Global stability of an SIR epidemic model with time delays. (English) Zbl 0811.92019

Beretta, Edoardo; Takeuchi, Yasuhiro

J. Math. Biol. 33, No. 3, 250-260 (1995).

Summary: An SIR disease transmission model is formulated under the assumption that the force of infection at the present time depends on the number of infectives at the past. It is shown that a disease free equilibrium point is globally stable if no endemic equilibrium point exists. Further the endemic point (if it exists) is globally stable with respect to the whole state space except the neighborhood of the disease free state.

MSC:

92D30	Epidemiology
34D05	Asymptotic properties of solutions to ordinary differential equations

Keywords:

global stability; time delay; Lyapunov functional; local stability; SIR disease transmission model; disease free equilibrium; endemic equilibrium