In this paper, an SEIRS epidemic model is proposed, incorporating appropriate compartments as isolated exposed class and diagnosed class, relevant to interventions. In the scenario of constant isolated proportion, the qualitative analyses are carried out in terms of the basic reproduction number \(\mathscr {R}_0\). The sensitivity of \(\mathscr {R}_0\) with respect to model parameters is discussed. The Pontryagin’s Maximum Principle is applied to characterize the optimal control problem analytically, aiming at finding the optimal value of the control to minimize the cost of interventions. A general explicit expression for the optimal control is obtained. Numerical simulations are performed to illustrate analytical results.

在本文中，提出了SEIRS流行病模型，其中包括与干预措施相关的适当隔离区作为隔离的暴露类和诊断类。在恒定孤立比例的情况下，根据基本复制数\（\ mathscr {R} _0 \）进行定性分析。讨论了\（\ mathscr {R} _0 \）对模型参数的敏感性。Pontryagin的“最大原理”用于分析最优控制问题的特征，旨在找到最优控制值，以最大程度地降低干预成本。获得了最优控制的通用显式表达式。进行数值模拟以说明分析结果。