Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India.
Department of Mathematics, University of Kalyani, Kalyani - 741235, India.
Math Biosci Eng. 2020 Nov 26;18(1):182-213. doi: 10.3934/mbe.2021010.
In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role.
在本文中，我们提出了一个数学模型，以评估在印度抗击 COVID-19 大流行中使用口罩、对有症状个体进行住院治疗和对无症状个体进行隔离的影响。我们对提出的模型进行了校准，以拟合四个数据集，即马哈拉施特拉邦、德里、泰米尔纳德邦和整个印度的数据，并估计易感人群与有症状人群的感染率和隔离人群的康复率。我们还估计了基本再生数，以说明研究区域的流行病学状况。我们的模拟推断，马哈拉施特拉邦和印度的感染人群将呈上升曲线，而泰米尔纳德邦和德里则趋于稳定。我们采用了复杂的敏感性分析技术来确定模型参数对基本再生数和有症状感染者的影响。研究结果表明，为了减轻印度的疾病负担，应有效实施具体的控制策略，以使基本再生数降至 1 以下。这三种控制策略被证明是降低疾病传播率的重要预防措施。该模型进一步扩展到其随机对应物，以包含在疾病传播中观察到的变化或不确定性。我们观察到感染人群的可变性，并在某些固定时间观察到其分布，这表明对于小种群，随机性将发挥重要作用。
