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

Abstract

Mathematical modeling and computer simulations aid in global transmission parameter estimation. Equations, tools, and behaviour assessments are vital in disease control modeling. The bacteria Vibrio cholera causes the waterborne infectious disease cholera, which causes severe diarrhoea and fast dehydration. Haiti; exemplifies cholera devastating impact. Although it has been acknowledged in history, there is a noticeable absence of efficient control strategies. In this paper, we review several papers on cholera 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 state about the model parameters. According to the sensitivity analysis, almost every model parameter might affect the virus's spread among susceptible, and the most sensitive parameters are 𝑎 and λ(B), where 𝑎 is the rate of contact with polluted water and 𝜆(𝐵) depended on the state 𝐵 (Density of toxigenic Vibrio cholera in water). So, to prevent the spread of this disease, depending on the simulations, the susceptible and infected people should be more careful about the parameters 𝑎 and λ(B). Finally; we intend to solve the Cholera disease using both the fifth order and fourth order ERK methods. We aim to then juxtapose our outcomes with those achieved through the classical fourth order Runge-Kutta Method. This comparison will be facilitated by an assessment of their respective relative local truncation error estimators.