Abstract:
This thesis explored how climate, particularly rainfall and temperature, affects malaria
transmission. We used a compartmental mathematical model to analyze the relationship
between these factors and disease progression. The study achieved several key results.
Mathematically, we proved the model's solution is unique and has well-defined properties. It
also determined the model's equilibrium points and a crucial parameter called the basic
reproduction number (R₀). This number indicates how contagious the disease is. The stability
of the model was investigated for both disease-free and endemic states (presence or absence
of malaria). Stability analysis methods like Routh-Hurwitz criteria and Lyapunov theorems
were employed. Additionally, sensitivity analysis identified parameters that significantly
impact R₀. Finally, a computer simulation using MATLAB confirmed the model's accuracy.
This research provides valuable insights for understanding and potentially controlling
malaria outbreaks by highlighting the dependence of disease spread on climatic factors.
