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

چکیده مقاله

This research examines a cholera outbreak, a serious intestinal illness caused by a significant presence of harmful bacteria in thebody. We developed a mathematical model to investigate how diseases spread following exposure to pathogens, emphasizing theemergence 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 bothprovide a biological explanation for the disorder’s unpredictable patterns and reach a stable equilibrium. We backed up ourconclusions with mathematical ideas that show how the system behaves over time, which will be essential for cholera research inthe future. To gain a better understanding of the fundamental causes of the disease, we developed a particular technique calledthe RK-4 and Non-Standard Finite Difference scheme (NSFD) for the continuous model. This approach, which employs a varietyof criteria to assess the stability of intervals with and without the presence of the disease under various conditions, facilitates acomprehensive analysis of the disease’s dynamics. Researchers can learn crucial information about the disease’s behavior andcommunity effects because of this approach. The results of this study can be used to forecast the spread of various infectiousdiseases through theoretical and numerical analyses. By using this method, researchers can gain important insight into howdiseases behave and how they might affect the affected communities. This study’s theoretical and numerical analyses may helpforecast how different infectious diseases will spread.