Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate

In this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a period solution.