofwaves are shown. Specifically, the breakup of spiral waves is from the core and thebreakup of target waves is from the far-field, and both kinds of waves becomeirregular patterns at last. Our results reveal that the spatiotemporal chaos isinduced by the breakup of waves. The results obtained confirm that diffusioncan form spiral waves, target waves or spatial chaos of high population density,which enrich the findings of spatiotemporal dynamics in the epidemic model.