Complex Network Epidemic Model With Global Asymptotic Stability And Branch

In this thesis,we mainly discuss mean field equations of SI model and SIS model.We focus on the globally asymptotic stability and bifurcation of equilibriums. The results show that it has some special characters of spreading on heterogeneous network.For SI model,we prove that the system will be globally stable at (1,1,...,1).For SIS model,the number of equilibriums changes as the infected rateλgrows.Moreover,by using Central Manifold theorem we prove that the system has bi-furcation at someλ.By discussing 3-dimensional mean field equations on heterogeneous network,we find that the number of the equilibriums has close relation with the roots in [0,1]of a polynomial which has degree 3.As n grows,the non-zero equilibriums of SIS model will change.