Mathematical model and analysis for within-host dynamics of the malaria parasite infection with optimal control strategies

Abstract

This study develops and analyzes the within-host dynamics of malaria parasite infection with optimal control strategies. We considered both the blood and liver stages of the malaria infection, taking into account the immunological response against the infection. The basic reproduction number, which indicates the potential spread of the parasite is evaluated. The parasite-free equilibrium point is locally and globally asymptotically stable when the basic reproduction is less than a unit. Sensitivity analysis reveals that the invention rate of red blood cells and the average number of merozoites per rupture infected red blood cell are the most influential parameters of the model. Furthermore, to investigate the most effective measurement of malaria parasite infection, we performed the optimal control strategies. The pre-erythrocytic vaccine, blood-stage vaccine, primary tissue schizontocides, blood schizontocides, and gametocytocidal drugs are incorporated as control measures. The controls are implemented to minimize the infected hepatocytes, infected red blood cells, gametocytes, and merozoites in the human host, as well as the associated costs. Pontryagin’s Minimum Principle is applied to establish optimal control strategies against infected red blood cells, infected hepatocytes, and malaria parasites. Several simulation situations are conducted to assess the analytical results and determine the effective control intervention measures. The results indicate that administering all four controls simultaneously would eradicate the prevalence of malaria infection in the human host.

Keywords

• Blood-stage vaccine
• Parasite persistence equilibrium
• Malaria infection
• Numerical simulation
• Pontryagin’s Minimum Principle
• Optimal control