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 \(({R}_{0})\) is lower than one. The basic reproduction number \({R}_{0}\) 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 \({R}_{0}>1\) under some appropriate conditions. Moreover, the global stability behaviors of DFE and EE are analyzed under some conditions using \({R}_{0}\). Finally, some numerical simulations are performed to interpret the theoretical findings.

在任何传染病爆发时，及时隔离感染者并采取预防措施是控制人群新感染的关键方法。因此，本研究旨在提供一种新颖的基于分数卡普托导数的易感者-感染者-隔离者-康复者-易感者流行病数学模型以及感染的非单调发生率。通过将总人口分为四个亚群，将新的隔离个体区室纳入易感-感染-恢复-易感区室模型中。感染的非单调发生率被认为是 Monod-Haldane 函数类型，以了解人群的心理影响。研究的定性分析表明，模型解是适定的，即它们是非负的并且有界于有吸引力的区域。结果表明，该模型具有两个平衡，即无病平衡（DFE）和地方病平衡（EE）。对局部和全局行为的平衡稳定性分析进行了研究。模型的数学分析表明，当基本再生数\(({R}_{0})\)小于1时，DFE是局部渐近稳定的。基本再生数\({R}_{0}\)采用下一代矩阵法计算。证明了EE的存在性，并研究了在适当的条件下当\({R}_{0}>1\)时EE是局部渐近稳定的。此外，使用\({R}_{0}\)分析了某些条件下 DFE 和 EE 的全局稳定性行为。最后，进行一些数值模拟来解释理论结果。