Mogambi, Nyasuguta Lucy2025-08-052025-08-052025-02https://ir-library.ku.ac.ke/handle/123456789/31107Project Submitted in Partial Fulfilment of the Requirements for the Award of the Degree of Master of Science (Applied Mathematics) in the School of Pure and Applied Sciences of Kenyatta University February, 2025 Supervisor: 1.Mary OpondoMalaria remains a leading global health challenge, causing millions of deaths annually, primarily through the bite of infected female Anopheles mosquitoes. In Kenya, Busia County records the highest malaria prevalence at 37%, yet it has often been excluded from mathematical modeling studies. Traditional SEIR models commonly used in malaria research fail to capture the persistence of asymptomatic Plasmodium parasites in individuals who have recovered from the disease. This study introduces an enhanced SIRSp model that incorporates this asymptomatic subpopulation to better understand malaria dynamics in Busia County. The model assumes a constant infection rate influenced by both susceptible and infected individuals, and its mathematical analysis yields reproduction numbers for humans and mosquitoes. Stability analysis of the disease-free equilibrium point indicates the feasibility of eradicating malaria in Busia County under certain conditions. Numerical simulations demonstrate that higher infection rates significantly amplify the prevalence of malaria, whereas improving recovery rates reduces infections among humans and mosquitoes while marginally increasing the pool of susceptible individuals. These results provide valuable insights into the dynamics of malaria transmission and emphasize the importance of tailored interventions for effective disease management in endemic regions.enThesis