A Numerical Simulation on the Effect of Vaccination and Treatments for the Fractional Hepatitis B Model

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Haile Habenom ◽  
D. L. Suthar ◽  
D. Baleanu ◽  
S. D. Purohit
Keyword(s):  
Hepatitis B ◽  
Nonlinear Equations ◽  
Control Strategies ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
B Virus ◽  
The Stability ◽  
Hbv Model ◽  
Raphson Method ◽  
Jacobi Collocation Method

Abstract The aim of this paper is to develop a fractional order mathematical model for describing the spread of hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free equilibrium (DFE) and the endemic equilibrium of the system based on the basic reproduction number. Here, the infectious disease HBV model is described mathematically in a nonlinear system of differential equations in a caputo sense, and hence, Jacobi collocation method is used to reduce into a system of nonlinear equations. Finally, Newton Raphson method is used for the systems of nonlinear equations to arrive at an approximate solution and matlab 2018 has helped us to simulate the nature of each compartment and effects of the possible control strategies (i.e., vaccination and isolation).

scholarly journals Application and Optimal Control for an HBV Model with Vaccination and Treatment

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jing Zhang ◽  
Suxia Zhang
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Least Squares Method ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Optimal Theory ◽  
B Virus ◽  
The Stability ◽  
Hbv Model

In this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reproductive number R0. Using the least squares method, the model is applied to simulate yearly new infected cases of hepatitis B in China from 2004 to 2016. Moreover, optimal control problem with newborn vaccination and treatment appearing as functions of time is analyzed by classical optimal theory. The existence of the solution to optimality system is proved, and the simulations are conducted to show the results when optimal control or current intervention is used.

scholarly journals Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 166
Author(s):  
Irina Volinsky ◽  
Salvo Danilo Lombardo ◽  
Paz Cheredman
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Interleukin 2 ◽  
Integral Form ◽  
Cauchy Matrix ◽  
Symmetry Properties ◽  
B Virus ◽  
The Stability ◽  
Hbv Model

Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.

scholarly journals PERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN

2013 ◽  
Vol 2 (2) ◽  
pp. 11
Author(s):  
NANDA NINGTYAS RAMADHANI UTAMI ◽  
I NYOMAN WIDANA ◽  
NI MADE ASIH
Keyword(s):  
Nonlinear Equations ◽  
Iteration Method ◽  
Initial Point ◽  
Iteration Process ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Newton Raphson ◽  
Raphson Method

System of nonlinear equations is a collection of some nonlinear equations. The Newton-Raphson method and Jacobian method are methods used for solving systems of nonlinear equations. The Newton-Raphson methods uses first and second derivatives and indeed does perform better than the steepest descent method if the initial point is close to the minimizer. Jacobian method is a method of resolving equations through iteration process using simultaneous equations. If the Newton-Raphson methods and Jacobian methods are compared with the exact value, the Jacobian method is the closest to exact value but has more iterations. In this study the Newton-Raphson method gets the results faster than the Jacobian method (Newton-Raphson iteration method is 5 and 58 in the Jacobian iteration method). In this case, the Jacobian method gets results closer to the exact value.

scholarly journals Hepatitis B virus infection in Nigeria: a systematic review and meta-analysis of data published between 2010 and 2019

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Busayo I. Ajuwon ◽  
Isabelle Yujuico ◽  
Katrina Roper ◽  
Alice Richardson ◽  
Meru Sheel ◽  
...  
Keyword(s):  
Systematic Review ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Disease Surveillance ◽  
Control Strategies ◽  
Meta Analysis ◽  
Population Based ◽  
North West ◽  
B Virus ◽  
The Impact

Abstract Background Hepatitis B virus (HBV) is an infectious disease of global significance, causing a significant health burden in Africa due to complications associated with infection, such as cirrhosis and liver cancer. In Nigeria, which is considered a high prevalence country, estimates of HBV cases are inconsistent, and therefore additional clarity is required to manage HBV-associated public health challenges. Methods A systematic review of the literature (via PubMed, Advanced Google Scholar, African Index Medicus) was conducted to retrieve primary studies published between 1 January 2010 and 31 December 2019, with a random-effects model based on proportions used to estimate the population-based prevalence of HBV in the Nigerian population. Results The final analyses included 47 studies with 21,702 participants that revealed a pooled prevalence of 9.5%. A prevalence estimate above 8% in a population is classified as high. Sub-group analyses revealed the highest HBV prevalence in rural settings (10.7%). The North West region had the highest prevalence (12.1%) among Nigeria’s six geopolitical zones/regions. The estimate of total variation between studies indicated substantial heterogeneity. These variations could be explained by setting and geographical region. The statistical test for Egger’s regression showed no evidence of publication bias (p = 0.879). Conclusions We present an up-to-date review on the prevalence of HBV in Nigeria, which will provide critical data to optimise and assess the impact of current prevention and control strategies, including disease surveillance and diagnoses, vaccination policies and management for those infected.

scholarly journals Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ruiqing Shi ◽  
Ting Lu ◽  
Cuihong Wang
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Fractional Order ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
B Virus ◽  
The Stability ◽  
Holling Ii Functional Response

In this paper, a fractional-order model is constructed to describe the transmission of Hepatitis B Virus (HBV). Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of two equilibriums are obtained. Thirdly, the stability of equilibriums are analyzed. After that, some numerical simulations are performed to verify the theoretical prediction. Finally, a brief discussion is presented.

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

scholarly journals The Stability of Hepatitis B Virus Antigen and HBV-DNA Contents in Injectable Drug Solutions.

1999 ◽  
Vol 25 (6) ◽  
pp. 621-626
Author(s):  
RYO MATSUSHITA ◽  
MARIKO ASAHI ◽  
FUJIO ICHIMURA ◽  
TAKUMA HASHIMOTO ◽  
EIKI MATSUSHITA ◽  
...  
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Virus Antigen ◽  
Hbv Dna ◽  
Injectable Drug ◽  
B Virus ◽  
Dna Contents ◽  
The Stability

scholarly journals Pseudogene-mediated DNA demethylation leads to oncogene activation

2020 ◽  
Author(s):  
Junsu Kwon ◽  
Yanjing V. Liu ◽  
Chong Gao ◽  
Mahmoud A. Bassal ◽  
Adrianna I. Jones ◽  
...  
Keyword(s):  
Hepatocellular Carcinoma ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Hematologic Malignancies ◽  
Dna Demethylation ◽  
B Virus ◽  
Specific Manner ◽  
Oncogene Activation ◽  
Hbv Model ◽  
Unique Mechanism

AbstractDespite being one of the leading causes of cancer-related deaths, there is an unmet clinical need for hepatocellular carcinoma (HCC) patients. The lack of effective treatment is, at least in part, due to our lack of understanding of the molecular pathogenesis of this disease. Oncofetal protein SALL4 is re-activated in patients with aggressive HCC along with other solid tumors and hematologic malignancies. This study identifies a previously unrecognized mechanism of SALL4 reactivation which is mediated by pseudogene-induced demethylation. Using a locus-specific demethylating technology, we identified the critical CpG region for SALL4 expression. We showed that SALL4 pseudogene 5 hypomethylates this region through interaction with DNMT1, resulting in SALL4 upregulation. Intriguingly, pseudogene 5 is significantly upregulated in a hepatitis B virus (HBV) model prior to SALL4 induction, and both are increased in HBV-HCC patients. Our results suggest that pseudogene-mediated demethylation represents a unique mechanism of oncogene activation in cancer.SignificanceOur study provides a mechanistic link between HBV infection, activation of the oncogene SALL4, and HCC. We reveal a previously undescribed capability of a pseudogene to epigenetically activate an oncogene by demethylation in a locus-specific manner.

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