Modeling Cholera Dynamics with Vaccination as the Control Strategy and Seasonal-forcing Transmission

Abstract: This study presents a seasonally forced cholera model that incorporates imperfect vaccination as a control strategy. The model captures the temporal dynamics of susceptible, vaccinated, infected, and recovered individuals, as well as the environmental pathogen concentration. A key focus is the instantaneous reproduction number, which serves as a threshold indicator for outbreak persistence or elimination. When reproduction number, the disease-free equilibrium is attainable; otherwise, endemic conditions persist. We conduct a sensitivity analysis to evaluate the influence of two critical parameters: the vaccination rate and the waning rate of immunity. Results show that increasing the vaccination rate and reducing the waning rate significantly decrease reproduction number, reinforcing the importance of sustained vaccine efficacy. Seasonal forcing amplifies the complexity of cholera dynamics, revealing the need for timely public health interventions, especially before high-transmission periods. This model demonstrates practical applicability in informing vaccination strategies, especially in resource-limited settings prone to seasonal outbreaks. It offers a flexible framework for public health planning, adaptable to other waterborne diseases. The findings suggest that integrated approaches combining vaccination, improved sanitation, and targeted education are essential to reducing cholera transmission and achieving long-term control.