In this article, a novel susceptible–infected–recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically. The Monod–Haldane functional response is considered for nonmonotonic behavior of both incidence rate and treatment rate. The model analysis shows that the model has two equilibria which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). The stability analysis has been performed for the local and global behavior of the DFE and EE. With the help of the basic reproduction number \( \left( {R_{0} } \right) \), we investigate that DFE is locally asymptotically stable when \( R_{0} < 1 \) and unstable when \( R_{0} > 1 \). The local stability of DFE at \( R_{0} = 1 \) has been analyzed, and it is obtained that DFE exhibits a forward transcritical bifurcation. Further, we identify conditions for the existence of EE and show the local stability of EE under certain conditions. Moreover, the global stability behavior of DFE and EE has been investigated. Lastly, numerical simulations have been done in the support of our theoretical findings.

在本文中，提出了一种具有非单调发病率和治疗率的新型易感-感染-康复流行病模型，并对其进行了数学分析。Monod-Haldane 功能反应被认为是发病率和治疗率的非单调行为。模型分析表明，该模型具有两个平衡，分别称为无病平衡（DFE）和地方病平衡（EE）。对 DFE 和 EE 的局部和全局行为进行了稳定性分析。在基本再现数\( \left( {R_{0} } \right) \)的帮助下，我们研究 DFE 在\( R_{0} < 1 \)时局部渐近稳定，而在\( R_ {0} > 1 \)。DFE 在\( R_{0} = 1 \)处的局部稳定性经分析，得出 DFE 呈现正向跨临界分岔。此外，我们确定了 EE 存在的条件，并显示了 EE 在某些条件下的局部稳定性。此外，还研究了 DFE 和 EE 的全局稳定性行为。最后，为了支持我们的理论发现，我们进行了数值模拟。