Epidemiology of Dengue Fever:A Model with Temporary Cross-Immunityand Possible Secondary Infection Shows Bifurcationsand Chaotic Behaviour in Wide Parameter Regions

Abstract

Basic models suitable to explain the epidemiology of dengue fever have previouslyshown the possibility of deterministically chaotic attractors, which might explain the observedfluctuations found in empiric outbreak data. However, the region of bifurcations and chaos requirestrong enhanced infectivity on secondary infection, motivated by experimental findings ofantibody-dependent-enhancement. Including temporary cross-immunity in such models, which iscommon knowledge among field researchers in dengue, we find bifurcations up to chaotic attractorsin much wider and also unexpected parameter regions of reduced infectivity on secondaryinfection, realistically describing more likely hospitalization on secondary infection when the viralload becomes high. The model shows Hopf bifurcations, symmetry breaking bifurcations of limitcycles, coexisting isolas, and two different possible routes to chaos, via the Feigenbaum perioddoubling and via torus bifurcations.