Dynamics of Delay Equations, Theory and Applications - Abstract

Hövel, Philipp

Dynamics of multi-strain epidemic models with delay

Modelling of epidemics has recently received a lot of attention. One important feature to include in mathematical models is the interactions between multiple pathogen strains and the corresponding host response. Such interactions are known to play a fundamental role in the dynamics of various infectious diseases, such as influenza and malaria. Complex immunological interactions between multiple strains can result in cross-immunity or cross-enhancement between genetically related strains, leading to a plethora of complicated behaviours, ranging from synchronous to emergent mixed coherent and incoherent states. We study a multi-strain generalization of a compartmental susceptible-infected-recovered (SIR) model with delay that accounts for temporary immunity. We show that in the isolated system, the stability of the endemic steady state depends on the delay time, and explore the underlying bifurcations via a linear stability analysis. For the parameter regime corresponding to stable oscillations, we investigate the dynamical Bscenarios of multiple SIR systems coupled on a ring in the strain space. Considering different coupling kernels, we identify various patterns, including states of mixed coherence and incoherence for the competing strains, giving rise to chimera states.