A Negative Binomial- Garch Model with Application to Meningitis Cases in Nigeria

Abstract

Meningitis, a contagious tropical disease, disproportionately affects low-income populations with limited access to quality medical care. While previous studies have explored various methodologies for modeling meningitis cases, the issue of overdispersion remains inadequately addressed. This study applies a Negative Binomial integer GARCH model to meningitis data collected weekly from the Nigeria Centre for Disease Control between 2006 and 2021. Initial analysis revealed overdispersion in the data, justifying the use of a negative binomial GARCH model. The Augmented Dickey-Fuller test confirmed stationarity in the dataset. After evaluating multiple models, NB-INGARCH (1,2) emerged as the optimal choice based on AIC and BIC criteria. The selected model demonstrated adequacy through probability integrated transform histograms and calibration plots. This research showcases the effectiveness of NB-INGARCH in addressing overdispersion in time series data. To mitigate meningitis cases, we recommend promoting modern housing systems with adequate ventilation and decongestion measures in densely populated areas. Additionally, a targeted health awareness campaign on meningitis is suggested.