Mathematical modelling and analysis of COVID-19 epidemic and predicting its future situation in Ethiopia
Abadi Abay Gebremeskel, Hailay Weldegiorgis Berhe, Habtu Alemayehu Atsbaha
Abstract
The epidemic of the coronavirus disease 2019 (COVID-19) has been rising rapidly and life-threatening worldwide since its inception. The lack of an established vaccine for this disease has caused millions of illnesses and hundreds of thousands of deaths globally. Mathematical models have become crucial tools in determining the potential and seriousness of the disease and in helping the types of strategic intervention measures to be taken to prevent and control the intensity of the spread of the disease. In this study, a compartmental epidemic model of COVID-19 is proposed and analyzed to predict the transmission dynamics of the disease in Ethiopia. Analytically, the basic reproduction number is determined. To observe the dynamics of the system, a detailed stability analysis of the disease-free equilibrium (DFE) of the proposed model is carried out. Our result shows that the DFE is stable if the basic reproduction number is less than unity and unstable otherwise. Also, the parameters of the assumed model are estimated using the actual data of COVID-19 from Ethiopia reported for three months between March and June 2020. Furthermore, we performed a sensitivity analysis of the basic reproductive number and found that reducing the rate of transmission is the most important factor in achieving disease control. Numerical simulations demonstrate the suitability of the proposed model for the actual COVID-19 data in Ethiopia. In particular, the numerical simulation shows an increase in the rate of transmission leads to a significant increase in the infected individuals. Thus, results of the numerical simulations are in agreement with the sensitivity results of the system. The possible implication of this is that declining the rate of transmission to the desired level could enable us to combat the disease. Numerical simulations are also performed to forecast the disease prevalence in the community.