Mathematical Modeling and the Spreading of the Cholera Epidemic Through Numerical Methods

Abstract

This research examines a cholera outbreak, a serious intestinal illness caused by a significant presence of harmful bacteria in the body. We developed a mathematical model to investigate how diseases spread following exposure to pathogens, emphasizing the emergence of symptoms. Initially, the model's predictions were consistent, but it later shifted to different mathematical equations, enhancing our understanding of the disease's molecular mechanisms. Our results indicate that the fixed-pattern model can both provide a biological explanation for the disorder's unpredictable patterns and reach a stable equilibrium. We backed up our conclusions with mathematical ideas that show how the system behaves over time, which will be essential for cholera research in the future. To gain a better understanding of the fundamental causes of the disease, we developed a particular technique called the RK-4 and Non-Standard Finite Difference scheme (NSFD) for the continuous model. This approach, which employs a variety of criteria to assess the stability of intervals with and without the presence of the disease under various conditions, facilitates a comprehensive analysis of the disease's dynamics. Researchers can learn crucial information about the disease's behavior and community effects because of this approach. The results of this study can be used to forecast the spread of various infectious diseases through theoretical and numerical analyses. By using this method, researchers can gain important insight into how diseases behave and how they might affect the affected communities. This study's theoretical and numerical analyses may help forecast how different infectious diseases will spread.