Open AccessThe analysis of hepatitis B virus (HBV) transmission using an epidemic model
Author(s) -
Tahir Khan,
Rahman Ullah,
Gul Zaman,
Imtiaz Ahmad
Publication year - 2021
Publication title -
natural and applied sciences international journal
Language(s) - English
Resource type - Journals
ISSN - 2788-4619
DOI - 10.47264/idea.nasij/2.1.6
Subject(s) - bounded function , basic reproduction number , transmission (telecommunications) , hepatitis b virus , stability theory , state (computer science) , mathematics , virology , epidemic model , disease , hepatitis b , position (finance) , vaccination , mathematical economics , computer science , demography , virus , biology , medicine , physics , mathematical analysis , algorithm , sociology , economics , population , telecommunications , finance , nonlinear system , quantum mechanics , pathology
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 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 verified the analytical results. Finally some important conclusion are given at the end of the article.