Forecasting the Monthly Reported Cases of Human Immunodeficiency Virus (HIV) at Minna Niger State, Nigeria

There has been a moderate\r\nincrease in newly diagnosed HIV-infected Minna populace, which calls for\r\nserious attention. This study used time series data based on monthly HIV\r\ncases from January 2007 to December 2018 taken from the statistical data\r\ndocument on HIV prevalence recorded in General Hospital Minna, Niger State. The methodology employed to analyze the data\r\nis based on mathematical models of ARMA, ARIMA and\r\nSARIMA which were computed and diagnosed. From the results of parameter estimation\r\nof the models, ARMA(2, 1) model was the best\r\nmodel among the other ARMA models using information criteria (AIC). Diagnostic\r\ntest was run on the ARMA(2, 1) model where the results show that the model was\r\nadequate and normally distributed using Box-Lung test and Q-Q plot respectively. Furthermore, ARIMA of first and second differences\r\nwas estimated and ARIMA(1, 0, 1) was the best model\r\nfrom the result of the AIC and diagnostic test carried out which revealed that\r\nthe model was adequate and normally distributed using Box-Lung and Q-Q plot\r\nrespectively. Furthermore, the results obtained in the ARMA and ARIMA models\r\nwere used to arrive at a combined model given as ARIMA(1, 0, 1) × SARIMA(1, 0, 1)12 which was subsequently estimated and found to\r\nbe adequate from the result of the Box-Lung and Q-Q plot respectively. Post\r\nforecasting estimation and performance evolution were evaluated using the RMSE\r\nand MAE. The results showed that, ARIMA(1, 0, 1) × SARIMA(1, 0, 1)12 is the best\r\nforecasting model followed by ARIMA(1, 0, 2) on monthly HIV prevalence in\r\nMinna, Niger state.