Stability Analysis of Hyperbolic Equilibria of the SEIR Model for COVID-19 Transmission

We formulate the SEIR mathematical model for the transmission dynamics of COVID-19. We study the stability of the equilibrium points for the system of differential equations modeling the disease. We obtain conditions for the local and global stabilities of the disease-free and endemic equilibria of the SEIR model. The basic reproduction number for the model is also derived. Values of the parameters used in the model are estimated and numerical simulation is conducted using the Scilab software application. The result of the simulation shows that the whole population becomes susceptible and the disease dies out very rapidly within a very short time, when the basic reproduction number is less than one. On the other hand, when the basic reproduction number is greater than one, a large proportion of the population gets infected while a much larger proportion die or recover from the disease.