Abstract：
COVID-19 highlighted the importance of considering human behavior change when modeling disease dynamics. This led to developing various models that incorporate human behavior. Our objective is to contribute to an in-depth, mathematical examination of such models. Here, we consider a simple deterministic compartmental model with endogenous incorporation of human behavior (i.e., behavioral feedback) through transmission in a classic Susceptible-Exposed-Infectious-Recovered (SEIR) structure. Despite its simplicity, the SEIR structure with behavior (SEIRb) was shown to perform well in forecasting, especially compared to more complicated models. We contrast this model with an SEIR model that excludes endogenous incorporation of behavior. Both models assume permanent immunity to COVID-19, so we also consider a modification of the models which include waning immunity (SEIRS and SEIRSb). We perform equilibria, sensitivity, and identifiability analyses on all models and examine the fidelity of the models to replicate COVID-19 data across the United States. Endogenous incorporation of behavior significantly improves a model\'s ability to produce realistic outbreaks. While the two endogenous models are similar with respect to identifiability and sensitivity, the SEIRSb model, with the more accurate assumption of the waning immunity, strengthens the initial SEIRb model by allowing for the existence of an endemic equilibrium, a realistic feature of COVID-19 dynamics. When fitting the model to data, we further consider the addition of simple seasonality affecting disease transmission to highlight the explanatory power of the models.
摘要：
新冠肺炎强调了在对疾病动力学进行建模时考虑人类行为变化的重要性。这导致开发了各种结合人类行为的模型。我们的目标是有助于深入，这种模型的数学检验。这里,我们考虑了一个简单的确定性隔室模型，该模型具有人类行为的内生整合(即，行为反馈）通过经典的易感暴露感染恢复（SEIR）结构中的传播。尽管它简单，具有行为的SEIR结构(SEIRb)在预测中表现良好，尤其是与更复杂的模型相比。我们将此模型与SEIR模型进行了对比，该模型排除了行为的内生整合。这两个模型都假定对COVID-19具有永久免疫力，因此我们还考虑对这些模型进行修改，包括减弱免疫力(SEIRS和SEIRSb)。我们进行均衡，灵敏度,并对所有模型进行可识别性分析，并检查模型在美国各地复制COVID-19数据的保真度。行为的内生整合显著提高了模型产生现实爆发的能力。虽然这两个内生模型在可识别性和敏感性方面相似，SEIRSb模型，随着免疫力下降的更准确的假设，通过允许存在地方性均衡来加强初始SEIRb模型，COVID-19动力学的一个现实特征。将模型拟合到数据时，我们进一步考虑增加影响疾病传播的简单季节性，以突出模型的解释力。
