Fitting Birth and Death Queuing Models using Maximum Likelihood Estimation with Application to COVID-19 Pandemic in Sub-Saharan Africa

Abstract

The COVID-19 pandemic has revealed facts about deficiencies in health resource planning of some countries having relatively high case count and death toll. The virus has undergone an observed increase of cases that led to a global pandemic. Many authors have developed different models for predicting or observing the current trend of COVID-19 pandemic. In this study, fitting birth and death models using maximum likelihood estimation (MLE) method with application to COVID-19 in sub-Sahara Africa is proposed. Real life data on COVID-19 from World Health Organization (WHO) and other online resources was used to determine probability distributions of infected, recovery and death of COVID-19 patient in some selected Sub-Sahara countries: Nigeria, Kenya, South Africa and Central African Republic (CAR) from inception of the disease to 10 th November, 2021. The MLE method was used to determine the probability of getting infected with COVID-19; the probability of having more than n COVID-19 active cases in a susceptible population; the average survival time of the virus in a system; and the average number of COVID-19 active cases per day. The result of the analysis showed that the probability of recovery is above 0.9 for the selected countries except for Central African Republic which is 0.5924 and South Africa has the highest mortality rate of 3.06%. Kenya has the highest probability of having more than 10 COVID-19 cases. Kenya also has the highest survival time for the virus and has the highest number of COVID-19 active cases per day. The results fit well to the case data of the sample corona center. Current preventive and responsive resource planning depends on accurately designed models and methods needed for the prediction of future threats, and mitigation costs.