Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

Ełaiw, A. M.; Agha, A. D. Al

doi:10.1186/s13662-019-2448-y

Cited by 8 publications

(13 citation statements)

References 46 publications

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“…This can be accounted for by modeling interactions as shown in [63]. Recently, many authors have argued that the virus moves freely in body and follows the Fickian diffusion (see, e.g., [64][65][66]). Therefore, it is more reasonable to study reaction-diffusion versions of our model.…”

Section: Resultsmentioning

confidence: 99%

Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses

Ełaiw

Alshaikh

2020

Adv Differ Equ

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We propose a discrete-time viral model with antibody and cell-mediated immune responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected. The incidence rate of infection as well as the production and removal rates of all compartments are modeled by general nonlinear functions. The model contains three types of intracellular time delays. We utilize nonstandard finite difference (NSFD) method to discretize the continuous-time model. We prove that NSFD preserves the positivity and boundedness of the solutions of the model. Based on four threshold parameters, the existence of the five equilibria of the model is established. We perform global stability of all equilibria of the model by using Lyapunov approach. Numerical simulations are carried out to illustrate our theoretical results. The impact of time delay on the viral dynamics is established.

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Section: Resultsmentioning

confidence: 99%

Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses

Ełaiw

Alshaikh

2020

Adv Differ Equ

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“…More recently, Manna and Hattaf 3 proposed an immunological model that incorporates the intracellular HBV DNA‐containing capsids, three delays, adaptive immunity, and general incidence rate that covers the bilinear incidence rate, the standard incidence, the Beddington–DeAngelis functional response, the Crowley–Martin functional response, and the Hattaf–Yousfi functional response. Recently, Elaiw and Al Agha studied the global dynamics of a generalized HBV infection model with capsids and adaptive immunity 7 …”

Section: Introductionmentioning

confidence: 99%

“…Recently, Elaiw and Al Agha studied the global dynamics of a generalized HBV infection model with capsids and adaptive immunity. 7 On the other hand, HBV infection in liver can spread via two different modes, one by virus-to-cell transmission, and the other by cell-to-cell transmission through direct contact. [8][9][10] However, most of the mathematical models considered only the first classical mode of transmission of HBV.…”

Section: Introductionmentioning

confidence: 99%

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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“…Within-host models, which study the interactions between SARS-CoV-2 and human cells, have received less attention than epidemiological models. Most of within-host SARS-CoV-2 models are based on Nowak and Bangham’s model [25] that was extended to study the dynamics of several viruses such as human immunodeficiency virus (HIV) [26] , [27] , [28] , hepatitis B virus (HBV) [29] , [30] , [31] , chikungunya virus (CHIKV) [32] , and other viruses. For example, Du and Yuan [8] studied a within-host model of COVID-19 infection.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of SARS-CoV-2/cancer model with immune responses

Ełaiw

Agha

2021

Applied Mathematics and Computation

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The world is going through a critical period due to a new respiratory disease called coronavirus disease 2019 (COVID-19). This disease is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Mathematical modeling is one of the most important tools that can speed up finding a drug or vaccine for COVID-19. COVID-19 can lead to death especially for patients having chronic diseases such as cancer, AIDS, etc. We construct a new within-host SARS-CoV-2/cancer model. The model describes the interactions between six compartments: nutrient, healthy epithelial cells, cancer cells, SARS-CoV-2 virus particles, cancer-specific CTLs, and SARS-CoV-2-specific antibodies. We verify the nonnegativity and boundedness of its solutions. We outline all possible equilibrium points of the proposed model. We prove the global stability of equilibria by constructing proper Lyapunov functions. We do some numerical simulations to visualize the obtained results. According to our model, lymphopenia in COVID-19 cancer patients may worsen the outcomes of the infection and lead to death. Understanding dysfunctions in immune responses during COVID-19 infection in cancer patients could have implications for the development of treatments for this high-risk group.

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Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

Cited by 8 publications

References 46 publications

Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses

Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses

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

Global dynamics of SARS-CoV-2/cancer model with immune responses

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