title: Dynamic analysis of an SEIR model with distinct incidence for exposed and infectives.
abstract: An SEIR model with vaccination strategy that incorporates distinct incidence rates for the exposed and the infected populations is studied. By means of Lyapunov function and LaSalle's invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. The sufficient conditions for the global stability of the endemic equilibrium are obtained using the compound matrix theory. Furthermore, the method of direct numerical simulation of the system shows that there is a periodic solution, when the system has three equilibrium points.
authors.affiliation: Department of Mathematics and Sciences, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, Hebei 075000, China. jhli2011@163.com
authors.forename: Junhong
authors.initials: J
authors.lastname: Li
authors.forename: Ning
authors.initials: N
authors.lastname: Cui
mesh_terms: D003140:Communicable Disease Control / Q000706:statistics & numerical data*; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D018562:Disease Transmission, Infectious / Q000517:prevention & control* / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D015233:Models, Statistical; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods; D014611:Vaccination / Q000706:statistics & numerical data*