Dynamical analysis for a hepatitis B transmission model with immigration and infection age (original) (raw)

Mathematical Analysis of the Control of Hepatitis B Virus in a Population with Vital Dynamics

In this paper, we developed and analysed a new mathematical model for the dynamics of hepatitis B virus (HBV) in a population with vital dynamics, incorporating vertical transmission, sexual maturity, the effect of public enlightenment campaign with respect to sexual behaviour, and vaccination as control measures. We obtained the effective basic reproduction number c R which can be used to control the transmission of the disease and hence, established the conditions for local and global stability of the disease free equilibrium. Bifurcation analysis was carried out using centre manifold theory which reveals a subcritical (backward) bifurcation for the model. Numerical simulations validated the analytical results and further reveals that HBV vaccination for sexually active individuals as the only control strategy can control (eliminate) the disease at even a low level of vaccination compliance.

The analysis of hepatitis B virus (HBV) transmission using an epidemic model

Natural and Applied Sciences International Journal (NASIJ), 2021

In this article, we propose an epidemic problem of hepatitis B with vaccination. So to do this, first we presents the model formulation and prove that the solutions are bounded and positive. We obtain the disease free equilibrium and calculate the basic reproduction number (R0). The reproductive number will be used to find the endemic state of the model. We discuss the qualitative analysis of the proposed problem and show that whenever, R0 < 1 then the disease free equilibrium is stable locally and globally. Moreover, whenever, R0 > 1, then the endemic state is asymptotically stable. We derive sufficient conditions for both the equilibria and its stabilities. Further more numerical simulation are carried out to illustrate the feasibility of the obtained results and verified that with actual data, we are in the position to put down the hepatitis B infection form the community. We also highlight the role of epidemic parameters in the disease propagation. Our numerical works veri...

Modeling approach to assess the transmission dynamics of Hepatitis B infection in Africa

International Journal of Advances in AppliedMathematics andMechanics, 2019

Hepatitis B virus infection remains a major public health concern in many developing countries in the world. In this paper, we formulate and analyse a simple deterministic model to assess the dynamics and control of the disease using ordinary differential equations. To analyse the effect of the initial transmission of the disease we compute the basic reproduction number R 0 and perform stability analysis. The results show that both the disease-free equilibrium and the endemic equilibrium are globally stable with respect to the value of R 0. Results also show that R 0 is highly affected by the vertical transmission and the recovery rate of the chronic carriers after screening and treatment. Therefore, effective mechanisms which will reduce vertical transmission are needed as well as effective screening of individuals, so that those who will be found infected get treated. Further results from numerical analysis show that when the disease is introduced in the population it is persistent and therefore effective control mechanisms are required. MSC: 00A71 • 93A30 • 93D05 • 93D20 • 97M10

Global stability analysis of hepatitis B virus dynamics

F1000Research

This paper considers the impact of an acute individual's spontaneous clearance, recovery of a chronic individual with full immunity, and risk factor reduction on a hepatitis B virus (HBV) model. The existence and the positivity solution of the model are established. The model threshold quantity is defined and sensitivity analysis is analyzed to demonstrate the effect of various parameters on the spread of the virus. The global stability analysis of the equilibrium is shown using Lyapunov and comparison theorem methods. Finally, computational simulation is presented to validate the analytical solution. The results show that treatment, spontaneous clearance and reduction of the risk factor are highly successful in transmitting and regulating HBV transmission. The effective measure of these parameters as substantiated by our simulations, providing an excellent control method of the transmissible infection of HBV.

A Mathematical study on the vaccination impact on the disease dynamics of HBV

Abstract: We develop a deterministic model to understand the underlying dynamics of HBV infection at population level. The model, which incorporates the vaccination and treatment of individuals, the re-infections of latent, carrier and recovery individuals, is rigorously analyzed to gain insight into its dynamical features. The mathematical analysis reveals that the model exhibits a backward bifurcation. This phenomenon resulted due to the exogenous re-infection of HBV disease . It is shown that, in the absence of such re-infection, the model has a disease-free equilibrium (DFE) which is globally asymptotically stable (GAS) using Lyapunov function and LaSalle Invariance Principle whenever the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium(EEP), for a special case, whenever the associate threshold quantity exceeds unity. This EEP is shown to be GAS, for a special case, using a non-linear Lyapunov function of Goh-Volterra type. Keywords: Hepatitis B virus (HBV), basic reproduction number, equilibria, stability, Lyapunov function, transmission dynamics, disease endemic equilibrium.

The stability analysis of an epidemic model with age-structure in the exposed and infectious classes

2017

In this paper, we propose an epidemic model with age-structure in the exposed and infectious classes for a disease like hepatitis-B. Asymptotic smoothness of semi-flow generated by the model is studied. By calculating the basic reproduction number and analyzing the characteristic equation, we study the local stability of disease-free and endemic steady states. By using Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable; if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable. https://doi.org/10.28919/cmbn/3337

Spreading dynamic of acute and carrier hepatitis B with nonlinear incidence

PloS one, 2018

Hepatitis B infection caused by the hepatitis B virus. It is one of the serious viral infection and a global health problem. In the transmission of hepatitis B infection different phases, i.e., acute and chronic carrier stages play an important role. The chronic carries individuals do not exhibit any symptoms and are able to transmit the infection. Here we assessed the transmissibility associated with different infection stages of hepatitis B and generated an epidemic model with nonlinear incidence rate. In order to do this, first we formulate the model by splitting the infectious class into two subclasses, namely acutely infected and chronic carries with both horizontal and vertical transmission. The basic properties of the proposed model are presented. The basic reproductive number is obtained by using the next generation matrix approach. Biological sense of the threshold condition is investigated and discussed in detail. We also find the conditions to investigate all possible equ...

Optimal control of hepatitis b virus disease in a population with infected immigrants

2015

This paper firstly presents a nonlinear extended deterministic model for assessing the impact of immigration on the spread of the Hepatitis B Virus (HBV) pandemic in a population with acute and chronic groups. This model studies the impact of optimal control on the treatment of immigrants and vaccination of HBV on the transmission dynamics of the disease in a homogeneous population with constant immigration. First, we derived the condition in which disease free equilibrium is locally and globally asymptotically stable. Second, we investigated by formulating the costs function problem as an optimal control problem, and we then use the Pontryagins Maximum Principle to solve the optimal control problems. The impact of each control mechanism individually and the combinations of these strategies in the control of HBV is also investigated. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the treatment and vaccination of infected ...