## Convergence results in $$SIR$$ epidemic models with varying population sizes.(English)Zbl 0879.34054

The authors study an $$SIR$$ epidemic model in which the force of infection involves a distributed delay and in which the population is not constant. The model exhibits both a disease-free equilibrium, $$E_0$$, which exists for all parameter values, and one in which the infection is endemic, $$E_+$$, which exists for certain parameter values. Their main result is that $$E_0$$ is globally asymptotically stable when $$E_+$$ doesn’t exist and that $$E_+$$ is locally asymptotically stable when it exists. The proof involves Lyapunov functionals. They also calculate the radius of a ball contained in the domain of attraction of $$E_+$$.
Reviewer: A.Hausrath (Boise)

### MSC:

 34D20 Stability of solutions to ordinary differential equations 92D30 Epidemiology
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### References:

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