UNDERSTANDING MALARIA TRANSMISSION DYNAMICS IN SICKLE CELL PATIENTS

ABSTRACT

In this thesis, we study the interaction between the dynamics of malaria and sickle cell. The main aim is to investigate the dynamics of malaria transmission in sickle cell populace and how to modulate or regulate the amount of malaria parasite in sickle cell gene carriers. For this, we developed a mathematical model that describes the interactions between malaria and sickle cell gene. The model includes both homozygous (SS) and heterozygous for sickle cell gene carriers (AS) and we assumed that AS individuals are not treated since they do not show clinical symptoms. We split our infected SS class into treated and non-treated groups. We then analyzed the model by computing the endemic and the disease free equilibria. Using the Jacobian matrix method, we observed that DFE is stable. We also calculated the reproductive number R0, and found that R0< 1, both our analytical and numerical results indicated that, when R0< 1, then malaria is wiped out in both populations. We also carried out numerical analysis and from our figures we observe that for R0< 1, the infected populations converged to zero as the susceptible populations increased for both SS and AS humans and mosquitoes. We thus concluded that Administering of drugs to both SS and AS individuals irrespective of whether symptoms show or not will help to reduce the infected classes to zero and increase the susceptible classes of both SS and AS genotypes.