Numerical and bifurcation analysis of spatio-temporal delay epidemic model

Jawaz, Muhammad; Rehman, M. A.; Ahmed, Nauman; Băleanu, Dumitru; Rafiq, Muhammad

doi:10.1016/j.rinp.2021.103851

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…Samsuzzoha et al 2 formulated a diffusive transmission model to analyze the dynamics of influenza with spatial and temporal effects. Jawaz et al 3 have investigated the transmission dynamics and control of HIV/AIDS using a mathematical spatio-temporal epidemic model. They proposed a non-standard finite difference numerical scheme for the numerical solution of the model due to its ability to preserve positivity.…”

Section: Introductionmentioning

confidence: 99%

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques

Khan

Ullah

Altanji

et al. 2023

Sci Rep

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In this paper, a new spatio-temporal model is formulated to study the spread of coronavirus infection (COVID-19) in a spatially heterogeneous environment with the impact of vaccination. Initially, a detailed qualitative analysis of the spatio-temporal model is presented. The existence, uniqueness, positivity, and boundedness of the model solution are investigated. Local asymptotical stability of the diffusive COVID-19 model at steady state is carried out using well-known criteria. Moreover, a suitable nonlinear Lyapunov functional is constructed for the global asymptotical stability of the spatio-temporal model. Further, the model is solved numerically based on uniform and non-uniform initial conditions. Two different numerical schemes named: finite difference operator-splitting and mesh-free operator-splitting based on multi-quadratic radial basis functions are implemented in the numerical study. The impact of diffusion as well as some pharmaceutical and non-pharmaceutical control measures, i.e., reducing an effective contact causing infection transmission, vaccination rate and vaccine waning rate on the disease dynamics is presented in a spatially heterogeneous environment. Furthermore, the impact of the aforementioned interventions is investigated with and without diffusion on the incidence of disease. The simulation results conclude that the random motion of individuals has a significant impact on the disease dynamics and helps in setting a better control strategy for disease eradication.

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Section: Introductionmentioning

confidence: 99%

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques

Khan

Ullah

Altanji

et al. 2023

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Based on parameters in the system, sensitivity analysis of the reproduction number has been investigated. HIV/AIDS is incurable for human beings mentioned in [ 26 ], and a diffusive compartmental model of HIV/AIDS has been proposed with a delay process. The proposed scheme had the advantage of producing a positive solution.…”

Section: Diffusive Epidemic Modelsmentioning

confidence: 99%

An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

et al. 2021

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An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Furthermore, the scheme’s stability for the general type of parabolic equation with source term is proved by employing von Neumann stability analysis. Furthermore, the consistency of the scheme is verified for the category of susceptible individuals. In addition to this, the convergence of the proposed scheme is discussed for the considered mathematical model.

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A novel approach to investigate the stability analysis and the dynamics of reaction–diffusion SVIR epidemic model

Salman,

Mohd,

Muhammad

2023

Communications in Nonlinear Science and Numerical Simulation

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Numerical and bifurcation analysis of spatio-temporal delay epidemic model

Cited by 4 publications

References 23 publications

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques

An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

A novel approach to investigate the stability analysis and the dynamics of reaction–diffusion SVIR epidemic model

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