Abstract:
This study introduces a mathematical framework that incorporates fractional-order derivatives to investigate how effective protective interventions are in high-risk cholera populations. The model establishes disease-free and endemic thresholds, with stability analyzed using the Routh-Hurwitz criteria. A key insight is that determining the basic reproduction number provides deeper understanding of cholera transmission dynamics. Through normalized sensitivity analysis, the ingestion rate of Vibrio cholerae emerges as the most influential factor in transmission. Meanwhile, vaccination coverage and awareness of protective measures are recognized as crucial elements for cholera control and eradication. The model uses the Caputo-Fabrizio fractional- order approach and is proven to be well-posed through the fixed-point theorem. Using the Laplace Adomian Decomposition Method (LADM), the results demonstrate that high vaccination rates and widespread adoption of protective measures among susceptible individuals in high-risk zones significantly reduce susceptibility, increase protected populations, and strengthen overall public health resilience against cholera.
