A Mathematical Analysis and Modelling of Hepatitis B Model with Non-Integer Time Fractional Derivative

Farman, Muhammad; Ahmad, Aqeel; Saleem, M. Umer; Hafeez, Amina

doi:10.26713/cma.v10i3.1154

Cited by 8 publications

(3 citation statements)

References 8 publications

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“…Fractional-order differential equations are potential tools to describe the effect of memory and hence used to model infectious diseases. Fractional-order differential equations models of HBV includes [14][15][16][17] and [18] just to mention a few.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection

2023

Eur. J. Math. Appl.

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Hepatitis B virus infection shall remain a public health concern in many developed and developing countries. In this paper, we formulate and analyse a simple fuzzy fractional model of HBV infection to assess the dynamics of the disease using fractional-order differential equations. To analyse the effect of the initial transmission of the disease, we computed the basic reproduction number R 0 , and used it to perform stability analysis. The results show that the disease-free and the endemic equilibrium are globally stable with respect to the value of R 0 . Numerical simulations were performed to study the variations of each sub-population with respect to time at different order (α). In general, results for the fractional model show that as the order (α) increases, the population of the susceptible and exposed individuals decreases. In contrast, the other sub-populations increase with an increase in α. Further results from the numerical analysis show that increase in α, decreases the diameter of the fuzzy triangular solutions for the susceptible and exposed individuals in the fuzzy fractional model.

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Section: Introductionmentioning

confidence: 99%

Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection

2023

Eur. J. Math. Appl.

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“…Farman et al analyzed an epidemic model for HBV infection consists of differential equations in Caputo sense. In this model, the population is assumed to be constant in the absence of the disease [6]. In this study we propose a more general model using fractional differential equations of Caputo sense considering newborn vaccination and also vaccination of susceptible individuals regardless of age.…”

Section: Introductionmentioning

confidence: 99%

A fractional order model of hepatitis B transmission under the effect of vaccination

Demirci

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this paper we present a fractional order mathematical model to explain the spread of Hepatitis B Virus (HBV) in a non-constant population. The model we propose includes both vertical and horizontal transmission of the infection and also vaccination at birth and vaccination of the susceptible class. We also use a frequency dependent transmission rate in the model. We give results on existence of equilibrium points of the model and analyze the stability of the disease-free equilibrium. Finally, numerical simulations of the model are presented.

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“…So far, some fractional order models about HBV have been set up [20][21][22][23][24][25]. Papers [20][21][22] considered the epidemic transmission SEIR model of HBV. In paper [23], a withinhost fractional order HBV model was proposed:…”

Section: Introductionmentioning

confidence: 99%

Analysis and Simulation of a Fractional Order Optimal Control Model for HBV

Yang

et al. 2020

Journal of Function Spaces

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In this paper, we propose a fractional optimal control model of anti-HBV infection based on saturation incidence and logistic proliferation of uninfected cells for the first time. We derive the basic reproduction number R0 and the cytotoxic T lymphocyte immune response reproductive number R1 and give the stable analysis based on R0 and R1. We analyse the optimal control condition and give two optimal control strategies about entecavir monotherapy and combination therapy of traditional Chinese medicine and entecavir with different fractional orders by simulation. The simulation shows that combination therapy may be a good choice in anti-HBV infection therapy. We also compare the objective function values of the optimal control strategies with other constant control strategies; the comparison shows that the optimal therapy can get similar or better treatment effect with less drug dose and side effects.

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A Mathematical Analysis and Modelling of Hepatitis B Model with Non-Integer Time Fractional Derivative

Cited by 8 publications

References 8 publications

Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection

Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection

A fractional order model of hepatitis B transmission under the effect of vaccination

Analysis and Simulation of a Fractional Order Optimal Control Model for HBV

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