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

Pan, Sonjoy; Chakrabarty, Siddhartha P.

doi:10.1007/s13226-020-0489-2

Cited by 8 publications

(3 citation statements)

References 37 publications

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“…[9][10][11] As we know, there is currently no effective vaccine against HCV, and research in this area is still ongoing. 12 Thanks to mathematical modeling providing important insights, quite a few models have been introduced to explore this in previous research [13][14][15][16][17][18][19][20] and references therein. Based on all available knowledge of the clinical and population epidemiology of HCV, they provide frameworks in which the maximum information may be drawn and have enriched our understanding of disease dynamics by practical approaches.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear HCV model in deterministic and randomly fluctuating environments

Liu

Wang

et al. 2022

Math Methods in App Sciences

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Two novel deterministic and stochastic nonlinear hepatitis C virus (HCV) models with nonlinear incidence rates as 𝛽S p E, 𝛽S p I, and 𝛽S p C q , containing acute and chronic infections, are developed, and an endeavor to understand their dynamics has been accomplished. For the former model, both the existence of unique equilibria and the sharp sufficient conditions of globally stable equilibria under different cases are established. Whereafter, the efforts taken to detect the asymptotic behaviors around equilibria, the existence of ergodic stationary distribution, and stochastic extinction of the latter model have been supplemented with meticulous theoretical proofs. At last, several numerical examples and discussions are illustrated to sustain and visualize our theoretical results. Compared and analyzed the numerical and theoretical results, we can find that the noise can influence the dynamics of disease and turn the disease from persistence to extinction. Moreover, several control measures are suggested based on our study.

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Section: Introductionmentioning

confidence: 99%

A nonlinear HCV model in deterministic and randomly fluctuating environments

Liu

Wang

et al. 2022

Math Methods in App Sciences

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“…In 2020, a cell-to-cell model with humoral immunity is considered by Mausumi et al [24]. After this, paper [25] further considered the time delay of humoral immunity. In addition, a stochastic HCV infection model with therapy was discussed by paper [26].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, a stochastic HCV infection model with therapy was discussed by paper [26]. However, paper [24][25][26] did not consider fractional order.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Cell-to-Cell Fractional-Order Model with Periodic Immune Response for HCV

Yang

et al. 2021

Symmetry

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In this paper, a Caputo fractional-order HCV Periodic immune response model with saturation incidence, cell-to-cell and drug control was proposed. We derive two different basic reproductive numbers and their relation with infection-free equilibrium and the immune-exhausted equilibrium. Moreover, there exists some symmetry in the relationship between the two equilibria and the basic reproduction numbers. We obtain the global stability of the infection-free equilibrium by using Lyapunov function and the local stability of the immune-exhausted equilibrium. The optimal control problem is also considered and two control strategies are given; one is for ITX5061 monotherapy, the other is for ITX5061 and DAAs combination therapy. Matlab numerical simulation shows that combination therapy has lower objective function value; therefore, it is worth trying to use combination therapy to treat HCV infection.

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Dynamics of an age‐structured multiscale hepatitis C virus model with two infection modes and antibody immune response

Wang,

Zhao,

Wang

2024

Math Methods in App Sciences

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The interference of direct‐acting antiviral agents (DAAs) within various steps of the life cycle of hepatitis C virus (HCV) results in a high cure rate for chronic HCV infection. To accurately quantify the effect of DAAs on treatment and to achieve an optimal drug combination for treatment, we formulate an age‐structured multiscale HCV model. This model incorporates intracellular virus RNA replication process corresponding to the mechanism of drug action, two modes of extracellular virus transmission (virus‐to‐cell infection and cell‐to‐cell infection), and antibody immune response. We prove that the threshold dynamics of the pre‐treatment model is completely determined by the basic reproduction number and the antibody immune reproduction number . Under reasonable assumptions, we obtain long‐term and short‐term approximations for post‐treatment viral loads and identify which approximation performs better under various scenarios. Numerical simulations show that the infection mode of cells mainly affects the reduction of viral load in the third stage, while the antibody immune response is mainly manifested in the clearance of viral particles in the first stage of viral load decrease. With effective treatments, blocking cell‐to‐cell infection and enhancing the antibody immune response can effectively reduce the viral load in a short time period achieving the eradication of infection. Our findings suggest that the HCV infection is highly dynamic post‐DAAs treatment, and early monitoring of viral load decline contributes to the implementation of subsequent treatment regimens.

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

Cited by 8 publications

References 37 publications

A nonlinear HCV model in deterministic and randomly fluctuating environments

A nonlinear HCV model in deterministic and randomly fluctuating environments

Optimal Control of a Cell-to-Cell Fractional-Order Model with Periodic Immune Response for HCV

Dynamics of an age‐structured multiscale hepatitis C virus model with two infection modes and antibody immune response

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