### Research of an epidemic model on adaptive networks

CHEN Lu1,2, ZHANG Xiao-guang1,2*

1. 1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China;
2. Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
• Online:2019-09-20 Published:2019-07-30

Abstract: By using the triple approximation formula under multinomial distributions, the SIS moment closure infectious disease model in the adaptive network is closed, the effects of adaptive behavior on the spread of infectious diseases under multinomial distributions is studied. Through the theory of qualitative and stability, the basic reproduction number R0 of the model is obtained and the stability of the equilibrium points are analyzed. Adaptive behavior of rewiring has multiple effects on infectious disease transmission are obtained: When the relative infection rate is small enough, the model has a standard forward bifurcation and when R0<1, the disease tends to be extinct; on the contrary, mathematically, it is rigorously proved that the rewiring can lead to the occurrence of complex dynamic behaviors such as the backward bifurcation and saddle-node bifurcation, ect. Therefore R0<1 is not enough to control the spread of infectious diseases.

CLC Number:

• O175
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