Rajak Anil Kumar
Department of Applied Mathematics, Delhi Technological University, New Delhi, Delhi 110042 India.
Department of Mathematics, Atma Ram Sanatan Dharma College (University of Delhi), New Delhi, 110021 India.
Iran J Sci Technol Trans A Sci. 2022;46(4):1249-1263. doi: 10.1007/s40995-022-01339-w. Epub 2022 Aug 9.
In any outbreak of infectious disease, the timely quarantine of infected individuals along with preventive measures strategy are the crucial methods to control new infections in the population. Therefore, this study aims to provide a novel fractional Caputo derivative-based susceptible-infected-quarantined-recovered-susceptible epidemic mathematical model along with a nonmonotonic incidence rate of infection. A new quarantined individual compartment is incorporated into the susceptible-infected-recovered-susceptible compartmental model by dividing the total population into four subpopulations. The nonmonotonic incidence rate of infection is considered as Monod-Haldane functional type to understand the psychological effects in the population. Qualitative analysis of the study shows that the model solutions are well-posed i.e., they are nonnegative and bounded in an attractive region. It is revealed that the model has two equilibria, namely, disease-free (DFE) and endemic (EE). The stability analysis of equilibria is investigated for local as well as global behaviors. Mathematical analysis of the model reveals that DFE is locally asymptotically stable when the basic reproduction number is lower than one. The basic reproduction number is computed using the next-generation matrix method. The existence of EE is shown and it is investigated that EE is locally asymptotically stable when under some appropriate conditions. Moreover, the global stability behaviors of DFE and EE are analyzed under some conditions using . Finally, some numerical simulations are performed to interpret the theoretical findings.
在任何传染病爆发中，及时隔离感染者以及采取预防措施策略是控制人群中新感染病例的关键方法。因此，本研究旨在提供一种基于分数阶Caputo导数的易感-感染-隔离-康复-易感（SIRS）流行病数学模型，以及一种非单调感染发生率。通过将总人口划分为四个亚群，在易感-感染-康复-易感（SIR） compartmental模型中纳入了一个新的隔离个体 compartment。将非单调感染发生率视为莫诺-哈代（Monod-Haldane）函数类型，以了解人群中的心理影响。该研究的定性分析表明，模型解是适定的，即它们是非负的且在一个吸引区域内有界。结果表明，该模型有两个平衡点，即无病平衡点（DFE）和地方病平衡点（EE）。对平衡点的稳定性分析研究了局部以及全局行为。该模型的数学分析表明，当基本再生数低于1时，DFE是局部渐近稳定的。基本再生数使用下一代矩阵方法计算。证明了EE的存在性，并研究了在一些适当条件下，当 时EE是局部渐近稳定的。此外，在某些条件下使用 分析了DFE和EE的全局稳定性行为。最后，进行了一些数值模拟以解释理论结果。
