Dynamics of Hepatitis C Virus Infection: Mathematical Modeling and Parameter Estimation

Rihan, Fathalla A.; Sheek-Hussein, Mohamud; Tridane, Abdessamad; Yafia, Radouane

doi:10.1051/mmnp/201712503

Cited by 23 publications

(12 citation statements)

References 27 publications

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“…Since modelling of dynamic systems by ODE cannot precisely describe experimental and measurement data [13], FDE are now being extensively applied to study and control the dynamics of infectious diseases. In [14], Rihan et al analyse a fractional model for HCV dynamics in the presence of interferon-α (IFN) treatment. According to numerical simulations and the real data, they also confirm that the FDE are better descriptors of HCV systems than ODE.…”

Section: (): V-volmentioning

confidence: 99%

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Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate

et al. 2021

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We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response, and the memory effect is described by the Caputo fractional derivative. Stability and instability of equilibrium points are determined in terms of the basic reproduction number. Furthermore, a fractional optimal control system is formulated and the best strategy for minimizing the spread of the disease into the population is determined through numerical simulations based on the derived necessary optimality conditions.

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Section: (): V-volmentioning

confidence: 99%

“…Remark 2 While it is not necessary to use quadratic controls in the cost functional (14), this is the most common way to penalize the use of controls: see, e.g. [36] or [37].…”

Section: Fractional Optimal Control Of the Modelmentioning

confidence: 99%

Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate

et al. 2021

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“…Mathematical models of in vitro viral infections help provide accurate estimations of the rates of the processes affecting virus-cell interactions and time scales on which these processes occur. These measures have been determined for a number of viruses, including HIV-1 and simian-human immunodeficiency virus [17][18][19][20][21][22], hepatitis C virus [23][24][25][26][27], poliovirus [28][29][30], influenza A virus and its various strains [31][32][33][34][35][36][37], West Nile virus [38] and Ebola virus [39,40]. Specifically in [10,20,21,32,36], different aspects of viral replication cycle were considered to provide a comprehensive description of in vitro viral spread.…”

Section: Introductionmentioning

confidence: 99%

Modelling Degradation and Replication Kinetics of the Zika Virus In Vitro Infection

Bernhauerová

Rezelj

Vignuzzi

2020

Viruses

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Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus–host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.

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“…One advantage of the fractional-order differential equation is that they provide a powerful instrument for incorporation of memory and hereditary properties of the systems as opposed to the integer-order models, where such effects are neglected or difficult to incorporate. In addition, when fitting data, the fractional models have one more degree of freedom than the integer-order model (see [21]). Based on these advantages, some authors have developed interesting applications to investigate the dynamics of such fractionalorder models with systems of memory [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

A Fractional‐Order Model for Zika Virus Infection with Multiple Delays

2019

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Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays τ1, τ2, and τ3. The model undergoes a Hopf bifurcation at the threshold parameters τ1∗, τ2∗, and τ3∗. Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model.

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Dynamics of Hepatitis C Virus Infection: Mathematical Modeling and Parameter Estimation

Cited by 23 publications

References 27 publications

Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate

Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate

Modelling Degradation and Replication Kinetics of the Zika Virus In Vitro Infection

A Fractional‐Order Model for Zika Virus Infection with Multiple Delays

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