Department of Applied Mathematics, Delhi Technological University, Delhi, 110042 India.
J Appl Math Comput. 2022;68(6):3835-3859. doi: 10.1007/s12190-021-01658-y. Epub 2022 Jan 6.
In this paper, an attempt has been made to study and investigate a non-linear, non-integer SIR epidemic model for COVID-19 by incorporating Beddington-De Angelis incidence rate and Holling type II saturated cure rate. Beddington-De Angelis incidence rate has been chosen to observe the effects of measure of inhibition taken by both: susceptible and infective. This includes measure of inhibition taken by susceptibles as wearing proper mask, personal hygiene and maintaining social distance and the measure of inhibition taken by infectives may be quarantine or any other available treatment facility. Holling type II treatment rate has been considered for the present model for its ability to capture the effects of available limited treatment facilities in case of Covid 19. To include the neglected effect of memory property in integer order system, Caputo form of non-integer derivative has been considered, which exists in most biological systems. It has been observed that the model is well posed i.e., the solution with a positive initial value is reviewed for non-negativity and boundedness. Basic reproduction number is determined by next generation matrix method. Routh Hurwitz criteria has been used to determine the presence and stability of equilibrium points and then stability analyses have been conducted. It has been observed that the disease-free equilibrium is stable for i.e., there will be no infection in the population and the system tends towards the disease-free equilibrium and for , it becomes unstable, and the system will tend towards endemic equilibrium . Further, global stability analysis is carried out for both the equilibria using . Lastly numerical simulations to assess the effects of various parameters on the dynamics of disease has been performed.
在本文中，通过纳入贝丁顿 - 德安吉利斯发病率和霍林II型饱和治愈率，尝试研究和调查一种针对COVID - 19的非线性、非整数阶SIR流行病模型。选择贝丁顿 - 德安吉利斯发病率来观察易感者和感染者所采取抑制措施的影响。这包括易感者采取的抑制措施，如佩戴合适口罩、保持个人卫生和保持社交距离，以及感染者采取的抑制措施，可能是隔离或任何其他可用的治疗设施。对于当前模型考虑了霍林II型治疗率，因为它能够捕捉在COVID - 19情况下可用有限治疗设施的影响。为了纳入整数阶系统中被忽略的记忆特性影响，考虑了大多数生物系统中存在的非整数导数的卡普托形式。已观察到该模型是适定的，即对具有正初始值的解进行非负性和有界性审查。通过下一代矩阵方法确定基本再生数。使用劳斯 - 赫尔维茨准则来确定平衡点的存在性和稳定性，然后进行稳定性分析。已观察到，当 时，无病平衡点 是稳定的，即人群中不会有感染，系统趋向于无病平衡点 ，而当 时，它变得不稳定，系统将趋向于地方病平衡点 。此外，使用 对两个平衡点进行了全局稳定性分析。最后，进行了数值模拟以评估各种参数对疾病动态的影响。
