In this paper,a hepatitis B and C virus model with logistic hepatocyte growth is investigated,where the type of incidence is standard.Both of the two thresholds of the model,determining whether the virus infection persists and whether the virus infection leads to the complete liver failure,are found.The complete dynamical behaviors are analyzed.The obtained results show that the existence of homoclinic orbits is possible,which implies that the outbreak of the virus infection may occur.
Yiqun Li,Jianquan Li,Hongmei Bi Dept.of Applied Math.and Physics,Air Force Engineering University,Xi’an 710051
In this paper, an SIR epidemic model with vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the temporary immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing a Lyapunov function, it is proved that the disease free equilibrium is globally stable when the basic reproduction number is less than or equal to one, and that the endemic equilibrium is globally stable when the basic reproduction number is greater than one.
Jianquan Li, Yali Yang (Dept. of Applied Math. and Physics, Air Force Engineering University, Xi’an 710051)
