An epidemic model with multiple delays for the propagation of worms in wireless sensor networks

Abstract

A delayed SEIRS worm propagation model with the inclusion of a finite communication radius and node density for wireless sensor networks is investigated in this paper. By using different combinations of the three delays as bifurcating parameter and analyzing distribution of roots of the corresponding characteristic equation, sufficient conditions are derived for local stability of the endemic equilibrium and the existence of a Hopf bifurcation at the endemic equilibrium are addressed. By constructing a suitable Lyapunov function, sufficient conditions for global stability of the endemic equilibrium are determined. Finally, numerical simulations for a set of parameter values are performed to illustrate the analytical findings.