Omame Andrew, Abbas Mujahid, Din Anwarud
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Abdus Salam School of Mathematical Sciences, Government College University Katchery Road, Lahore 54000, Pakistan.
Math Comput Simul. 2023 Feb;204:302-336. doi: 10.1016/j.matcom.2022.08.012. Epub 2022 Aug 29.
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.
已经开发了几种数学模型来研究严重急性呼吸综合征冠状病毒2（SARS-CoV-2）及其不同变体的动态变化。大多数多毒株SARS-CoV-2模型没有捕捉到这类模型一个重要且更符合实际的特征，即随机性。由于大多数流行病，尤其是SARS-CoV-2的动态行为无疑受到多种随机因素的影响，因此考虑一个针对两种SARS-CoV-2毒株的随机疫苗接种合并感染模型是合适的。在这项工作中，提出了一个针对两种SARS-CoV-2变体的新随机模型。推导了该随机模型唯一全局解的存在性和唯一性条件。通过构造一个合适的李雅普诺夫函数，推导了随机系统围绕确定性系统的地方病平衡点波动的条件。还研究了新合并感染模型的平稳分布和遍历性。进行了数值模拟以验证理论结果。观察到当白噪声强度大于某些阈值且相关的随机再生数小于1时，两种毒株都会以单位概率灭绝。此外，观察到，对于弱白噪声强度，随机系统的解围绕确定性模型的地方病平衡点（EE）波动。还研究了频率分布以显示由于随机白噪声强度引起的随机波动。本文给出的结果还揭示了疫苗接种在减少给定人群中SARS-CoV-2变体共同传播方面的影响。
