Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ADE and temporary cross immunity

Abstract

We analyse an epidemiological model of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, is known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra, has to be applied in comparison to get further insight into such dynamical structures. Here we present for the first time multi-parameter studies in a range of biologically plausible values for dengue. The multi-strain interaction with the immune system is expected to have implications for the epidemiology of other diseases also.