Analysis of a mathematical model of malaria transmission

Abstract

In this thesis, we analyze a mathematical model for the spread of malaria that consists of ten components. The human host population is divided into two main categories: semiimmune, which included all individuals who were immune to malaria, and non-immune, which included all individuals who were not. However, we further categorized semiimmune people into vulnerable, exposed, infectious, and recovered; non-immune people into vulnerable, exposed, and infectious; and the mosquito population into three classes: susceptible, exposed, and infected. We compute an explicit formula for the reproductive number, which depends on the weight of transmission from non-immune people to mosquitoes and from mosquitoes to non-immune humans, as well as the weight of transmission from semi-immune humans to mosquitoes and from mosquitoes to semi-immune humans. As a result, the square root of the sum of the squares of these weights for the two contact kinds represents the reproductive number for the entire population. The DFE point is GAS if R0 ≤ 1, indicating that malaria dies away, and stable if R0 > 1, indicating that malaria persists in the population. The model outcome confirms that the disease-free equilibrium is asymptotically stable when the reproductive number less than one and unstable when the reproductive number greater than one, and we discuss the possibility of a control for malaria transmission throughout a definite sub-group such as non-immune, semi-immune, or mosquitoes.