Fuzzy-fractional modeling of cholera transmission via water reservoirs and asymptomatic carriers: Analysis using WHO data

Vibrio cholerae is the organism that causes cholera, which is a life-threatening waterborne disease that is usually transmitted by contaminated water and food sources. In an effort to improve on the complicated transmission processes of the cholera disease, this paper develops and analyzes three fuzzy-fractional epidemiological models. SEIAHRD is the first model, and it comprises susceptible, exposed, infected, asymptomatic, hospitalized, recovered, and deceased classes. This second model is the SEIHRDW, which uses a water reservoir compartment but does not use asymptomatic individuals. SEIAHRDW is the third model, as the framework involves the combination of both asymptomatic carriers and water reservoirs to be a more realistic way of disease transmission. The models are developed based on actual epidemiological statistics of Angola presented by the World Health Organization. In the present modeling, the application of Caputo fractional derivatives allows the models to consider the long-term dependencies in the cholera disease progression, and the fuzzification of the parameters with triangular fuzzy numbers solves the problems of uncertainty and imprecision of the real-world data. A stability analysis determines the conditions under which cholera persists or dies out, while a sensitivity analysis identifies the main epidemiological parameters that drive the transmission of the disease. The analysis of the dynamics of the epidemics on the basis of numerical modeling and with the help of contour plots has shown the effect of different values of the fractional order and fuzzy limits. The Laplace residual power series method is used to find solutions and analyze fuzzy-fractional systems, and its usefulness is proved by the possibility to deal with the two complex problems, which are memory dependence and uncertainty of the parameters. The findings indicate that the concept of asymptomatic infections and contaminated water sources are critical in maintaining the cholera epidemics, and thus integrated control measures are important. These include timely case detection, improved sanitation, safe water supply, vaccination, and public health awareness campaigns. Overall, the combined use of fuzzy-fractional calculus and the Laplace residual power series method provides a reliable framework that advances the mathematical understanding of cholera dynamics. The insights gained not only strengthen predictive capabilities but also offer practical guidance for policymakers and health organizations in designing sustainable and effective intervention strategies for cholera disease prevention and control.