THEORY OF SOME DISCRETE SEIR MODELS AND THEIR APPLICATION TO COVID-19

Abstract

In this thesis we explore the mathematical theory of some epidemiological models that represent infectious disease and try to establish the mathematical properties of the differential equations representing the models. We describe the SEIR models we study with time varying transmission and recovery coefficients and constant latency and vaccination rates. We prove that the models satisfy the requirements such as existence and uniqueness of solutions and the continuous dependence of solutions on initial conditions. Using these properties we derive the long term behavior and the condition for an outbreak to occur of the solutions. This helps us to understand the biological implications and the control measures that can be applied. We also develop an implicit discrete formulation for the numerical algorithms to use data and verify that the model can be used on the COVID-19 data.