In (Connell McCuskey, Nonlinear Anal RWA 11:3106–3109, 2010), the authors presented an SIR model of disease transmission with delay in a particular nonlinear incidence. In their work, they showed the global stability of the endemic equilibrium for the reproduction number R0 is greater than one. In this chapter, we reviewed on the same model with delay in general incidence function. The global stability of the endemic equilibrium is studied for R0  1 by using a Lyapunov functional. With supposed well-known parameters, we built simple observer and a high-gain observer using a canonical controller form. Then, we proposed nonlinear auxilary dynamical systems which are used for the implementation. Numerical simulations are included in order to test the behaviour and the performance of the given observers.

Epidemic model SIR Delays Global stability Lyapunov function Reproduction number General incidence function Observability Observer High gain