Global stability for SIR and SIRS models with nonlinear incidence and removal terms via Dulac functions | Zendy

Attila Dénes | Zendy; Gergely Röst | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Global stability for SIR and SIRS models with nonlinear incidence and removal terms via Dulac functions

Author(s) -

Attila Dénes,

Gergely Röst

Publication year - 2016

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2016.21.1101

Subject(s) - lyapunov function , mathematics , nonlinear system , stability (learning theory) , attractor , epidemic model , exponential stability , bifurcation , bistability , control theory (sociology) , mathematical analysis , computer science , control (management) , physics , artificial intelligence , population , demography , quantum mechanics , machine learning , sociology

We prove the global asymptotic stability of the disease-free and the endemic equilibrium for general SIR and SIRS models with nonlinear incidence. Instead of the popular Volterra-type Lyapunov functions, we use the method of Dulac functions, which allows us to extend the previous global stability results to a wider class of SIR and SIRS systems, including nonlinear (density-dependent) removal terms as well. We show that this method is useful in cases that cannot be covered by Lyapunov functions, such as bistable situations. We completely describe the global attractor even in the scenario of a backward bifurcation, when multiple endemic equilibria coexist.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research