Optimal Control And Fractional Order Modeling Of The Within-Host Dynamics Of Malaria Parasite Infection

Abstract

Malaria is a major global health challenge, with nearly half of the world’s population at risk of infection. It is caused by parasites of the genus Plasmodium and transmitted through the vectors. Malaria remains a significant global health concern with substantial socioeco- nomic implications. Understanding the within-host dynamics of the malaria parasite infection is crucial for designing effective intervention strategies. In this dissertation, we developed and analyzed mathematical models to investigate within-host dynamics and optimal control strategies for malaria infection. First, we presented the blood stage dynamical model that captures the interactions between infected cells, malaria parasites, and the host immune re- sponse using the nonlinear Michaelis-Menten-Monod function. We analyzed the stability of the parasite-free and parasite persistence equilibrium and determined the basic reproduction number as a key epidemiological threshold. Next, we extend the model to incorporate anti- malarial drug treatment, analyzing the effect of stage-specific interventions. We then proposed a within-host model that incorporates the adaptive immune responses, characterizing the sta- bility of the equilibria using Routh-Hurwitz criteria. Moreover, we developed an optimal con- trol framework to investigate the most effective intervention strategies. We considered four control variables targeting the elimination of infected hepatocytes, infected red blood cells, merozoites, and gametocytes. Applying Pontryagin’s Minimum Principles, we derived an op- timality system that characterizes the optimal control interventions. The result suggested that simultaneous application of all control measures could effectively eliminate malaria infection within the host cell. Finally, we formulated a fractional order derivative model of within-host malaria infection to investigate the impact of memory effects on parasite dynamics. We estab- lished the existence, uniqueness, boundedness, and positivity of solutions, qualitative analysis, and presented numerical simulations using the generalized predictor-corrector method. Our findings provide valuable insights into the complex within-host dynamics of malaria and offer a framework for developing optimal control strategies to combat this global health threat. In future work, to understand more about the complexity of malaria infection, the researcher will be extend the models by considering different strains of malaria parasite, time delay model, and reaction-diffusion model.