In this paper, we have considered a deterministic epidemic model with logistic growth rate of the susceptible population, non-monotone incidence rate, nonlinear treatment function with impact of limited hospital beds and performed control strategies. The existence and stability of equilibria as well as persistence and extinction of the infection have been studied here. We have investigated different types of bifurcations, namely Transcritical bifurcation, Backward bifurcation, Saddle-node bifurcation and Hopf bifurcation, at different equilibrium points under some parametric restrictions. Numerical simulation for each of the above-defined bifurcations shows the complex dynamical phenomenon of the infectious disease. Furthermore, optimal control strategies are performed using Pontryagin’s maximum principle and strategies of controls are studied for two infectious diseases. Lastly using efficiency analysis we have found the effective control strategies for both cases.

在本文中，我们考虑了一个确定性流行病模型，该模型具有易感人群的逻辑增长率、非单调发病率、具有有限病床影响的非线性治疗函数，并执行了控制策略。此处研究了平衡的存在和稳定性以及感染的持续和消退。我们研究了不同类型的分岔，即跨临界分岔、后向分岔、鞍节点分岔和 Hopf 分岔，在一些参数限制下的不同平衡点。上述定义的每个分叉的数值模拟显示了传染病的复杂动力学现象。此外，使用 Pontryagin 的最大原理执行最佳控制策略，并研究了两种传染病的控制策略。最后使用效率分析，我们发现了两种情况下的有效控制策略。