Global Stability of an Epidemic Model with Latent Stage and Vaccination
In this paper, an epidemic model with latent stage and vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the partial immunity against infection before gaining the complete immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing the Lyapunov functions, 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 unique endemic equilibrium is globally stable when the basic reproduction number is greater than one. When proving the global stability of the endemic equilibrium, the derivative of the given Lyapunov function may be rearranged in the different forms to show its negative definiteness or semi-definiteness.
epidemic model vaccination globally stability Lyapunov function
Jianquan Li Yiqun Li Lin Li Xiuchao Song
Department of Applied Mathematics and Physics,Air Force Engineering University,Xian 710051,China
国际会议
The 5th International Congress on Mathematical Biology(第五届国际生物数学大会 ICMB 2011)
南京
英文
1268-1273
2011-06-01（万方平台首次上网日期，不代表论文的发表时间）