Dynamics Analysis Of Infectious Disease Model Under The Network Environment

In this paper, the dynamic behavior of epidemic model is investigated. The content is asfollows:At first, the recent researches of achievement and development on epidemic modelwere summarized, and the research of epidemic spreading on networks is illustrated briefly.Secondly, a SIQR epidemic model with nonmonotone incidence rate is investigated, themodel considered the two important factors: quarantine and nonmonotone infection rate.Based on the theoretical analysis of the model, The existence of the equilibriums is discussed,and by means of eigenvalue method, Hurwit criterion and limit equation theory we haveproved that if the threshold R0<1, then the disease-free equilibrium is globally stable. Basedon the method of Lasalle invariance principle and Liapunov function, global stability of theendemic equilibrium is obtained. Finally numerical simulations are provided to illustrate theeffectiveness of the results.Thirdly, As the actual needs, epidemic model researched on network, and then an SIQRepidemic model on small-world network is investigated, The existence of threshold and theequilibrium is discussed and analyzed its stability，Numerical simulations are provided toillustrate the effectiveness of the results; Also an SIQR epidemic model on the Scale-freenetwork is investigated, The existence of the equilibriums is discussed and analyzed itsstability. Obtained that the SIQR epidemic model has a very small threshold on the Scale-freenetwork by numerical simulation, this is due to the limited scale of the network scale, andsome preventive measures have been given.Finally, we point out the insufficiency about this thesis and prospect the development ofcomplex networks.