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Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2

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  • Omame, Andrew
  • Abbas, Mujahid
  • Din, Anwarud

Abstract

Several mathematical models have been developed to investigate the dynamics SARS-CoV-2 and its different variants. Most of the multi-strain SARS-CoV-2 models do not capture an important and more realistic feature of such models known as randomness. As the dynamical behavior of most epidemics, especially SARS-CoV-2, is unarguably influenced by several random factors, it is appropriate to consider a stochastic vaccination co-infection model for two strains of SARS-CoV-2. In this work, a new stochastic model for two variants of SARS-CoV-2 is presented. The conditions of existence and the uniqueness of a unique global solution of the stochastic model are derived. Constructing an appropriate Lyapunov function, the conditions for the stochastic system to fluctuate around endemic equilibrium of the deterministic system are derived. Stationary distribution and ergodicity for the new co-infection model are also studied. Numerical simulations are carried out to validate theoretical results. It is observed that when the white noise intensities are larger than certain thresholds and the associated stochastic reproduction numbers are less than unity, both strains die out and go into extinction with unit probability. More-over, it is observed that, for weak white noise intensities, the solution of the stochastic system fluctuates around the endemic equilibrium (EE) of the deterministic model. Frequency distributions are also studied to show random fluctuations due to stochastic white noise intensities. The results presented herein also reveal the impact of vaccination in reducing the co-circulation of SARS-CoV-2 variants within a given population.

Suggested Citation

  • Omame, Andrew & Abbas, Mujahid & Din, Anwarud, 2023. "Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 302-336.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:302-336
    DOI: 10.1016/j.matcom.2022.08.012
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    References listed on IDEAS

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    1. Edilson F Arruda & Shyam S Das & Claudia M Dias & Dayse H Pastore, 2021. "Modelling and optimal control of multi strain epidemics, with application to COVID-19," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-18, September.
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    Cited by:

    1. Lin Hu & Lin-Fei Nie, 2022. "Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching," Mathematics, MDPI, vol. 10(19), pages 1-20, September.
    2. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    3. Anwar, Nabeela & Ahmad, Iftikhar & Kiani, Adiqa Kausar & Shoaib, Muhammad & Raja, Muhammad Asif Zahoor, 2024. "Novel intelligent predictive networks for analysis of chaos in stochastic differential SIS epidemic model with vaccination impact," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 251-283.

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