Mathematical Modelling of COVID-19 Transmission Dynamics with Vaccination: A Case Study in Ethiopia

Abstract

Mathematical modelling is important for better understanding of disease dynamics and developing strategies to manage rapidly spreading infectious diseases. In this work, we consider a mathematical model of COVID-19 transmission with double-dose vaccination strategy to control the disease. For the analytical analysis purpose, we divided the model into two parts: model with vaccination and without vaccination. Analytical and numerical approach is employed to investigate the results. In the analytical study of the model, we have shown the local and global stability of disease-free equilibrium, existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium, and sensitivity analysis of the model is conducted. From these analyses, for the full model (model with vaccination), we found that the disease-free equilibrium is globally asymptotically stable for $R_v<1$ and is unstable for $R_v>1$ . A locally stable endemic equilibrium exists for $R_v>1$ , which shows the persistence of the disease if the reproduction parameter is greater than unity. The model is fitted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 1, 2021 to January $31,2022$ . The unknown parameters are estimated using the least square method with the MATLAB built-in function “lsqcurvefit.” The basic reproduction number $R_0$ and controlled reproduction number $R_v$ are calculated to be $R_0=1.17$ and $R_v=1.15$ , respectively. Finally, we performed different simulations using MATLAB. From the simulation results, we found that it is important to reduce the transmission rate and infectivity factor of asymptomatic cases and increase the vaccination coverage and quarantine rate to control the disease transmission.