A new chaotic attractor in a basic multi-strain epidemiological model with temporary cross-immunity

TL;DR

This paper demonstrates that multi-strain epidemiological models with temporary cross-immunity can exhibit chaos even in realistic parameter regions, challenging previous assumptions that chaos required high secondary infectivity.

Contribution

It introduces a new chaotic attractor in multi-strain models with temporary cross-immunity, especially in the inverse ADE parameter region, broadening understanding of chaos in epidemiology.

Findings

Chaos occurs in realistic parameter regions for dengue models.

Deterministic chaos is possible with reduced secondary infectivity.

Wide ranges of chaotic attractors can inform data analysis.

Abstract

An epidemic multi-strain model with temporary cross-immunity shows chaos, even in a previously unexpected parameter region. Especially dengue fever models with strong enhanced infectivity on secondary infection have previously shown deterministic chaos motivated by experimental findings of antibody-dependent-enhancement (ADE). Including temporary cross-immunity in such models, which is common knowledge among field researchers in dengue, we find a deterministically chaotic attractor in the more realistic parameter region of reduced infectivity on secondary infection (''inverse ADE'' parameter region). This is realistic for dengue fever since on second infection people are more likely to be hospitalized, hence do not contribute to the force of infection as much as people with first infection. Our finding has wider implications beyond dengue in any multi-strain epidemiological systems with altered infectivity upon secondary infection, since we can relax the condition of rather high infectivity on secondary infection previously required for deterministic chaos. For dengue the finding of wide ranges of chaotic attractors open new ways to analysis of existing data sets.