Dynamics of a Model of Coronavirus Disease with Fear Effect, Treatment Function, and Variable Recovery Rate

Rubayyi T. Alqahtani (), Abdelhamid Ajbar and Nadiyah Hussain Alharthi
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Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
Abdelhamid Ajbar: Department of Chemical Engineering, King Saud University, Riyadh 11362, Saudi Arabia
Nadiyah Hussain Alharthi: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia

Mathematics, 2024, vol. 12, issue 11, 1-16

Abstract: In this work, we developed, validated, and analysed the behaviour of a compartmental model of COVID-19 transmission in Saudi Arabia. The population was structured into four classes: susceptible (S), exposed (E), infectious (I), and removed (R) individuals. This SEIR model assumes a bilinear incidence rate and a nonlinear recovery rate that depends on the quality of health services. The model also considers a treatment function and incorporates the effect of fear due to the disease. We derived the expression of the basic reproduction number and the equilibrium points of the model and demonstrated that when the reproduction number is less than one, the disease-free equilibrium is stable, and the model predicts a backward bifurcation. We further found that when the reproduction number is larger than one, the model predicts stable periodic behaviour. Finally, we used numerical simulations with parameter values fitted to Saudi Arabia to analyse the effects of the model parameters on the model-predicted dynamic behaviours.

Keywords: COVID-19; SEIR model; fear effect; variable recovery rate; backward bifurcation; Hopf bifurcation; periodic behaviour; Saudi Arabia (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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