Najmeh Davarian - Department of Mathematics, Payame Noor University, P. O. Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Hassan Saberi Nik - Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

This paper deals with the global stability of the endemic equilibrium for infectious disease with xed controls. The classical method of Lyapunov functions combined with the Volterra-Lyapunov matrix properties, which lead to the proof of the endemic global stability of infectious disease model. All the analytical results are veri ed by simulation works.

Global stability; Epidemic model; Vaccination; Treatment; Lyapunov function; Volterra-Lyapunov stability.