Hybrid multi-scale mathematical modelling of malaria infection transmission

Abstract

Malaria is a lifc-thrcatening discasc causcd by a protozoan parasitc called plasmod-ium, which livcs part of its lifo in the humans and part in Anophelcs mosquito. The dcvclopment of malaria parasitc in a human host commencc in the livcr cclls where the malaria parasitcs undcrgo ascxual multiplication to producc mcrozoitcs that are eventually rclcascd into the blood strcam to invadc red blood cells. The infcctcd red blood cclls burst aftcr 2-3 days to release merozoites and gametocytes into the blood stream. This is associatcd with the clinical symptoms of the disease. Anophe-les mosquito bccome infccted whcn they fced and ingest human blood that contains mature gametocytes. The gametocytes devclop into male and fcmale gametes that fcrtilize to become zygotes in the mid-gut wall of the mosquito.

We model malaria using non-linear differential equations. We analyse the existence and stability of steady state solution, existence of equilibrium point without disease, local stability of disease free equilibrium, existence of endemie equilibrium state, local stability of endemie equilibrium, global stability of the diseasc free equilibrium. The key to our model analysis is to calculate the rcproduction number. Wc also pcrform the sensitivc analysis using the reproduction number R0 with respect to the parameter. This sensitive analysis allow us to compare the cffoctivcness of different control strntegics.