Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

Gilberto Gonzalez-Parra and Abraham J. Arenas
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Gilberto Gonzalez-Parra: Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA
Abraham J. Arenas: Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 230002, Colombia

Mathematics, 2021, vol. 9, issue 13, 1-22

Abstract: Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R 0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

Keywords: SARS-CoV-2 virus; global stability analysis; Lyapunov functions; variants; basic reproduction number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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