Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids

Danane, Jaouad; Allali, Karam

doi:10.3390/ht7040035

Cited by 12 publications

(21 citation statements)

References 28 publications

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“…The basis of linearization is to ensure that for eigenvalues with negative real part, the equilibria k x are locally asymptotically stable. This affirms the fact that in addition to system equilibria 0 E and 1 E , there are several other physical steady states and non-physical steady state, which could be derived from those of [1,2,15,16,42]. Now, using the above basic properties as background, we can then address the main goal of our investigation, which amount to the maximization of the system performance index measured in terms of the concentration of susceptible double lymphocyte cells and dual adaptive immune system induced by minimal chemotherapy cost.…”

Section: Equilibria and Stability Analysissupporting

confidence: 77%

“…Death rate of infected HBV non-virus producing cells Table 2, is a reflection of models [1,2,42,50], modified to accommodate the present investigation.…”

Section: Problem Statement and Mathematical Equationsmentioning

confidence: 99%

“…In collaboration with this present study, mathematical models formulated to account for the monolytic HIV, HBV infections include [32][33][34][35][36][37][38][39][40]. The inclusion of the vital role of adaptive immune system and delay intracellular as defense mechanism were studied by [1,2,6,15,20,27,[41][42][43][44][45][46][47][48]. Other monolytic models, which had focused on the methodological application of treatment strategies and optimal maximization of healthy population, can be found in [1,2,16,28,29,[49][50][51][52][53][54][55][56][57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control Dynamics: Multi-therapies with Dual Immune Response for Treatment of Dual Delayed HIV-HBV Infections

Bassey¹

2020

IJMSC

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It has been of concern for the most appropriate control mechanism associated with the growing complexity of dual HIV-HBV infectivity. Moreso, the scientific ineptitude towards an articulated mathematical model for coinfection dynamics and accompanying methodological application of desired chemotherapies inform this present investigation. Therefore, the uniqueness of this present study is not only ascribed by the quantitative maximization of susceptible state components but opined to an insight into the epidemiological identifiability of dual HIV-HBV infection transmission routes and the methodological application of triple-dual control functions. Using ODEs, the model was formulated as a penultimate 7-Dimensional mathematical dynamic HIV-HBV model, which was then transformed to an optimal control problem, following the introduction of multi-therapies in the presence of dual adaptive immune system and time delay lags. Applying classical Pontryagin's maximum principle, the system was analyzed, leading to the derivation of the model optimality system and uniqueness of the system. Specifically, following the dual role of the adaptive immune system, which culminated into triple-dual application of multi-therapies, the investigation was characterized by dual delayed HIV-HBV virions decays from infected double-lymphocytes in a biphasic manner, accompanied by more complex decay profiles of infectious dual HIV-HBV virions. The result further led to significant triphasic maximization of susceptible double-lymphocytes and dual adaptive immune system (cytotoxic T-lymphocytes and humeral immune response) achieved under minimal systemic cost. Therefore, the model is comparatively a monumental and intellectual accomplishment, worthy of emulation for related and future dual infectivity.

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Section: Equilibria and Stability Analysissupporting

confidence: 77%

“…Death rate of infected HBV non-virus producing cells Table 2, is a reflection of models [1,2,42,50], modified to accommodate the present investigation.…”

Section: Problem Statement and Mathematical Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Control Dynamics: Multi-therapies with Dual Immune Response for Treatment of Dual Delayed HIV-HBV Infections

Bassey¹

2020

IJMSC

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“…Motivated by the work of [6,13,30,31], we study the following general HBV infection model with capsids and two forms of adaptive immune response:…”

Section: A Diffusive Hbv Dynamics Model With Capsids and Adaptive Immmentioning

confidence: 99%

“…In a very recent work, Danane and Allali [31] explored an HBV infection model with capsids and adaptive immunity. However, the spatial mobility of viruses was ignored and the global stability of the equilibria was not analyzed.…”

mentioning

confidence: 99%

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

Ełaiw

Agha

2019

Adv Differ Equ

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This paper studies the global dynamics of a general diffusive hepatitis B virus (HBV) infection model. The model includes both enveloped viruses and DNA containing capsids. Two immune responses are recruited to attack the virus and infected hepatocytes. These are the cytotoxic T-lymphocytes (CTL) which kill the infected liver cells, and B cells which send antibodies to attack the virus. The non-negativity and boundedness of the solutions are discussed. The existence of spatially homogeneous equilibrium points is examined. The global stability of all possible equilibrium points is proved by choosing suitable Lyapunov functionals. Some numerical simulations are performed to enhance the theoretical results and present the behavior of solutions in space and time.

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Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Sutradhar,

Dalal

2023

Math Methods in App Sciences

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Hepatitis B virus (HBV) infection is a major public health concern throughout the world. It can be treated effectively through proper medication and vaccination, although it is very difficult to cure, especially in people who have had the chronic infection. So, it is necessary to pay proper attention for its eradication. In this study, two nonlinear fractional‐order HBV infection models with recycling effects of capsids are presented via the Caputo derivative. Each model contains four compartments, namely, susceptible hepatocytes, infected hepatocytes, HBV capsids, and viruses. In the first model, the order of fractional derivatives is equal for each compartment, whereas, in the second model, the order is incommensurate. The existence and uniqueness of solutions for both models are discussed separately. The parameters are estimated in order to validate the proposed model with experimental data obtained from a chimpanzee. Stability analyses are carried out for both models theoretically. The models are solved numerically using the predictor–corrector Adams–Bashforthm–Moulton method (for commensurate order) and implicit product integration of trapezoidal type method (for incommensurate order) with various choices of fractional orders and initial conditions. All the results are presented graphically. Interestingly, the results reveal the importance of fractional‐order derivatives in capturing the dynamics of HBV transmission in the host. It is also noticed that with the decrease in the order of fractional derivative, the peak level of infection decreases, but the disease takes a long time to be cured.

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Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids

Cited by 12 publications

References 28 publications

Optimal Control Dynamics: Multi-therapies with Dual Immune Response for Treatment of Dual Delayed HIV-HBV Infections

Optimal Control Dynamics: Multi-therapies with Dual Immune Response for Treatment of Dual Delayed HIV-HBV Infections

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

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

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