Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

Macías‐Díaz, Jorge E.; Ahmed, Nauman; Rafiq, Muhammad

doi:10.3390/math7121157

Cited by 25 publications

(15 citation statements)

References 44 publications

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“…The same type of approximation is used for the diffusion at the third step of the splitting process. In such way, the following are algebraically simplified forms of the finite-difference approximations for equations (12):…”

Section: Methodsmentioning

confidence: 99%

“…It is worth pointing out that most of the deterministic models available in the literature are based on the use of ordinary differential equations, which means that a constant diffusion among the population is assumed. However, there are approaches which hinge on the use of systems of partial differential equations in order to account for imperfect mixing modelled by diffusion 11‐14 . Here, we focus our attention on the spreading in populations where the diffusion is nonconstant.…”

Section: Introductionmentioning

confidence: 99%

“…However, there are approaches which hinge on the use of systems of partial differential equations in order to account for imperfect mixing modelled by diffusion. [11][12][13][14] Here, we focus our attention on the spreading in populations where the diffusion is nonconstant.…”

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confidence: 99%

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Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

Macías‐Díaz

Ahmed

Jawaz

et al. 2020

Math Methods in App Sciences

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In this work, we propose a time‐delayed reaction–diffusion model to describe the propagation of infectious viral diseases like COVID‐19. The model is a two‐dimensional system of partial differential equations that describes the interactions between disjoint groups of a human population. More precisely, we assume that the population is conformed by individuals who are susceptible to the virus, subjects who have been exposed to the virus, members who are infected and show symptoms, asymptomatic infected individuals, and recovered subjects. Various realistic assumptions are imposed upon the model, including the consideration of a time‐delay parameter which takes into account the effects of social distancing and lockdown. We obtain the equilibrium points of the model and analyze them for stability. Moreover, we examine the bifurcation of the system in terms of one of the parameters of the model. To simulate numerically this mathematical model, we propose a time‐splitting nonlocal finite‐difference scheme. The properties of the model are thoroughly established, including its capability to preserve the positivity of solutions, its consistency, and its stability. Some numerical experiments are provided for illustration purposes.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

Macías‐Díaz

Ahmed

Jawaz

et al. 2020

Math Methods in App Sciences

Self Cite

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show abstract

“…It is worth pointing out that most of the deterministic models available in the literature are based on the use of ordinary differential equations, which means that a constant diffusion among the population is assumed. However, there are approaches which hinge on the use of systems of partial differential equations in order to account for imperfect mixing modelled by diffusion [12] , [13] , [14] , [15] . In the present work, we focus our attention to the spreading of COVID-19 in populations where the diffusion is constant.…”

Section: Introductionmentioning

confidence: 99%

Design of a nonlinear model for the propagation of COVID-19 and its efficient nonstandard computational implementation

Rafiq

Macías‐Díaz

Raza

et al. 2021

Applied Mathematical Modelling

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Highlights Mathematical considerations of a SEIQR model to describe the propagation of COVID-19 are proposed. We derive analytically the reproductive number and the equilibria with and without COVID-19. Necessary and sufficient conditions for the stability of the equilibria are mathematically established. An efficient nonstandard method to solve the continuous problem is proposed and analyzed. The numerical simulations confirm the analytical and numerical results derived in this work.

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“…The proposed epidemic model is also subject, in the most general framework, to feedback vaccination and treatment controls. It is tested through numerical worked and tested examples under parameterizations related to the recent COVID-19 pandemic, which is exhaustively studied in the medical and computational background literature; see, for instance, [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] and references therein. Therefore the current study is of important potential interest, although nowadays there is no yet an approved vaccine for COVID-19 to be applied on the population.…”

Section: Introductionmentioning

confidence: 99%

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

Sen¹,

Ibeas

2021

Adv Differ Equ

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In this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.

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Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

Cited by 25 publications

References 44 publications

Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

Design of a nonlinear model for the propagation of COVID-19 and its efficient nonstandard computational implementation

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

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