Using annual time series data on the number of adults (ages 15 and above) newly infected with HIV in Burundi from 1990 – 2018, the study predicts the annual number of adults who will be newly infected with HIV over the period 2019 – 2025. The study applied the Box-Jenkins ARIMA methodology. The diagnostic ADF tests as well as correlogram analysis show that the G series under consideration is an I (2) variable. Based on the AIC, the study presents the ARIMA (0, 2, 1) model as the optimal model. The residual correlogram and the inverse roots of the applied model further reveal that the presented model is stable and suitable for forecasting new HIV infections in adults in Burundi. The results of the study indicate that the number of new HIV infections in adults in Burundi will most likely decline, over the period 2019 – 2023, from approximately 698 to almost 90 new HIV infections. By 2025, Burundi could experience her first zero new HIV infections in adults! This implies that, despite the fact that Vision Burundi 2025 is a highly ambitious blue-print; Vision Burundi 2025 will largely be achieved as far as HIV/AIDS prevention and control is concerned.

Using annual time series data on the number of people who practice open defecation in Kenya from 2000 – 2017, the study predicts the annual number of people who will still be practicing open defecation over the period 2018 – 2021. The authors apply the Box-Jenkins ARIMA methodology. The diagnostic ADF tests show that the ODK series under consideration is an I (1) variable. Based on the AIC, the study presents the ARIMA (0, 1, 2) model as the optimal model. The diagnostic tests further indicate that the presented model is quite stable and its residuals are stationary in levels. The results of the study indicate that the number of people practicing open defecation in Kenya is likely to decline, although slightly, over the period 2018 – 2022, from approximately 9.9% to almost 8.2% of the total population. Hence, it is possible for Kenya to completely eliminate the practice of open defecation by 2030. The study basically suggested a 3-fold policy recommendation to be put into consideration, especially by the government of Kenya.

Using annual time series data on the total number of new HIV infections in Togo from 1990 – 2018, the study makes predictions for the period 2019 – 2030. The research applies the Box-Jenkins ARIMA methodology. The diagnostic ADF tests show that, J, the series under consideration is an I (2) variable. Based on the AIC, the study presents the ARIMA (0, 2, 2) model as the optimal model. The diagnostic tests further indicate that the presented model is indeed stable and its residuals are not serially correlated and are also normally distributed. The results of the study indicate that the total number of new HIV infections in Togo is projected to decline sharply by 53.5% from the estimated 4791 new infections in 2019 to approximately 2229 new infections by 2030.

Using annual time series data on the prevalence of anemia in children under 5 years of age in Sierra Leone from 1990 – 2016, the study makes predictions for the period 2017 – 2025. The study applies the Box-Jenkins ARIMA methodology. The diagnostic ADF tests show that the AS series under consideration is an I (0) variable. Based on the AIC, the study presents the AR (4) model, also known as the ARIMA (4, 0, 0) model as the optimal model. The diagnostic tests further show us that the presented model is stable and its residuals are not serially correlated. The results of the study indicate that the prevalence of anemia in children in Sierra Leone will rise over the out-of-sample period. By 2025, the country will be having a prevalence of anemia in children of approximately 78.6%.

Using annual time series data on the number of people who practice open defecation in Malawi from 2000 – 2017, the study predicts the annual number of people who will still be practicing open defecation over the period 2018 – 2021. The study applies the Box-Jenkins ARIMA methodology. The diagnostic ADF tests show that the M series under consideration is an I (1) variable. Based on the AIC, the study presents the ARIMA (3, 1, 0) model as the optimal model. The diagnostic tests further show that the presented model is stable and its residuals are stationary in levels. The results of the study indicate that the number of people practicing open defecation in Malawi is likely to decline, over the period 2018 – 2022, from approximately 5.1% to almost 2.8% of the total population. Indeed, by 2030, open defecation can be eliminated in Malawi: hence, the country is in the right track with regards to its vision 2030 (on water, sanitation and hygiene). The study suggested a 3-fold policy recommendation to be put into consideration, especially by the government of Malawi.