Samiran Ghosh, Arnaud Ducrot, Malay Banerjee and Vitaly
Volpert
Vol. 12 (2024), No. 4, 359–387
DOI: 10.2140/memocs.2024.12.359
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.