Ramalingam Ramesh, Gnanaprakasam Arul Joseph, Boulaaras Salah
Department of Mathematics, SRM Institute of Science and Technology, Faculty of Engineering and Technology, Ramapuram, Kanchipuram District, Tamil Nadu, 600 089, India.
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu District, Tamil Nadu, 603 203, India.
Sci Rep. 2025 Mar 17;15(1):9095. doi: 10.1038/s41598-025-93994-3.
In this work, we investigate a mathematical model that depicts the dynamics of COVID-19, with an emphasis on the effectiveness of detection and diagnosis procedures as well as the impact of quarantine measures. Using data from May 1 to May 31, 2020, the current study compares three states: Tamil Nadu, Maharashtra, and Andhra Pradesh. A compartmental model has been developed in order to forecast the pandemic's trajectory and devise an effective control strategy. The study then examines the dynamic progression of the pandemic by including important epidemiological factors into a modified SEIR (Susceptible, Exposed, Infectious, Recovered) model. Our method is a thorough analysis of the equilibria of the deterministic mathematical model in question. We use rigorous techniques to find these equilibrium points and then conduct a comprehensive investigation of their stability. Furthermore, an optimum control problem is applied to reduce the illness fatality, taking into account both pharmaceutical and nonpharmaceutical intervention options as control functions. With the aid of Pontryagin's maximal principle, an objective functional has been created and solved in order to minimize the number of infected people and lower the cost of the controls. In terms of the basic reproduction number, the stability of biologically plausible equilibrium points and the qualitative behavior of the model are examined. We found that the disease transmission rate has an effect on reducing the spread of diseases after conducting sensitivity analysis with regard to the basic reproduction number. According to the findings, Tamil Nadu had the lowest reproduction number ([Formula: see text]) and Maharashtra the highest ([Formula: see text]), indicating regional differences in the efficacy of public health initiatives. Furthermore, it has been demonstrated that appropriate control strategies, such as vaccination (Μ), can successfully reduce infection levels and improve recovery rates. In our study compared to the other two states, Tamil Nadu is notable for its quick recovery and decrease in infection rates. In our findings are more dependable and applicable when mathematical analysis and numerical simulations are combined, which also helps to provide a more thorough understanding of the dynamics at work in the COVID-19 environment. This research also offers suggestions for how government agencies, health groups, and legislators can lessen the effects of COVID-19 and distribute resources as efficiently as possible . Finally, we conclude by discussing the optimal control strategy to contain the epidemic.
在这项工作中，我们研究了一个描述新冠疫情动态的数学模型，重点关注检测和诊断程序的有效性以及隔离措施的影响。利用2020年5月1日至5月31日的数据，本研究比较了三个邦：泰米尔纳德邦、马哈拉施特拉邦和安得拉邦。为了预测疫情的发展轨迹并制定有效的控制策略，已经开发了一个 compartments 模型。然后，该研究通过将重要的流行病学因素纳入一个修改后的SEIR（易感、暴露、感染、康复）模型，来研究疫情的动态发展。我们的方法是对所讨论的确定性数学模型的平衡点进行全面分析。我们使用严格的技术来找到这些平衡点，然后对它们的稳定性进行全面研究。此外，应用一个最优控制问题来降低疾病死亡率，同时考虑药物和非药物干预选项作为控制函数。借助庞特里亚金极大值原理，创建并求解了一个目标泛函，以尽量减少感染人数并降低控制成本。在基本再生数方面，研究了生物学上合理的平衡点的稳定性以及模型的定性行为。在对基本再生数进行敏感性分析后，我们发现疾病传播率对减少疾病传播有影响。根据研究结果，泰米尔纳德邦的再生数最低（[公式：见原文]），马哈拉施特拉邦最高（[公式：见原文]），这表明公共卫生举措的效果存在地区差异。此外，已经证明适当的控制策略，如接种疫苗（Μ），可以成功降低感染水平并提高康复率。在我们的研究中，与其他两个邦相比，泰米尔纳德邦以其快速康复和感染率下降而引人注目。当数学分析和数值模拟相结合时，我们的研究结果更可靠且适用，这也有助于更全面地理解新冠疫情环境中起作用的动态。这项研究还为政府机构、卫生组织和立法者如何减轻新冠疫情的影响以及尽可能高效地分配资源提供了建议。最后，我们通过讨论控制疫情的最优控制策略来得出结论。
