Optimal Control Analysis and Simulation of a Mathematical Model for Recurrent Malaria Dynamics via the Caputo Fractional-Order Derivative

The Caputo fractional derivative is employed to investigate the role of memory effects in modeling the transmission dynamics of recurrent malaria in interacting human–vector populations. The model generalizes an existing classical version accounting for the three major forms of recurrent malaria, including re-infection, recrudescence, and relapse. The formulated noninteger-order nine-dimensional system is shown to be biologically and mathematically well-posed through the generalized mean value theorem, while the existence and uniqueness of the model solutions are established with the help of Banach fixed point theory. The Ulam–Hyers stability approach is adopted to investigate the stability of the unique solution of the fractional-order model. In particular, the study investigates the fractional-order optimal control by incorporating four time-varying intervention strategies such as the use of insecticide-treated bednets (ITNs), antirelapse intervention, effective treatment effort, and mosquito reduction measures using indoor residual spraying. To examine the significance of different control combinations in stemming the problem of malaria recurrence, the time-varying control interventions are further re-classified into four intervention strategies combining any three of the control measures. The influence of implementing each of the intervention strategies with and without memory effects is examined on the subpopulations of the fractional-order recurrent malaria model. The findings show that optimizing intervention measures with memory significantly minimizes recurrent malaria transmission in the population.