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.

Stochastic analysis of a SIRI epidemic model with double saturated rates and relapse

Infectious diseases have for centuries been the leading causes of death and disability worldwide and the environmental fluctuation is a crucial part of an ecosystem in the natural world. In this paper, we proposed and discussed a stochastic SIRI epidemic model incorporating double saturated incidence rates and relapse. The dynamical properties of the model were analyzed. The existence and uniqueness of a global positive solution were proven. Sufficient conditions were derived to guarantee the extinction and persistence in mean of the epidemic model. Additionally, ergodic stationary distribution of the stochastic SIRI model was discussed. Our results indicated that the intensity of relapse and stochastic perturbations greatly affected the dynamics of epidemic systems and if the random fluctuations were large enough, the disease could be accelerated to extinction while the stronger relapse rate were detrimental to the control of the disease.