Modeling and Forecasting the Prevalence of Human Immuno-Deficiency Virus (HIV) in Birnin Gwari Local Government Area of Kaduna State

Human immunodeficiency virus (HIV) has been prevalent in millions of people worldwide for more than 50 years. Therefore, its prevalence must be monitored to make well-informed decisions and create efficient health plans. This paper dwelt on the modeling and prediction of the prevalence of HIV among inpatients and outpatients visiting Jibril Mai-Gwari I Memorial Hospital in Birnin Gwari Local Government Area of Kaduna State. An expo-facto research methodology was adopted for this study through the collection of twelve (12) years of monthly data spanning the period 2010-2021 as extracted from the hospital’s inpatient and outpatient department records. Box and Jenkins analytical approach was used to model the data due to its presence of unit root, as a non-stationarity data cannot be modeled using the conventional time series models. Iterative methods were applied in the identification of several ARIMA models as ARIMA (2, 1, 5) model was found to be the best fit among the 25 iterated models based on its higher loglikelihood (-435.57), lower variance (24.95) and lower AIC (887.13). More so, the model was found to scale through the portmanteau tests of residual independence (Ljung-Box Chi-square 5.9261, p-value > 0.05) and normality (Wilk 0.9830, p-value > 0.05), a confirmatory test of model reliability and accuracy. Although the prognosis suggests that HIV prevalence may not change significantly in the upcoming years, the expanding uncertainty band suggests that it will be challenging to estimate HIV prevalence in the future with high confidence. To manage prevalence and lower the chance of an unanticipated increase, public health measures must be consistent and effective.