A numerical study of COVID-19 epidemic model with vaccination and diffusion

Ahmed Alshehri; Saif Ullah; Ahmed Alshehri; Saif Ullah

doi:10.3934/mbe.2023215

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4643-4672. doi: 10.3934/mbe.2023215

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A numerical study of COVID-19 epidemic model with vaccination and diffusion

Ahmed Alshehri ¹,
Saif Ullah ^{2
,
,}

1.
Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan

Academic Editor: Jesús Martín Vaquero

Received: 01 November 2022 Revised: 15 December 2022 Accepted: 17 December 2022 Published: 28 December 2022

The coronavirus infectious disease (or COVID-19) is a severe respiratory illness. Although the infection incidence decreased significantly, still it remains a major panic for human health and the global economy. The spatial movement of the population from one region to another remains one of the major causes of the spread of the infection. In the literature, most of the COVID-19 models have been constructed with only temporal effects. In this paper, a vaccinated spatio-temporal COVID-19 mathematical model is developed to study the impact of vaccines and other interventions on the disease dynamics in a spatially heterogeneous environment. Initially, some of the basic mathematical properties including existence, uniqueness, positivity, and boundedness of the diffusive vaccinated models are analyzed. The model equilibria and the basic reproductive number are presented. Further, based upon the uniform and non-uniform initial conditions, the spatio-temporal COVID-19 mathematical model is solved numerically using finite difference operator-splitting scheme. Furthermore, detailed simulation results are presented in order to visualize the impact of vaccination and other model key parameters with and without diffusion on the pandemic incidence. The obtained results reveal that the suggested intervention with diffusion has a significant impact on the disease dynamics and its control.
- space-time COVID-19 transmission model,
- finite difference operator-splitting scheme,
- existence and uniqueness,
- numerical simulation
Citation: Ahmed Alshehri, Saif Ullah. A numerical study of COVID-19 epidemic model with vaccination and diffusion[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4643-4672. doi: 10.3934/mbe.2023215

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Abstract

The coronavirus infectious disease (or COVID-19) is a severe respiratory illness. Although the infection incidence decreased significantly, still it remains a major panic for human health and the global economy. The spatial movement of the population from one region to another remains one of the major causes of the spread of the infection. In the literature, most of the COVID-19 models have been constructed with only temporal effects. In this paper, a vaccinated spatio-temporal COVID-19 mathematical model is developed to study the impact of vaccines and other interventions on the disease dynamics in a spatially heterogeneous environment. Initially, some of the basic mathematical properties including existence, uniqueness, positivity, and boundedness of the diffusive vaccinated models are analyzed. The model equilibria and the basic reproductive number are presented. Further, based upon the uniform and non-uniform initial conditions, the spatio-temporal COVID-19 mathematical model is solved numerically using finite difference operator-splitting scheme. Furthermore, detailed simulation results are presented in order to visualize the impact of vaccination and other model key parameters with and without diffusion on the pandemic incidence. The obtained results reveal that the suggested intervention with diffusion has a significant impact on the disease dynamics and its control.

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