A time domain modelling of human immunodeficiency virus infection rate based on some endogenous variables

Human Immunodeficiency Virus (HIV) remains a public health concern, especially among the adults. Thus, understanding the dynamics of HIV transmission is crucial for effective prevention and control strategies. The need for time-based modeling of infectious diseases based on autogenous symptoms calls for the extension of traditional Autoregressive integrated moving average (ARIMA) and Seasonal autoregressive integrated moving average (SARIMA) to accommodate the identified symptoms. This article, proposed ARIMAX and SARIMAX to model the seasonal and non-seasonal spread of HIV among adults using daily HIV incidence data obtained from a Teaching Hospital between 2008 and 2021. Results showed that both ARIMAX and SARIMAX models accurately captured the trends and seasonality of HIV incidence. Both models demonstrate comparable fit through their measures of Variance (ARIMAX 2.044; SARIMAX 0.03148), Log Likelihood (ARIMAX 48.630; SARIMAX 23.42), AIC (ARIMAX 131.27; SARIMAX 88.83), BIC (ARIMAX 164.760; SARIMAX 130.6), which suggests that the SARIMAX outperformed the ARIMAX model, and thus established that HIV spread is seasonal based. Among the endogenous variables considered, fever, diarrhea, headache, weight loss, excessive sweat, abdominal pain, cough with sputum, catarrh, loss of appetite, skin rash, genital infection, and body weight loss have exhibited strong influence on the morbidity of HIV. Age has been negatively significant in both models, indicating that older age correlates with lower HIV rates. Hence SARIMAX was engaged in a 2-years quarterly forecast, and the first quarter consistently occasioned the highest number of adults with HIV infection, a situation which further confirmed the seasonality of the HIV spread.