Mathematical models for hepatocytic-erythrocytic dynamics and therapeutic control of malaria

Abstract

Malaria is a mosquito-borne infectious disease caused by parasites of the genus Plasmodium. Mortality and morbidity due to malaria infection is a serious burden to malaria endemic countries. Despite the many years of prevention and control, malaria cases and mortality are still quite high. In 2018, the World Health Organization (WHO) reported about 219 million cases and 435000 deaths due to malaria globally. The threat of parasite resistance, minimal efficacy of malaria vaccines and the high burden of malaria prevention and control measures offer serious challenge to malaria elimination efforts. Improved therapeutic measures is hence necessary for malaria control and possible eradication. In this study, deterministic in-host malaria models with therapeutic control measures are extended and mathematically analysed. Effects of antimalarial drugs and malaria vaccines on disease severity are established analytically and numerically. Parasite resistance and the effects of competition between different parasite strains are also investigated numerically. Each model is analysed and vital properties such as positivity, existence of steady states and their stability conditions are precisely determined. By Pontryagin’s Maximum Principle, the optimal control therapy measure against P. falciparum malaria is determined. Results indicate that a combination of different malaria vaccine antigens yield better therapeutic outcome compared to individual vaccine antigens. A highly efficacious malaria vaccine (efficacy > 90%) is likely to offer the much needed protection against P. falciparum malaria. Multiple-strain infection is likely to increase parasitaemia and hence the severity and cost of malaria control. Malaria therapeutic control efforts should focus on reducing: the parasite invasion rate, the proportions of merozoites that become gametocytes per dying blood schizont, the average number of merozoites released per bursting blood schizonts and the rate of development of resistance during multiple-strain infections. Moreover, a combination of pre-erythrocytic vaccine antigen, blood schizontocide and gametocytocide drugs is likely to offer the best therapeutic control strategy against P. falciparum malaria. In conclusion, future malaria control efforts should consider efficacious malaria vaccines and vaccine combinations. To reduce development of resistance and morbidity, only efficacious antimalarials such as ACT should be used against P. falciparum malaria. The administration and use of current antimalarial drugs alongside efficacious malaria vaccines is likely to offer the much needed therapeutic combination against P. falciparum. Regular and strict surveillance on quality and standards of antimalarial drugs in medical facilities in malaria endemic countries is therefore very critical. Collectively, results from this study highlights the need for continued investment in malaria drug development and urgent drive to improve the efficacy of malaria vaccine candidates such as RTS,S/AS01.