Nonlinear Optimal Control of Epidemic Dynamics under Healthcare Capacity Constraints

Healthcare saturation can amplify epidemic mortality, yet most models assume constant fatality rates. This study develops a nonlinear optimal control framework for an SUDTHREV epidemiological model incorporating healthcarecapacity- dependent mortality via a sigmoidal function. The Pontryagin Maximum Principle is used to solve the optimal control problem, resulting in a coupled forward-backward system for vaccination, testing, treatment, and transmission techniques. Numerical findings indicate a shift to a subcritical regime with a 90% decrease in mortality and an 85% decrease in peak infections. Sensitivity analysis shows that survival outcomes are influenced by therapy, but epidemic magnitude is determined by transmission controls. These findings provide a framework for designing interventions in capacity-constrained settings.