Abstract
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.
Highlights
Multiple waves of COVID-19 are still attacking many countries around the world
The use of mathematical models to predict disease transmission is useful for analysis and prediction when the model is validated against the available disease data
The term T ( I ) = (1+cIbI ) represents the treatment function where b represents the saturation factor measuring the effect of the infected individual when delayed for treatment, and c is the maximal supplied medical resources
Summary
Multiple waves of COVID-19 are still attacking many countries around the world. The severity of the pandemic is accentuated by the emergence of new and more contagious strains of the virus. We adopt a nonlinear expression of the incidence rate βSI/(1 + αI ) that includes an inhibition 1/(1 + αI ) effect reflecting the behavior of susceptible persons as the infection spreads. We adopt the saturated treatment cI/(1 + bI ) function suggested by Zhang and Liu [17] This form has the advantage of producing a constant value when the number of infected persons (I) is very low and reaches an asymptotic constant value if the number of infected individuals is large. The novelty in the proposed SEIR model is that it includes a saturated incidence rate and a saturated treatment function in addition to a vaccination rate.
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