用于理解SARS-CoV-2病毒在宿主体内水平上的灭绝、持续与控制问题的随机数学建模研究
Stochastic Mathematical Modelling Study for Understanding the Extinction, Persistence and Control of SARS-CoV-2 Virus at the Within-host Level
AI总结：
本文通过随机微分方程建立SARS-CoV-2宿主体内仓室模型，分析解的存在性、有界性、持续性及无感染平衡态的指数稳定性，并利用随机最优控制研究抗病毒药物和免疫调节剂的有效性，揭示环境噪声可导致疾病灭绝。
摘要：
以不确定性为特征的随机微分方程在病毒动力学建模中十分有效，并为传统确定性模型提供了一种替代方案。流行病模型不可避免地会受到系统内部随机性或环境噪声的影响。本文分析了SARS-CoV-2病毒的宿主体内随机仓室模型，并探讨其动力学行为。我们首先利用伊藤公式考察了模型解的存在性与正性，并建立了模型的随机有界性和持续性。建立了无感染平衡态的指数稳定性。通过数值模拟对理论结果进行了补充验证。研究发现环境噪声在疾病动力学中起着关键作用，甚至可能导致疾病灭绝。该模型还被扩展为一个随机最优控制问题，并研究了抗病毒药物和免疫调节剂等控制措施的有效性。
英文摘要：
Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the system or the environmental noise. In this paper, we analyze the stochastic within host compartment model for SARS-CoV-2 virus and explore its dynamics. We first examine the existence and positivity of the solution of the model using Ito's formula and the establish the stochastic boundedness and permanence of the model. Exponential stability of the infection free equilibrium state is established. Numerical simulations are conducted to complement the theoretical results. Environmental noise is found to play a crucial role in the dynamics of the disease and can even lead to the extinction of the disease. The model is also extended to a stochastic optimal control problem and the effectiveness of control measures, such as antiviral drugs and immunomodulators is investigated.
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