OPTIMAL CONTROL MATHEMATICAL MODEL OF MALARIA AND TYPHOID FEVER CO-INFECTION DYNAMICS WITH ENVIRONMENTAL DEPENDENCY

Abstract

This study develops an optimal control mathematical model for malaria-typhoid co-infection dynamics with environmental dependency. The model incorporates, human populations, mosquito breeding vectors environments, Salmonella typhi bacteria reservoirs, and multiple control strategies within a unified framework. A system of nonlinear ordinary differential equations is used to describe the transmission dynamics. The Disease-free Equilibrium (DFE), Endemic Equilibrium Point (EEP), and basic reproduction numbers (????0) are derived and analysed. Stability analysis shows that DFE is locally asymptotically stable when ????0 < 1 and unstable when ????0 > 1. Sensitivity analysis identifies the key parameters that have the greatest influence on the disease transmission and persistence. Pontryagin’s Maximum Principle is applied to determine the optimal control strategies by minimizing the number of infected individuals, environmental reservoirs diseases, and the implementation costs of the control measures. Numerical simulations show that the combined implementation of treatment and environmental sanitation effectively reduces malaria-typhoid co-infection and disease burden. The findings emphasize the importance of integrating treatment with environmental management to support optimal and sustainable public health interventions for controlling malaria-typhoid co-infection and also provide useful insights for policymakers.