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Complete global stability for an SIR epidemic model with delay - distributed or discrete. (English) Zbl 1185.37209
In modelling the transmission of an infectious disease, a common model structure involves dividing the population into susceptible, infectious and recovered individuals. If the immunity that is obtained upon recovery is permanent, then one gets an SIR model. In this paper the author considers SIR models with mass action incidence and constant recruitment. In Section 2 an SIR model with distributed delay is given. In Section 3, some results from the literature relating to earlier work on this model are given. Section 4 contains a proof of the global asymptotic stability of the endemic equilibrium for ${\Re }_{0}>1$. In Section 5, an SIR model with discrete delay is presented and the endemic equilibrium is shown to be globally asymptotically stable for ${\Re }_{0}>1$.

##### MSC:
 37N40 Dynamical systems in optimization and economics 92D30 Epidemiology
##### Keywords:
delay; distributed delay; global stability; Lyapunov functional
##### References:
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