Mathematical Modeling of Cholera Transmission Capturing Vaccine Effect and Age Structure Using Homotopy Perturbation Method

Abstract

This research presents a detailed mathematical model for cholera transmission, incorporating age structure and vaccine effects. The model is analysed using mathematical methods to examine the disease-free and endemic equilibria, positivity, existence, uniqueness, and well-posedness of the epidemic model. The basic reproduction number is calculated, helping to assess cholera's transmission potential and the effectiveness of interventions. Local stability analyses around the disease-free and endemic equilibria provide insights into the system's behavior under different conditions, while global stability analyses determine the long-term behavior of the epidemic. Sensitivity analysis, conducted using the homotopy perturbation method, evaluates how variations in model parameters affect disease dynamics. By integrating age structure and vaccination into the model, the study explores how demographic factors influence cholera control strategies. The model's uniqueness is mathematically proven, ensuring the reliability of the results. Overall, this research advances the understanding of cholera dynamics, offering insights for designing sustainable and effective public health interventions to control the disease by health practitioners.