Chronic hepatitis B infection and HBV DNA-containing capsids: Modeling and analysis

Manna, Kalyan; Chakrabarty, Siddhartha P.

doi:10.1016/j.cnsns.2014.08.036

Cited by 54 publications

(40 citation statements)

References 35 publications

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“…The model proposed and studied here generalizes some existence results in the literatures. 10,18,19 We have obtained two threshold values, ℜ 0 and ℜ 1 , which determine the existence of the equilibria of the model. Moreover, by constructing Lyapunov functionals, we have proved that the global stabilities of the equilibria of the model are completely determined by the two threshold values.…”

Section: Discussionmentioning

confidence: 99%

“…Since the classical virus dynamic model that includes three ordinary differential equations has been proposed, 1,2 many extended virus dynamic models for studying infectious diseases have been constructed and studied. Particularly, a number of researchers have devoted their efforts in studying the global stability of those mathematical models [3][4][5][6][7][8][9][10] and references therein. For example, Manna and Chakrabarty 10 proposed and analyzed an hepatitis B virus (HBV) infection model with HBV DNA-containing capsids.…”

Section: Introductionmentioning

confidence: 99%

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Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

Geng

2018

Math Methods in App Sciences

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The goal of this paper is to investigate the dynamical behavior of a general nonlinear delayed viral infection model with cytotoxic T lymphocyte (CTL) immune response. The intrinsic growth rate of uninfected hepatocytes, incidence rate of infection, removal rate of infected hepatocytes and capsids, production and removal rate of viruses, activation rate of CTLs, and decay rate of CTLs are given by general nonlinear functions with a set of conditions on these general nonlinear functions, which make the analysis of the model more difficult. The global threshold dynamics with respect to the reproduction numbers for viral infection ℜ 0 and for CTL immune response ℜ 1 have been presented by constructing suitable Lyapunov functionals. Numerical simulations are carried out for a model with specific forms of the general functions to confirm the theoretical results and show that both the numerical and theoretical results are consistent.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

Geng

2018

Math Methods in App Sciences

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“…Pengembangan model dengan menggunakan tingkat infeksi nonlinear juga dipaparkan oleh Hattaf dan Yousfi [5] dan Zhang et al [6]. Manna dan Chakrabarty [7] mengembangkan model dengan memperhatikan populasi kapsid DNA-VHB. Pengembangan tersebut didasari karena kapsid DNA-VHB, yang merupakan cikal bakal virion, juga berpengaruh dalam tercapainya infeksi akut maupun kronis.…”

Section: Pendahuluanunclassified

“…Pada sebagian besar model VHB, termasuk model [3], [4], [5], [6], [7], tidak mencantumkan proses adsorpsi virus. Proses adsorpsi adalah proses menempelnya virus pada dinding sel, yang dilanjutkan dengan penetrasi materi genetik virus ke dalam sel.…”

Section: Pendahuluanunclassified

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Model Matematika Infeksi Virus Hepatitis B dengan Adsorpsi

Sari

2017

JMI

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AbstrakInfeksi Hepatitis B terus berlanjut menjadi masalah kesehatan global. Termotivasi hal tersebut, kami memperkenalkan model matematika infeksi virus Hepatitis B (VHB). Berangkat dari fakta bahwa tingkat infeksi bilinear tidak selalu benar dalam menggambarkan interaksi virus dengan sel rentan di kehidupan nyata, maka digunakan tingkat infeksi nonlinear pada model. Fase adsorpsi dalam proses infeksi virus dipertimbangkan dalam model sebagai salah satu penyebab penurunan populasi partikel virus. Pada model, populasi partikel virus dibagi menjadi dua kompartemen yaitu, virion dan kapsid intraseluler yang mengandung DNA-VHB. Populasi sel dibagi menjadi dua kompartemen yaitu, sel rentan dan sel terinfeksi. Perilaku dinamik model dianalisis dengan menentukan titik kesetimbangan bebas infeksi dan endemik, bilangan reproduksi dasar, serta kestabilan lokal dari titik kesetimbangan tersebut. Hasil analisis dan simulasi numerik menunjukkan bahwa stabilitas titik kesetimbangan bebas infeksi maupun endemik bergantung pada bilangan reproduksi dasar. Kata kunci: adsorpsi, analisis dinamik, bilangan reproduksi dasar, model matematika, virus Hepatitis B. AbstractHepatitis B infection continues to be a global health problem. Motivated with this, we introduce a mathematical model of hepatitis B virus infection (HBV). Based on the fact that bilinear infection rate is not always true in describing viral interactions with susceptible cells in real life, we use nonlinear infection rate on the model. The adsorption phase in the viral infection process is considered in the model as one of the causes of the population decline in viral particles. In the model, the viral particle population is divided into two compartments:, virions and intracellular capsid containing HBV-DNA. Cell population is divided into two compartments: susceptible cells and infected cells. The dynamic behavior of the model is analyzed by determining the free-infection equilibrium point and endemic equilibrium point, the basic reproduction number, and the local stability of the equilibrium points. The analysis and numerical simulation results show that the stability of the equilibriia, free-infection or endemic, depend on the basic reproduction number.

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A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study

Manna

Hattaf²

2022

Math Methods in App Sciences

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In this paper, we formulate a generalized hepatitis B virus (HBV) infection model with two modes of infection transmission and adaptive immunity and investigate its dynamical properties. Both the virus‐to‐cell and cell‐to‐cell infection transmissions are modeled by general functions which satisfy some biologically motivated assumptions. Furthermore, the model incorporates three distributed time delays for the production of active infected hepatocytes, mature capsids, and virions. The well‐posedness of the proposed model is established by showing the non‐negativity and boundedness of solutions. Five equilibria of the model are identified in terms of five threshold parameters R0,0.1emR1,0.1emR2,0.1emR3$$ {R}_0,{R}_1,{R}_2,{R}_3 $$, and R4$$ {R}_4 $$. Further, the global stability analysis of each equilibrium under certain conditions is carried out by employing suitable Lyapunov function and LaSalle's invariance principle. Finally, we present an example with numerical simulations to illustrate the applicability of our study. Nonetheless, the results obtained in this study are valid for a wide class of HBV infection models.

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Chronic hepatitis B infection and HBV DNA-containing capsids: Modeling and analysis

Cited by 54 publications

References 35 publications

Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

Threshold dynamics of a delayed virus infection model with cellular immunity and general nonlinear incidence

Model Matematika Infeksi Virus Hepatitis B dengan Adsorpsi

A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study

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