Modeling Climate-Driven Cholera Outbreaks: A Negative Binomial Regression Framework with Improved Handling of Overdispersion and Extreme Events

Alshaikh A. Shokeralla
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Aqiq 65931, Saudi Arabia

Ahlam Ali Alzharani
Department of Management Information Systems, Faculty of Business, Al-Baha University, Saudi Arabia

Ali H. Abdalla
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Aqiq 65931, Saudi Arabia

Yousif M. Modawy
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Aqiq 65931, Saudi Arabia

Ibrahim Elshamy
Higher Institute of Engineering & Technology, Almanzala, Egypt; Mathematics Department, Faculty of Science, Al-Baha University, Saudi Arabia

Fathelrhman El Guma
Department of Mathematics, Faculty of Science, Al-Baha University, Al-Aqiq 65931, Saudi Arabia

Abstract

Using a refined Negative Binomial Regression framework, this study investigates the relationship between climatic variables and cholera outbreaks in Sudan from 2015 to 2024. Cholera, a waterborne disease sensitive to climate change and environmental stressors, continues to pose severe threats in fragile health systems where sanitation and healthcare access remain limited. We integrate temperature, precipitation, and sociopolitical factors into a model designed to overcome key limitations of traditional infectious disease forecasting approaches, including overdispersion, zero inflation, and outliers. Methodological enhancements such as log transformation, Ridge regularization, and bootstrapped validation were employed to improve robustness, interpretability, and prediction accuracy. The findings show that a rise in average annual temperature of one degree Celsius is associated with a high cholera incidence, while moderate amounts of rainfall reduce cholera incidence. The interaction terms also show that the temperature level moderates the effect of precipitation. Despite only annual data, the model also demonstrated a good predictive power (R² = 0.85). By applying marginal effects, we derived policy-relevant insights that highlight the importance of public health analytics. This paper provides an elaborate epidemiological design that can be easily scaled up and implemented in other LMICs, stressing the practicality of climate-based prediction for prevention.

Keywords: Cholera Modeling, Negative Binomial Regression, Climate Change, Temperature, Precipitation, Overdispersion, Suda, Infectious Disease Forecasting, Public Health Analytics