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

TL;DR

This paper investigates complex dynamics, including bifurcations and chaos, in a dengue fever model with antibody-dependent enhancement and temporary cross-immunity, revealing rich behaviors and coexisting attractors.

Contribution

It introduces multi-parameter analysis of a dengue model with ADE and temporary immunity, highlighting novel bifurcation structures and chaotic attractors.

Findings

Chaotic attractors are enlarged by temporary cross-immunity.

Coexisting attractors are identified using combined bifurcation and Lyapunov analysis.

Multi-parameter studies are performed in biologically relevant ranges.

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 (in dengue known as antibody dependent enhancement, ADE). Such 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 also have implications for the epidemiology of other diseases.