Mathematical Modeling of COVID-19 Transmission and Vaccination: The Case of UAE

Abstract

Mathematical models are widely used in simulating infectious diseases. They are employed to investigate the disease transmission dynamics, forecast its spreading pattern, check the effectiveness of the interventions, or any other point of interest regarding the disease progression. In general, models are expressed in terms of Differential Equations. In this thesis, we propose a mathematical model called the SEIR-VD model (S: Susceptible, E: Exposed, I: Infected, R: Recovered, V: Vaccinated, and D: Deaths) to study the COVID-19 progression and forecast its spreading. We examine the model characteristics and complete its mathematical analysis (stability points, basic reproduction number, and sensitivity analysis). We use the data of the UAE during the vaccination intervention as a case study. Our numerical analysis includes parameter estimation, curve fitting, prediction, and model validation. For the numerical analysis of our proposed SEIR-VD model, we employed a switched hybrid forced model developed in [1] for which the main time interval is divided into sub-intervals, and over these subintervals, the model parameters are forced to be a time-dependent function with the time considered continuous for some selected parameters and discrete for others. Different scenarios for vaccine intervention are considered in order to determine certain rates of fully immunized population. The proposed model can be used to investigate COVID-19 dynamics in other countries when relevant data are available to feed the model.