Saha Amit Kumar, Podder Chandra Nath, Niger Ashrafi Meher
Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh.
Infect Dis Model. 2022 Jun;7(2):138-160. doi: 10.1016/j.idm.2022.04.005. Epub 2022 May 4.
A novel coronavirus (COVID-19) has emerged as a global serious public health issue from December 2019. People having a weak immune system are more susceptible to coronavirus infection. It is a double challenge for people of any age with certain underlying medical conditions including cardiovascular disease, diabetes, high blood pressure and cancer etc. Co-morbidity increases the probability of COVID-19 complication. In this paper a deterministic compartmental model is formulated to understand the transmission dynamics of COVID-19. Rigorous mathematical analysis of the model shows that it exhibits backward bifurcation phenomenon when the basic reproduction number is less than unity. For the case of no re-infection it is shown that having the reproduction number less than one is necessary and sufficient for the effective control of COVID-19, that is, the disease free equilibrium is globally asymptotically stable when the reproduction threshold is less than unity. Furthermore, in the absence of reinfection, a unique endemic equilibrium of the model exists which is globally asymptotically stable whenever the reproduction number is greater than unity. Numerical simulations of the model, using data relevant to COVID-19 transmission dynamics, show that the use of efficacious face masks publicly could lead to the elimination of COVID-19 up to a satisfactory level. The study also shows that in the presence of co-morbidity, the disease increases significantly.
自2019年12月以来，一种新型冠状病毒（COVID-19）已成为全球严重的公共卫生问题。免疫系统较弱的人更容易感染冠状病毒。对于任何年龄且患有某些基础疾病（包括心血管疾病、糖尿病、高血压和癌症等）的人来说，这都是双重挑战。合并症会增加COVID-19并发症的可能性。本文建立了一个确定性的 compartmental 模型来理解COVID-19的传播动态。对该模型进行的严格数学分析表明，当基本再生数小于1时，它会出现向后分岔现象。对于无再感染的情况，结果表明再生数小于1是有效控制COVID-19的充要条件，即当再生阈值小于1时，无病平衡点是全局渐近稳定的。此外，在无再感染的情况下，该模型存在唯一的地方病平衡点，只要再生数大于1，该平衡点就是全局渐近稳定的。使用与COVID-19传播动态相关的数据对该模型进行的数值模拟表明，公众普遍使用有效的口罩可以将COVID-19消除到令人满意的水平。该研究还表明，在存在合并症的情况下，疾病会显著增加。
