Multiple Optimal Control Strategies in a Trypanosomiasis-Malaria co-infection Reaction-Diffusion Model
Abstract
A reaction--diffusion model is formulated to investigate the spatial movement of humans and vectors in the co-transmission dynamics of trypanosomiasis and malaria. The existence, positivity, and boundedness of solutions are rigorously established, thereby ensuring the mathematical well-posedness of the model. Prevention and treatment interventions are incorporated as spatio-temporal control variables to characterise optimal control strategies aimed at minimising the populations of exposed and infected humans and vectors at the least possible cost. The optimal control characterisation is derived through the state and adjoint systems by applying the directional derivative of the objective functional with respect to the control variables. Numerical simulations are presented to validate the analytical results and demonstrate the effectiveness of the proposed control strategies.
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