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

Abstract In this paper, we introduce the data-driven optimal control problem combined with a class of nonlinear SEIRS epidemic model. By extending the classical SEIR model framework, we formulate a nonlinear SEIRS epidemic model by considering the immune loss rate of recovered population and a nonlinear incidence rate with saturation effect. In the SEIRS model, the number of population in each compartment is unknown and the parameters are time-varying. Combined with the ODE system derived from theSEIRS model, we leverage real-time data to define the loss function and obtain a data-drivenoptimal control problem. Employing the generalized Pontryagin's Maximum Principle,we state the necessary conditions for optimal solution to the data-driven optimal controlproblem. Futhermore, 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 estimateunknown population numbers and obtain time-varying parameters within our SEIRS 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 effective contact 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.