<p>The paper introduces the data-driven optimal control problem combined with a class of nonlinear SEIRS epidemic model. By extending the classical SEIR model framework, a nonlinear SEIRS epidemic model is formulated by considering the immune loss rate of recovered population and a nonlinear incidence rate with saturation effect. In the SEIRS epidemic model, the number of population in each compartment is unknown and the parameters are time-varying. Combined with the ODE system derived from the SEIRS epidemic model, we leverage real-time data to define the loss function and obtain a data-driven optimal control problem. Employing the generalized Pontryagin’s maximum principle, we state the necessary conditions for optimal solution to the data-driven optimal control problem. Furthermore, we meticulously devise an algorithmic framework, inclusive of detailed steps, to address this complex optimization task. We conduct numerical experiments using reported COVID-19 data, which enable us to estimate unknown population numbers and obtain time-varying parameters within the SEIRS epidemic model. The results of numerical experiments validate the effectiveness and rationality of our algorithm. Ultimately, by controlling the growth of the number of infected population and dead population over the subsequent 30 days, we obtain the temporal evolution trend of key parameters. Notably, our findings emphasize the strategic importance of reducing both the infection rate and the immune loss rate as effective means to control propagation of epidemics. This conclusion, rooted in our data-driven approach, offers a fresh perspective on epidemic control strategies.</p>

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A Data-Driven Optimal Control Approach for a Class of Nonlinear SEIRS Epidemic Model

  • Yadong Chen,
  • Wenli Cai

摘要

The paper introduces the data-driven optimal control problem combined with a class of nonlinear SEIRS epidemic model. By extending the classical SEIR model framework, a nonlinear SEIRS epidemic model is formulated by considering the immune loss rate of recovered population and a nonlinear incidence rate with saturation effect. In the SEIRS epidemic model, the number of population in each compartment is unknown and the parameters are time-varying. Combined with the ODE system derived from the SEIRS epidemic model, we leverage real-time data to define the loss function and obtain a data-driven optimal control problem. Employing the generalized Pontryagin’s maximum principle, we state the necessary conditions for optimal solution to the data-driven optimal control problem. Furthermore, we meticulously devise an algorithmic framework, inclusive of detailed steps, to address this complex optimization task. We conduct numerical experiments using reported COVID-19 data, which enable us to estimate unknown population numbers and obtain time-varying parameters within the SEIRS epidemic model. The results of numerical experiments validate the effectiveness and rationality of our algorithm. Ultimately, by controlling the growth of the number of infected population and dead population over the subsequent 30 days, we obtain the temporal evolution trend of key parameters. Notably, our findings emphasize the strategic importance of reducing both the infection rate and the immune loss rate as effective means to control propagation of epidemics. This conclusion, rooted in our data-driven approach, offers a fresh perspective on epidemic control strategies.