Analyzing the Impact of Temperature and Rainfall on Malaria Transmission Dynamics: A Mathematical Modeling Approach

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.