A nonlinear SEIR model is formulated and analyzed. This model accounts for three important interventions — the saturated treatment on infective individuals, the screening on the exposed individuals and the information induced self-protection on susceptible individuals. Existence and stability of equilibria are discussed. A sensitivity analysis for the model parameters is performed and we identified the parameters which are more sensitive to the model system. The sensitivity analysis is further followed up with the two parameters heat plot that determines the regions for the parametric values in which the system is either stable or unstable. Further, an optimal control problem is formulated by considering screening and treatment as control variables and corresponding cost functional is constructed. Using Pontryagin’s Maximum Principle, paths of optimal controls are obtained analytically. A comparative study is conducted numerically to explore and analyze analytical results. We note that in absence of treatment, screening policy may be a cost-effective choice to keep a tab on the disease. However, comprehensive effect of both screening and treatment has a huge impact, which is highly effective and least expensive. It is also noted that treatment is effective for mild epidemic whereas screening has a significant effect on the disease burden while epidemic is severe. For a range of basic reproduction number, effect of self-protection and saturation in treatment is also explored numerically.

中文翻译：

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在霍林 III 型饱和药物治疗和自我保护的情况下传染病的动态

建立并分析了非线性 SEIR 模型。该模型解释了三个重要的干预措施——对感染个体的饱和治疗、对暴露个体的筛查以及对易感个体的信息诱导自我保护。讨论了平衡的存在性和稳定性。对模型参数进行敏感性分析，我们确定了对模型系统更敏感的参数。灵敏度分析进一步跟进两个参数热图，确定系统稳定或不稳定的参数值区域。此外，通过将筛选和处理作为控制变量来制定最优控制问题，并构造相应的成本函数。使用 Pontryagin 的最大值原理，最优控制路径是通过解析获得的。以数值方式进行比较研究以探索和分析分析结果。我们注意到，在没有治疗的情况下，筛查政策可能是密切关注疾病的一种具有成本效益的选择。但是，筛查和治疗的综合效果影响巨大，效果显着，成本最低。还值得注意的是，治疗对轻度流行病有效，而筛查对疾病负担有显着影响，而流行病很严重。对于一定范围的基本再生数，还对处理中的自我保护和饱和效应进行了数值探索。筛查政策可能是密切关注疾病的一种具有成本效益的选择。但是，筛查和治疗的综合效果影响巨大，效果显着，成本最低。还值得注意的是，治疗对轻度流行病有效，而筛查对疾病负担有显着影响，而流行病很严重。对于一定范围的基本再生数，还对处理中的自我保护和饱和效应进行了数值探索。筛查政策可能是密切关注疾病的一种具有成本效益的选择。但是，筛查和治疗的综合效果影响巨大，效果显着，成本最低。还值得注意的是，治疗对轻度流行病有效，而筛查对疾病负担有显着影响，而流行病很严重。对于一定范围的基本再生数，还对处理中的自我保护和饱和效应进行了数值探索。