Poisson Autoregressive and Poisson Exponential Weighted Moving Average Models for Infectious Disease Prevalence among Farmers in Benue State, Nigeria

Abstract

Aims: This study aims to model and analyze the infection rates of Human Immunodeficiency Virus (HIV), Tuberculosis (TB), and Viral Hepatitis (VHP) among farmers in Benue State, Nigeria, and to examine their temporal dynamics and co-infection patterns using Poisson-based time series models. Study Design: The study adopts a quantitative, retrospective time series design utilizing count data models, specifically the Poisson Autoregressive (PAR(1)) and Poisson Exponential Weighted Moving Average (PEWMA) models. Place and Duration of Study: The study was conducted in Benue State, Nigeria, using monthly secondary data on serologically confirmed cases of HIV, TB, and VHP from January 2010 to December 2022. Methodology: Descriptive statistics, time plots, bar charts, and the Anderson-Darling normality test were employed to explore the data characteristics. The PAR(1) model was used to assess persistence in infection rates, while the PEWMA model captured dynamic changes and co-infection relationships. Model performance was evaluated using coefficients of determination and diagnostic checks for dispersion and predictive accuracy. Results: The findings revealed increasing trends in HIV, TB, and VHP infections with clear non-Gaussian distributions. Peak infection rates occurred between 2017 and 2019, while the lowest rates were observed in 2010. The PAR(1) model indicated strong persistence with lag coefficients of 0.7362 (HIV), 0.7036 (TB), and 0.6718 (VHP). Monthly increases were estimated at 2.25% for HIV, 1.22% for TB, and 12.08% for VHP. The models demonstrated strong goodness-of-fit with R² values of 83.3%, 78.8%, and 80.8% for HIV, TB, and VHP, respectively. The PEWMA model highlighted significant co-infection dynamics, particularly between HIV and TB, and showed that VHP incidence is closely associated with both infections. Diagnostic results confirmed minimal over-dispersion and strong predictive capability. Conclusion: The study concludes that infection rates of HIV, TB, and VHP among farmers in Benue State are increasing and exhibit strong temporal dependence and co-infection interactions. The findings underscore the need for continuous surveillance, targeted interventions, and integrated public health strategies. Further research is recommended to investigate the underlying drivers of these trends and the observed non-normality in the data.