Mathematical models of the interrelated dynamics of hepatitis D and B

Packer, Aaron; Forde, Jonathan E.; Hews, Sarah; Kuang, Yang

doi:10.1016/j.mbs.2013.10.004

Cited by 18 publications

(28 citation statements)

References 31 publications

(46 reference statements)

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“…As a result, the proliferation of uninfected cells may be density-dependent and can follow the logistic growth law. Some different dynamical behaviors were found in [10,[30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Zhuang

2017

MCA

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Abstract:Viruses have important influences on human health: they not only cause some common diseases, but also cause serious illnesses. Moreover, the conventional medicines usually fail to prevent or treat them, and viral infections are hard to treat because viruses live inside the body's cells. However, some mathematical models can help to understand the viral transmission mechanism and control viral diseases. In this paper, a delayed viral infection model with spatial diffusion and logistic growth is presented. The asymptotic stability of nonnegative uniform steady states is investigated by utilizing the linearized method and constructing the proper Lyapunov functional, respectively. The existence of Hopf bifurcation from the positive equilibrium point is established by analyzing the corresponding characteristic equation and the direction of bifurcation, and the properties of bifurcating periodic solutions are derived by the aid of the normal form theory for partial functional differential equations. Then, the cross-diffusion system is introduced. Furthermore, some numerical simulations are carried out and discussions are given.

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“…As a result, the proliferation of uninfected cells may be density-dependent and can follow the logistic growth law. Some different dynamical behaviors were found in [10,[30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Zhuang

2017

MCA

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“…In an attempt to show the important role that HBV plays in HDV dynamics, Packer et al in reference [2], start with presenting a model for HBV alone, they considered three distinct population concentrations within the liver: healthy hepatocytes (x), infected hepatocytes (y), and free HBV virions (v). The dynamics are governed by the following set of assumptions: 1.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Virions die at a specified rate. Where the production of virions and the death of virions and infected cells occur at constant per capita rates, and since the time scale of virion production is much shorter than the time scale of the hepatocytes life-cycle, Aaron Packer et al [2] assume that the free virus population is in quasi-steady-state with the infected cell population. Thus, the free virions v is proportional to the infected hepatocytes y (v = γ µ y), then the HBV model is first simplified into a planar system, by replacing the incidence function…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Studies suggest HDV infects around 70.000 people in the United States who have been already affected with HBV, but it had also been noted that region, has relatively low incidence rate of HDV which could be reasoned due to a low incidence rate of HBV as well as immunization provided against viral infection linked with Hepatitis B and D. Whereas, some countries in Middle east, Eastern Europe, central Africa and south America encounter high incidence rate of infection around 1.4 million and 1.9 million of people are affected with Hepatitis D [1,5]. In this article, it is suggested to follow new optimal control strategies associated with two types of inhibitors for HBV and HDV based on a HBV-HDV coinfection models developed in reference [2]. These two models have describe the interaction of HBV and HDV infection, one with and one without infected hepatocyte replication.…”

Section: Introductionmentioning

confidence: 99%

“…These two models have describe the interaction of HBV and HDV infection, one with and one without infected hepatocyte replication. Packer et al in reference [2], consider lamivudine as treatment for blocking HBV reproduction, and showed that HDV infection is sustained during lamivudine treatment only if the HBV infected cell population does not become extinct. For a more general view, when any other type of available treatments is used, the subject is extended here towards an optimal control problem, by introducing into two pre-validated models, two control functions representing the inhibition of HBV and HDV infection respectively.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Effectiveness of an Optimal Antiviral Bitherapy in HBV-HDV Coinfection Model

Zakary¹,

Rachik²,

Elmouki³

2015

IJCA

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In this work, dynamics between uninfected cells, HBV infected cells, HDV infected cells and HBV-HDV coinfected cells are studied, based on two systems of four ordinary differential equations. The two pre-validated differential systems which are considered in this paper, are respectively associated to the case when there is no infected cell proliferation of HBV, HDV and HBV-HDV coinfected populations, and to the case when there is an infected cell proliferation. Optimal control theory is applied to these two systems. Seeking to reduce the infected groups and increase the number of uninfected hepatocytes, two control functions are introduced in the two mathematical models, representing two types of treatments. In fact, the main goal of this work is to discuss the effectiveness of an antivial bitherapy that could include any inhibitor for HDV infection such as lonafarnib, with other classical treatments often used against HBV infection such as interferons, lamivudine, adefovir and entecavir. The optimal controls are characterized in terms of the optimality system, which is solved numerically using an iterative method with a progressive-regressive RungeKutta fourth order scheme with a change of several parameters.

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Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon‐alpha therapy via mathematical modeling

et al. 2014

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There is little information on the early kinetics of hepatitis delta virus (HDV) and hepatitis B surface antigen (HBsAg) during interferon-α therapy. Here a mathematical model was developed and fitted to frequent HDV and HBsAg kinetic data from 10 patients during the first 28 weeks of pegylated-interferon-α2a (peg-IFN) therapy. Three patients achieved a complete virological response (CVR), defined as undetectable HDV 6 months after treatment stopped with loss of HBsAg and anti-HBsAg seroconversion. After initiation of therapy a median delay of 9 days (interquartile range IQR:[5;15]) was observed with no significant changes in HDV level. Thereafter, HDV declined in a biphasic manner, where a rapid first-phase lasting for 25 days (IQR:[23;58]) was followed by a slower or plateau second-phase. The model predicts that the main effect of peg-IFN is to reduce HDV production/release with a median effectiveness of 96% (IQR:[93;99.8]). Median serum HDV half-life (t1/2) was estimated to 2.9 days (IQR:[1.5;5.3]) with pretreatment production and clearance of about 1010 (IQR:[109.8-1010.8]) virions/day. None of the patients with flat 2nd phase in HDV achieved CVR. HBsAg kinetics of decline paralleled the second-phase of HDV decline consistent with HBsAg-productive-infected cells being the main source of production of HDV, with a median t1/2 of 135 days (IQR:[20-460]. The interferon lambda-3 polymorphism (rs12979860) was not associated with kinetic parameters. Conclusions Modeling results provide insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action and its effectiveness. The observation that a flat second phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV-infected patients.

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Mathematical models of the interrelated dynamics of hepatitis D and B

Cited by 18 publications

References 31 publications

Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

Spatiotemporal Dynamics of a Delayed and Diffusive Viral Infection Model with Logistic Growth

On Effectiveness of an Optimal Antiviral Bitherapy in HBV-HDV Coinfection Model

Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon‐alpha therapy via mathematical modeling

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