Threshold dynamics of HCV model with cell-to-cell transmission and a non-cytolytic cure in the presence of humoral immunity

Pan, Sonjoy; Chakrabarty, Siddhartha P.

doi:10.1016/j.cnsns.2018.02.010

Cited by 48 publications

(24 citation statements)

References 34 publications

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“…The dynamics of HCV infection with both viral and cellular transmissions and cure rate in the presence of humoral immune response was analyzed in [24]. This model assumed that subsequent to the entry of the virions, the humoral immune response is stimulated to instantaneously generate B cells.…”

Section: Mathematical Modelmentioning

confidence: 99%

Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C

Pan

Chakrabarty

2020

Indian J Pure Appl Math

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Section: Mathematical Modelmentioning

confidence: 99%

Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C

Pan

Chakrabarty

2020

Indian J Pure Appl Math

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“…There are a few model studies on hepatitis C; Curve regression model, SEACR dynamic model and multi-stage SEIR model, which are widely used [11,[17][18][19]. Our previous study explored the principle of a Susceptiblehttps://www.cambridge.org/core/terms.…”

Section: Introductionmentioning

confidence: 99%

The transmissibility of hepatitis C virus: a modelling study in Xiamen City, China

Wang

Zhao

Wang³

et al. 2020

Epidemiol. Infect.

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This study is aimed at estimating the transmissibility of hepatitis C. The data for hepatitis C cases were collected in six districts in Xiamen City, China from 2004 to 2018. A population-mixed Susceptible-Infectious-Chronic-Recovered (SICR) model was used to fit the data and the parameters of the model were calculated. The basic reproduction number (R 0) and the number of newly transmitted cases by a primary case per month (MNI) were adopted to quantitatively assess the transmissibility of HCV. Eleven curve estimation models were employed to predict the trends of R 0 and MNI in the city. The SICR model fits the reported HCV data well (P < 0.01). The median R 0 of each district in Xiamen is 0.4059. R 0 follows the Cubic model curve, the Compound curve, and the Power function curve. The median MNI of each district in Xiamen is 0.0020. MNI follows the Cubic model curve, the Compound curve, and the Power function curve. The https://www.cambridge.org/core/terms.

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“…Nowak and Bangham have formulated the basic virus dynamics model that characterizes the dynamics of viruses with susceptible host cells and infected cells. In fact, this model has given opportunities to develop many models that describe the within‐host dynamics of different viruses such as human immunodeficiency virus (HIV), hepatitis B virus (HBV), hepatitis C virus (HCV), and human T‐cell leukemia virus (HTLV) . The basic model presented in Nowak and Bangham has been extended by assuming that the time from the contact of viruses and susceptible cells to the death of the cells is modeled by dividing the process into n short stages I 1 → I 2 →....→ I n as the following:

({, \begin{matrix} left \\ array \dot{S} (t) = ¥ (S (t)) - ℵ_{11} (S (t)) ℵ_{12} (V (t)), \\ array İ_{1} (t) = ℵ_{11} (S (t)) ℵ_{12} (V (t)) - b_{1} ℏ_{1} (I_{1} (t)), \\ array İ_{2} (t) = d_{1} ℏ_{1} (I_{1} (t)) - b_{2} ℏ_{2} (I_{2} (t)), \\ array İ_{3} (t)... \end{matrix})

…”

Section: Introductionmentioning

confidence: 99%

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

Ełaiw

AlShamrani

2019

Math Methods in App Sciences

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This paper studies an (n+4)-dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infectedsusceptible and virus-susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions. KEYWORDS adaptive immune response, global stability, Lyapunov function, multistaged infected cells, viral and cellular infections CLASSIFICATION 34D20; 34D23; 37N25; 92B05

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Threshold dynamics of HCV model with cell-to-cell transmission and a non-cytolytic cure in the presence of humoral immunity

Cited by 48 publications

References 34 publications

Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C

Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C

The transmissibility of hepatitis C virus: a modelling study in Xiamen City, China

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

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