Mathematical model analysis and numerical simulation of intervention strategies to reduce transmission and re-activation of hepatitis B disease

Abstract

Background: Because of its asymptomatic nature, the Hepatitis B Virus (HBV) has become the most lethal and silent killer. In this research, we offer HBV virus transmission characteristics in the form of a mathematical model. We suggested and examined a seven-compartment compartmental nonlinear deterministic mathematical model for transmission dynamics with immigration and HBV reactivation after recovery, as well as control measures for Hepatitis B virus disease transmission. By considering the following facts and cases, this work will provide new knowledge. First, re-infection of HBV after liver transplantation, chemotherapy, and other therapies is one of the most essential aspects in HBV transmission, although reactivation of HBV was not taken into account in some compartmental models of HBV transmission. Furthermore, the exposure rate, immigration rate, and level of infectiousness of the chronic infective class were not given enough weight in the numerical assessment of the force of HBV infection. These facts influenced the development of our model. Methods: We demonstrated that the solution of the dynamical system under consideration is positive and bounded. The effective reproductive number that represents the epidemic indicator is generated from the biggest eigenvalue of the netgeneration matrix, and the model is examined qualitatively using differential equation stability theory. For disease-free and endemic equilibria, both local and global asymptotic stability criteria are determined. Results: A full explanation of the parameters and their numerical findings is presented and debated well based on the numerical simulation. Conclusions: According to the findings of this study, vaccination and treatment interventions play a critical role in reducing HBV transmission and reproduction. It has also been demonstrated that HBV reactivation contributes significantly to an increase in theinfective population, which boosts virus transmission, and that a combination of vaccination and treatment will be the most effective strategy for controlling HBV infection and reinfection after recovery.

Modeling and Optimal Control Analysis Applied to Real Cases of COVID-19 Pandemic with Double Dose Vaccination in Ethiopia

“…Proof. To proof global stability of E def , we first construct the Lyapunov function [25]. Let the Lyapunov function be V : R 7 + ⟶ R + and defined as…”

“…So in this section, we estimate the numerical value of R c for Equation (2). Substituting the corresponding parameter's value in Equation (25) and Equation ( 26) from Table 1, we get the following estimated results. R 0 = 2:105062463, R c = 0:0007495074407, and R 1 = 0:00008555327934.…”