Global Stability of a Variation Epidemic Spreading Model on Complex Networks

Epidemic spreading on networks becomes a hot issue of nonlinear systems, which has attracted many researchers’ attention in recent years. A novel epidemic spreading model with variant factors in complex networks is proposed and investigated in this paper. One main feature of this model is that virus variation is investigated in the process of epidemic dynamical spreading. The global dynamics of this model involving an endemic equilibrium and a disease-free equilibrium are, respectively, discussed. Some sufficient conditions are given for the existence of the endemic equilibrium. In addition, the global asymptotic stability problems of the disease-free equilibrium and the endemic equilibrium are also investigated by the Routh-Hurwitz stability criterion and Lyapunov stability criterion. And the uniform persistence condition of the new system is studied. Finally, numerical simulations are provided to illustrate obtained theoretical results.