STABILITY ANALYSIS OF THE MODELS FOR MALARIA'S EFFECTS ON HUMANS BASED ON THE GENETIC STRUCTURE

Abstract

Malaria, according to encyclopedia Britannica, is a relapsing infection caused by plasmodium, transmitted to humans through the bite of an anopheles mosquito.  The composition of the genes in humans can either be homozygous (AA, SS) or heterozygous (AS), the homozygous are usually prone to the infection of malaria. The homozygous sickle cell genes (SS) encounter serious problems with blood shortage due to the sickle cell, this makes the malaria infection in them more complicated.  The heterozygous sickle cell, however, develops a resistance to the infection through the immunity offered by the single sickle cell.  This paper studies malaria’s effects on the homozygous and heterozygous genes through the system of ordinary differential equations.  The model was analyzed for stability, the reproduction number was obtained, and a simulation was performed using the reproduction number and some of the parameters to find out which of the parameters is most sensitive to the control of the spread of malaria. We found that contact rates and infection rates are highly sensitive parameters in malaria transmission. Therefore, minimizing mosquito-human contact is essential for disease control. Furthermore, our results showed that individuals with sickle cell trait have improved recovery rates, underscoring the protective benefits of this trait against malaria.