title: Dynamic behavior for an SIRS model with nonlinear incidence rate and treatment.
abstract: This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.
authors.affiliation: Department of Mathematics and Sciences, Hebei Institute of Architecture & Civil Engineering, Zhangjiakou, Hebei 075000, China.
authors.forename: Junhong
authors.initials: J
authors.lastname: Li
authors.affiliation: Department of Mathematics and Sciences, Hebei Institute of Architecture & Civil Engineering, Zhangjiakou, Hebei 075000, China.
authors.forename: Ning
authors.initials: N
authors.lastname: Cui
mesh_terms: D000465:Algorithms; D003140:Communicable Disease Control / Q000706:statistics & numerical data*; D003198:Computer Simulation; D015994:Incidence; D015233:Models, Statistical; D017711:Nonlinear Dynamics