# Chimera states in multi-strain epidemic models with temporary immunity

## TL;DR

This paper explores how time delays and cross-immunity influence the complex dynamics of multi-strain epidemic models, revealing phenomena like chimera states and various synchronization patterns.

## Contribution

It introduces a comprehensive analysis of delay-induced bifurcations and the emergence of chimera states in multi-strain epidemic models with different coupling topologies.

## Key findings

- Delay causes Hopf and saddle-node bifurcations affecting disease dynamics.
- Cross-immunity induces complex behaviors like traveling waves and chimera states.
- Chimera states occur with narrower cross-immunity kernels, impacting disease spread understanding.

## Abstract

We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibits emergence and anni- hilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary immunity. Effects of all-to-all and non-local coupling topologies are systematically investigated by means of numerical simulations, and they suggest that cross-immunity is able to induce a diverse range of complex dynamical behaviors and synchro- nization patterns, including discrete traveling waves, solitary states, and amplitude chimeras. Interestingly, chimera states are observed for narrower cross-immunity kernels, which can have profound implications for understanding the dynamics of multi-strain diseases.