Mathematical model to investigate transmission dynamics of COVID-19 with vaccinated class

Mdi Begum Jeelani; Abeer S Alnahdi; Rahim Ud Din; Hussam Alrabaiah; Azeem Sultana; Mdi Begum Jeelani; Abeer S Alnahdi; Rahim Ud Din; Hussam Alrabaiah; Azeem Sultana

doi:10.3934/math.20231531

AIMS Mathematics

2023, Volume 8, Issue 12: 29932-29955. doi: 10.3934/math.20231531

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Mathematical model to investigate transmission dynamics of COVID-19 with vaccinated class

1.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
2.
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan
3.
College of Engineering, Al Ain University, Al Ain, UAE
4.
Department of Mathematics, Tafila Technical University, Tafila, Jordan
5.
Practicing Dentist, Rabia Dental Hospital, Hyderabad, India

Received: 29 July 2023 Revised: 27 September 2023 Accepted: 08 October 2023 Published: 06 November 2023
MSC : 03C65, 26A33, 34A08

The susceptible, exposed, infected, quarantined and vaccinated (SEIQV) population is accounted for in a mathematical model of COVID-19. This model covers the therapy for diseased people as well as therapeutic measures like immunization for susceptible people to enable understanding of the dynamics of the disease's propagation. Each of the equilibrium points, i.e., disease-free and endemic, has been proven to be globally asymptotically stable under the assumption that $ \mathscr{R}_0 $ is smaller or larger than unity, respectively. Although vaccination coverage is high, the basic reproduction number depends on the vaccine's effectiveness in preventing disease when $ \mathscr{R}_0 > 0 $. The Jacobian matrix and the Routh-Hurwitz theorem are used to derive the aforementioned analysis techniques. The results are further examined numerically by using the standard second-order Runge-Kutta (RK2) method. In order to visualize the global dynamics of the aforementioned model, the proposed model is expanded to examine some piecewise fractional order derivatives. We may comprehend the crossover behavior in the suggested model's illness dynamics by using the relevant derivative. To numerical present the results, we use RK2 method.
- crossover behavior,
- reproduction number,
- SEIQV model,
- numerical solution,
- RK2 method,
- fractional order
Citation: Mdi Begum Jeelani, Abeer S Alnahdi, Rahim Ud Din, Hussam Alrabaiah, Azeem Sultana. Mathematical model to investigate transmission dynamics of COVID-19 with vaccinated class[J]. AIMS Mathematics, 2023, 8(12): 29932-29955. doi: 10.3934/math.20231531

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Abstract

The susceptible, exposed, infected, quarantined and vaccinated (SEIQV) population is accounted for in a mathematical model of COVID-19. This model covers the therapy for diseased people as well as therapeutic measures like immunization for susceptible people to enable understanding of the dynamics of the disease's propagation. Each of the equilibrium points, i.e., disease-free and endemic, has been proven to be globally asymptotically stable under the assumption that $ \mathscr{R}_0 $ is smaller or larger than unity, respectively. Although vaccination coverage is high, the basic reproduction number depends on the vaccine's effectiveness in preventing disease when $ \mathscr{R}_0 > 0 $. The Jacobian matrix and the Routh-Hurwitz theorem are used to derive the aforementioned analysis techniques. The results are further examined numerically by using the standard second-order Runge-Kutta (RK2) method. In order to visualize the global dynamics of the aforementioned model, the proposed model is expanded to examine some piecewise fractional order derivatives. We may comprehend the crossover behavior in the suggested model's illness dynamics by using the relevant derivative. To numerical present the results, we use RK2 method.

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