A MATHEMATICAL MODEL OF MALARIA TRANSMISSION DYNAMICS IN GENETICALLY RESISTANT AND SUSCEPTIBLE POPULATION

The variation in host response to infection might have a genetic basis. Exposure to Plasmodium infection developed genetic mechanisms of protection against severe disease. Two genes affecting red cell confer relative host resistance to P. falciparum: the autosomal gene for haemoglobin S (Hb S) and the sex-linked gene for the glucose-6-phosphate dehydrogenase $(G6PD)$ variant. A mathematical model was developed to understand the transmission and spread of malaria parasites.  The existence of the region where the model is epidemiologically feasible and mathematically well-posed was established.  The reproduction number $R_0$ was obtained from next generation matrix and the stability analysis of disease-free equilibrium was conducted.  Numerical simulations of the model were presented by solving the system of differential equations to explore the behaviour of the model and confirm the analytical results.  The results of this study shows a reduction in the number of death of genetically resistant human population which leads to increase in the number of death cases of susceptible human and increase in the number of infected mosquitoes.  This study suggest that if genetically resistant person are encouraged to take prophylactic treatment the number of infected mosquitoes could reduce