A Mathematical Model on the Dynamics of the fractional-order of Cholera Disease with Vaccination - Talib, Taufan; Laamena, Novita Serly (Universitas Sulawesi Barat, 2025)
Cholera is a severe infectious disease caused by the bacterium Vibrio cholerae, often transmitted through contaminated water and food. This study develops a fractional-order mathematical model to analyze the dynamics of cholera disease while considering the effects of vaccination. The proposed model modifies existing cholera models by incorporating a vaccination compartment and employs fractional-order derivatives to account for memory effects in disease dynamics. The study evaluates the stability of the disease-free and endemic equilibrium points using Jacobian matrix analysis and Gershgorin's theorem. Numerical simulations highlight the impact of vaccination rates, immunity loss, and fractional orders on disease progression. Results show that higher vaccination rates and fractional orders significantly enhance disease control, while immunity loss challenges long-term stability. This model offers a more flexible approach to designing effective cholera control strategies.