Nonlinear Optimal Control of Epidemic Dynamics under Healthcare Capacity Constraints
M. O. Durojaye
Department of Mathematics, University of Abuja, Abuja, Nigeria.
T. A. Ogunjemiyo
Department of Mathematics, University of Abuja, Abuja, Nigeria.
J. K. Odeyemi *
Department of Mathematics and Statistics, Federal Polytechnic Ilaro, Ogun State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Healthcare saturation, optimal control theory, sigmoidal response, Pontryagin maximum principle