Optimal Control of a Delayed Spatiotemporal Epidemic Model (Journal of Nonlinear Modeling and Analysis, 2025)
This study presents an advanced delayed spatiotemporal epidemiological model that incorporates a Holling type II incidence rate to capturethe saturation effects observed in disease transmission dynamics during theCOVID-19 pandemic. The model integrates two crucial intervention measures - vaccination of susceptible individuals and hospitalization of severe cases - while accounting for both spatial diffusion and the latent period within theepidemic compartments. This framework facilitates the precise optimizationof vaccination and hospitalization strategies as functions of spatial locationand temporal evolution, yielding new insights into spatially targeted publichealth interventions. We rigorously analyze the model equilibrium points, establishing conditions for their existence and local stability. An optimal controlproblem is formulated, uniquely considering the combined effects of spatialdiffusion and latent period, with controls dynamically varying across spaceand time. The well-posedness of the control problem is verified, supportedby proofs of existence, uniqueness, positivity, and boundedness of the strongsolution. First-order necessary optimality conditions are derived, characterizing the optimal vaccination and hospitalization strategies through state andadjoint variables. Numerical simulations across diverse intervention scenariosdemonstrate the effectiveness of adaptive, space-time-specific control strategiesin mitigating COVID-19 transmission. This work offers a novel mathematicaland computational approach to the optimal spatiotemporal management ofepidemic control measures.
Keywords: Delayed spatiotemporal epidemic model; vaccination; hospitalization; reaction-diffusion equations; optimal control.