Bifurcation, sensitivity, and noise: Stochastic dynamics of cholera with vaccination and sanitation controls

This study develops the novel SVAITRS-B model, unifying deterministic and stochastic frameworks to capture cholera dynamics with vaccination, asymptomatic carriers, and environmental pathways. We demonstrate analytically that person-to-person transmission exhibits backward bifurcation, while environmental transmission follows classical forward bifurcation-establishing distinct elimination thresholds that explain disease persistence even when the basic reproduction number ℛ0D falls below one. Stochastic simulations reveal that human-contact transmission generates 30% greater outbreak variability than environmental routes, highlighting its role in unpredictable epidemics. Environmental transmission, however, dominates long-term endemicity, contributing 68% to ℛ0D. We identify critical hysteresis effects governed by vaccine efficacy (fV) and bacterial shedding (ξA, ξI), and uncover a logarithmic sensitivity of bacterial concentration to sanitation-indicating that standard intervention targets may underestimate effort by 15–20%. These results provide a mathematical foundation for dual-pathway control strategies, combining human-focused interventions with environmental management. Our accompanying computational toolkit enables scenario testing for public health planning, though field validation of spatial heterogeneity remains essential for localized application.Author summary: Cholera continues to cause significant illness and death in regions with limited access to clean water and healthcare. While mathematical models help us understand how cholera spreads, most fail to capture the full complexity involving both person-to-person contact and bacteria in water sources. Here we develop a new model that includes vaccination, asymptomatic carriers who can silently spread the disease, treatment failure, and bacterial growth in the environment. Our analysis reveals three important findings for public health: First, simply reducing the reproduction number below 1 may not eliminate cholera due to a phenomenon called backward bifurcation-stronger interventions are needed. Second, person-to-person transmission creates more unpredictable outbreaks than environmental transmission, making short-term forecasting challenging. Third, our sensitivity analysis shows that vaccination and sanitation efforts must be more aggressive than previously thought to achieve elimination. These insights suggest that effective cholera control requires integrated strategies targeting both direct contact and water sanitation simultaneously. Our MATLAB simulation toolkit can help health agencies adapt these findings to local conditions for better outbreak planning and resource allocation.