Global Dynamics of a Virus Dynamical Model with Cell-to-Cell Transmission and Cure Rate.
The cure effect of a virus model with both cell-to-cell transmission and cell-to-virus transmission is studied. By the method of next generation matrix, the basic reproduction number is obtained. The locally asymptotic stability of the virus-free equilibrium and the endemic equilibrium is considered by investigating the characteristic equation of the model. The globally asymptotic stability of the virus-free equilibrium is proved by constructing suitable Lyapunov function, and the sufficient condition for the globally asymptotic stability of the endemic equilibrium is obtained by constructing suitable Lyapunov function and using LaSalle invariance principal.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China ; State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China.
Tongqian
T
Zhang
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China ; State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China.
Xinzhu
X
Meng
Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia.
Tonghua
T
Zhang
D050936:Basic Reproduction Number; D003198:Computer Simulation; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D014777:Virus Diseases / Q000453:epidemiology / Q000635:transmission* / Q000821:virology; D014779:Virus Replication