Domain of Attraction Estimation for SIRS Epidemic Models Via Sum-Of-Square Optimization

Estimation of the domain of attraction of a class of susceptible infectious removed susceptible (SIRS) epidemic models for varying-size population with constant immigration is investigated. On assumption that the disease-free equilibrium and the endemic equilibrium exist, the domain of attraction of epidemic model is estimated by using sum-of-squares optimization approach. An invariant subset of domain of attraction is computed and an enlargement obtained. Simulation results, given in a comparison presentation, demonstrate feasibility and validity of the proposed technique as well as reveal that this algorithm outperforms other ones in applications to the epidemic model.