Dynamical behavior of a new epidemiological model

A new epidemiological model is introduced with nonlinear incidence,in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain time τ. the existence,uniqueness,and stability of the disease-free equilibrium and endemic equilibrium are discussed. the basic reproductive number r 0 is given. the model is studied in two cases: with and without time delay. for the model without time delay,the disease-free equilibrium is globally asymptotically stable provided that r 0 ≤ 1; if r 0 > 1,then there exists a unique endemic equilibrium,and it is globally asymptotically stable. for the model with time delay,a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. hopf bifurcation in endemic equilibrium with respect to the time τ is also addressed. © 2014 zizi wang and zhiming guo.