Faculty, Staff and Student Publications
Publication Date
3-29-2023
Journal
Journal of Mathematical Biology
Abstract
We consider the dynamics of a virus spreading through a population that produces a mutant strain with the ability to infect individuals that were infected with the established strain. Temporary cross-immunity is included using a time delay, but is found to be a harmless delay. We provide some sufficient conditions that guarantee local and global asymptotic stability of the disease-free equilibrium and the two boundary equilibria when the two strains outcompete one another. It is shown that, due to the immune evasion of the emerging strain, the reproduction number of the emerging strain must be significantly lower than that of the established strain for the local stability of the established-strain-only boundary equilibrium. To analyze the unique coexistence equilibrium we apply a quasi steady-state argument to reduce the full model to a two-dimensional one that exhibits a global asymptotically stable established-strain-only equilibrium or global asymptotically stable coexistence equilibrium. Our results indicate that the basic reproduction numbers of both strains govern the overall dynamics, but in nontrivial ways due to the inclusion of cross-immunity. The model is applied to study the emergence of the SARS-CoV-2 Delta variant in the presence of the Alpha variant using wastewater surveillance data from the Deer Island Treatment Plant in Massachusetts, USA.
Keywords
Humans, Animals, Wastewater, Wastewater-Based Epidemiological Monitoring, COVID-19, SARS-CoV-2, Deer, Harmless delay, Delay differential equation, COVID-19, Wastewater, Competitive exclusion
DOI
10.1007/s00285-023-01900-0
PMID
36988621
PMCID
PMC10054223
PubMedCentral® Posted Date
3-29-2023
PubMedCentral® Full Text Version
Post-print
Published Open-Access
yes