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 ℛ 0 D 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 ℛ 0 D . We identify critical hysteresis effects governed by vaccine efficacy ( f V ) and bacterial shedding ( ξ A , ξ I ), 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.