Abstract

In the last seventy years, around 250 zoonotic diseases have emerged or re-emerged, exerting a substantial influence on human populations. We develop a new mathematical model based on the combination of nonlocal reaction-diffusion equations and ordinary differential equations, to investigate the emergence and re-emergence of epidemics in humans caused by mutations in animal strains. Virus mutation is modeled as random motion in the genotype space considered as continuous variable.

Modeling results reveal that the combination of strain mutation and cross-immunity leads to periodic outbreaks with specific gaps in the strain space. Employing semigroup theory, we establish the existence of solutions for both an animal submodel and a complete animal-human interaction model. We derive analytical conditions for epidemic emergence, the wave speed of infection progression in the genotype space, and the time interval between consecutive outbreaks. Our numerical simulations illustrate how cross-immunity efficacy, the symmetric nature of cross-immunity function, and the nature of initial strains influence epidemic progression. Furthermore, immunity waning leads to new outbreaks due to re-emergence of existing strains.

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