Singh Negi Sunil, Sharma Nitin, Priyadarshi Anupam
Department of Mathematics, National Institute of Technology, Uttarakhand, Srinagar Garhwal 246174, India.
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India.
Gene. 2025 Mar 15;941:149033. doi: 10.1016/j.gene.2024.149033. Epub 2024 Oct 22.
The study investigates the intricate dynamics of SARS-CoV-2 transmission, with a particular focus on both close-contact interactions and environmental factors. Using advanced mathematical modeling and epidemiological analysis, explored the effects of these transmission pathways on the spread of COVID-19. The equilibrium points for both disease-free and endemic states are calculated and evaluated to determine their global stability. Additionally, the basic reproduction number (R) is derived to quantify the transmission potential of the virus. To ensure model accuracy, numerical simulations are performed using MATLAB, utilizing daily COVID-19 case data from India. Parameter values are sourced from existing literature, with certain parameters estimated through fitting the model to observed data. Crucially, the model incorporates environmental transmission factors, such as surface contamination and airborne spread. The inclusion of these factors provides a more comprehensive understanding of the virus's spread, demonstrating the importance of interventions like use of face masks, environmental sanitization, vaccine efficacy, availability of treatment resources underappreciated when focusing solely on direct human contact. A sensitivity analysis is conducted to assess the impact of different parameters on R, with results visualized through heat maps to identify the most influential factors. Furthermore, Pontryagin's maximum principle is employed to develop an optimal control model, enabling the formulation of effective intervention strategies. By analysing both interpersonal and environmental transmission mechanisms, this study offers a more holistic framework for understanding SARS-CoV-2 transmission. The insights gained are critical for informing public health strategies, emphasizing the necessity of addressing both direct contact and environmental sources of infection to more effectively manage current and future outbreaks.
该研究调查了新冠病毒传播的复杂动态，特别关注密切接触互动和环境因素。通过先进的数学建模和流行病学分析，探究了这些传播途径对新冠疫情传播的影响。计算并评估了无病状态和地方病状态的平衡点，以确定其全局稳定性。此外，推导了基本再生数（R）以量化病毒的传播潜力。为确保模型准确性，使用MATLAB进行数值模拟，利用来自印度的每日新冠病例数据。参数值来自现有文献，某些参数通过将模型拟合到观测数据进行估计。至关重要的是，该模型纳入了环境传播因素，如表面污染和空气传播。纳入这些因素能更全面地理解病毒的传播，表明诸如使用口罩、环境消毒、疫苗效力、治疗资源可用性等干预措施的重要性，而这些在仅关注直接人际接触时往往被低估。进行了敏感性分析以评估不同参数对R的影响，结果通过热图可视化以识别最具影响力的因素。此外，采用庞特里亚金极大值原理开发了一个最优控制模型，从而能够制定有效的干预策略。通过分析人际和环境传播机制，本研究为理解新冠病毒传播提供了一个更全面的框架。所获得的见解对于为公共卫生策略提供信息至关重要，强调了应对直接接触和环境感染源以更有效地管理当前和未来疫情爆发的必要性。
