The dynamics of fractional order Hepatitis B virus model with asymptomatic carriers

Gul, Nadia; Bilal, Rubi; Algehyne, Ebrahem A.; Alshehri, Maryam G.; Khan, Muhammad Altaf; Chu, Yu‐Ming; Islam, Saeed

doi:10.1016/j.aej.2021.02.057

Cited by 38 publications

(23 citation statements)

References 41 publications

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“…By the help of the presented technique, we can get some simulations of this model under study (6), and this will be done through Figures 24-27 as following:…”

Section: àTmentioning

confidence: 99%

“…The importance and the very wide range of applications of the fractional models (described by the fractional derivatives) directed mathematicians and physicians to study the numerical and approximate solutions for fractional differential equations (FDEs) using many approximate techniques. We have a lot of examples for the applications of such kind of equations in our life as in fluid mechanics, [1][2][3] image processing, 4 biology, [5][6][7][8][9][10][11][12] engineering, [13][14][15] physics, [16][17][18][19][20] electrical circuits and filters, [21][22][23][24][25][26][27][28][29][30][31][32] and others. [33][34][35][36] Definition 1.…”

Section: Introductionmentioning

confidence: 99%

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Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

Khader

Gómez-Aguilar²,

Adel

2021

Circuit Theory & Apps

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In the presented work, we present an accurate procedure, which is the spectral method, to find a solution to a certain class of the very important fractional (described by the Liouville-Caputo sense) models of the electrical RL, RC, and RLC circuits. This method is collocated using some important advantages of the generalized Legendre polynomials to obtain the numerical solution for these models. Besides, we compare the approximate solutions that are obtained using the presented technique for the proposed models with their exact solution in the given numerical examples.

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“…By the help of the presented technique, we can get some simulations of this model under study (6), and this will be done through Figures 24-27 as following:…”

Section: àTmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

Khader

Gómez-Aguilar²,

Adel

2021

Circuit Theory & Apps

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show abstract

“…Theorem 9. Given an optimal control u * and solutions S * , I * , R * , D * of corresponding state system (25) that minimizes J(u * ) over U, then there exist adjoint variables λ…”

Section: Characterization Of Optimal Controlmentioning

confidence: 99%

“…Mathematical epidemiological models have been demonstrated to be vital tools that can help understand this disease and provide solutions to phenomena that are complex to measure in the field. e literature on epidemic models on the spread of infectious diseases is quite substantial and it also contains some recent research works (see [24][25][26][27][28]). In [24], a new definition of a fractional derivative with nonsingular kernel in the sense of Caputo was proposed, which generalized various forms existing in the literature.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of HSV-2 in the Presence of Optimal Counseling and Education among Prisoners

Mhlanga

2021

Discrete Dynamics in Nature and Society

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Herpes simplex virus type 2 (HSV-2) is one of the major sexually transmitted infections in sub-Saharan prisons and the major driver of HIV. In this paper, we propose and analyze a basic mathematical model for the spread of HSV-2 in prisons. We compute the basic reproduction number and demonstrate that it is a sharp threshold for disease dynamics. The impacts of counseling and education of HSV-2-infected individuals are examined. Equilibrium states of the model are determined and their stability is investigated. The basic model is then extended to incorporate a time-dependent intervention strategy. The aim of the control is tied to reducing the number of infectious individuals through early detection, education, and counseling of the infected. The Pontryagin’s Maximum Principle is used to characterize the optimal level of the control, and the resulting optimality system is solved numerically.

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“…Some related literature and works regarding the Hepatitis are considered in [7]- [11]. In addition, Gul et al [12] studied symptomatic carrier effect on the dynamics of hepatitis B virus. Saad et al [13] studied hepatitis C virus by fractional order modeling.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of Transmission of Hepatitis B and C Viruses with External Source of disease by Mathematical Model

Mohsen

Hattaf

Al-Husseiny

2021

Preprint

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In this paper, we develop a deterministic mathematical model of the Hepatitis B and C viruses transmission in population, which allows transmission by two way vertical such as from pregnant mother to fetus and horizontal. Also, by two way through direct contact and due to the external source of infective such as blood transfusion or other. In reality, we know that there is a vaccination against the hepatitis B virus but so far, there is no vaccine against the hepatitis C virus this is why it is considered more dangerous than hepatitis B. Furthermore, we study the vaccination effect with the failure in the vaccine. We propose an SVIBICR model using a system of ordinary differential equations. First the major basic analysis, like the uniqueness, boundedness and positivity of the solution for the proposed model. Second the existence of all biological equilibrium points, basic reproduction number and stability analysis of all equilibrium points. The numerical simulation indicated to confirm the analytic results and the government must apply all control strategies in combating hepatitis virus at short periods of time.

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The dynamics of fractional order Hepatitis B virus model with asymptomatic carriers

Cited by 38 publications

References 41 publications

Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

Dynamics of HSV-2 in the Presence of Optimal Counseling and Education among Prisoners

Dynamical Analysis of Transmission of Hepatitis B and C Viruses with External Source of disease by Mathematical Model

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