Abstract
In this paper a HBV infection model with impulsive vaccination is considered. By using fixed point theorem and stroboscopic map we prove the existence of disease-free T-periodic solution. Also by comparative theorem of impulsive differential equation we get the global asymptotic stability of the disease-free periodic solution and permanence of the disease. Numerical simulations show the influence of parameters on the dynamics of HBV, which provided references for seeking optimal measures to control the transmission of HBV.
Highlights
Hepatitis B is a potentially life-threatening liver infection caused by the hepatitis B virus (HBV) and is a major global health problem
We divide the population into six epidemiological groups: the susceptible individuals to infection S; latently infected L; those acute infectors I1; chronic sufferers I2; and recovered R; V denotes the density of vaccinees who have begun the vaccination process
That μωυI2 denotes newborns who have been infected in perinatal infection and in chronic infection compartment, the rest μω(1−υI2) newborns become susceptible individuals
Summary
Hepatitis B is a potentially life-threatening liver infection caused by the hepatitis B virus (HBV) and is a major global health problem. HBV transmission in low endemicity populations typically occurs in adults via parenteral exposures and intravenous drug use or through sexual contact [2]. It can cause acute and chronic infection status. Zou et al [15] promote an age structure model to predict the dynamics of HBV transmission and evaluate the long-term effectiveness of the vaccination programme in China. Epidemic models including incomplete immune compartment V have been studied in [20,21,22,23,24], but the HBV transmission with the incomplete HepB vaccine immune is rarely considered.
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