Integrating Sensitivity Analysis and Explicit Runge-Kutta Method for Modeling the Effect of Exposure Rate to Contaminated Water on Cholera Disease Spread

Mathematical modeling and computer simulations aid global transmission parameter estimation. Equations, tools, and behavior assessments are vital in disease control modeling. The bacteria Vibrio cholera that causes the water-borne infectious disease cholera., which causes severe diarrhea and fast dehydration. Haiti exemplifies cholera's devastating impact. Despite its historical recognition, effective control plans are lacking. In this paper we review several paper choleras models. First, it can answer important questions about global health care and provide useful recommendations. After that, we examine the cholera model using sensitivity analyses with numerical simulation for all states. Full normalizations, half normalizations, and non-normalizations are used to evaluate the local sensitivities to each model states in relation to the model parameters. According to the sensitivity analysis, almost every model parameter might have an effect on the virus's spread among susceptible, and the most sensitive parameters are a and λ(B). So for preventing the spread of this disease with depending on the simulations the susceptible and infected people should be more careful about the parameters a (Rate of contact with polluted water) and λ(B). Finally, we intend to solve the Cholera disease using both the 5th order and 4th order ERK methods. Our aim is to then juxtapose our outcomes with those achieved through the conventional 4th order Runge-Kutta Method. This comparison will be facilitated by an assessment of their respective relative local truncation error estimators.