Study of Dynamics of a COVID-19 Model for Saudi Arabia with Vaccination Rate, Saturated Treatment Function and Saturated Incidence Rate

This paper proposes, validates and analyzes the dynamics of the susceptible exposed infectious recovered (SEIR) model for the propagation of COVID-19 in Saudi Arabia, which recorded the largest number of cases in the Arab world. The model incorporates a saturated incidence rate, a constant vaccination rate and a nonlinear treatment function. The rate of treatment is assumed to be proportional to the number of infected persons when this number is low and reaches a fixed value for large number of infected individuals. The expression of the basic reproduction number is derived, and the model basic stability properties are studied. We show that when the basic reproduction number is less than one the model can predict both a Hopf and backward bifurcations. Simulations are also provided to fit the model to COVID-19 data in Saudi Arabia and to study the effects of the parameters of the treatment function and vaccination rate on disease control.

On dynamics of fractional incommensurate model of Covid-19 with nonlinear saturated incidence rate

In December 2019, a new virus belonging to the coronavirus strain has been discovered in Wuhan, China, this virus has attracted world-wide attention and it spread rapidly in the world, reaching nearly 216 countries in the world in November 2020. In this chapter, we study the fractional incommensurate SIQR (susceptible, infections, quarantined and removed) COVID-19 model with nonlinear saturated incidence rate using Atangana-Baleanu fractional derivatives. The existence and uniqueness of the solutions for the fractional model is proved using fixed point theorem, the model are shown to have two equilibrium point (disease free and an endemic equilibrium). Some numerical simulations using Euler method are also carried out to support our theoretical results. We estimated the value of the fractional orders and the parameters of the proposed model using the least squares method. Further, the sensitivity analysis of the parameter is performed as a result, our incommensurate model gives a good approximation to real data of COVID-19.