Epidemic Model in Well-Mixed Multiplex Network with Distributed Time Delay

• Main Authors: Lin, Yu-Chen, 林煜程
• Other Authors: Juang, Jonq
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/5bvh2e

碩士 === 國立交通大學 === 應用數學系數學建模與科學計算碩士班 === 105 === In this paper, we consider an epidemic model in well-mixed multiplex networks with distributed time delay. Specifically, the model consists of two layers of well-mixed networks, where two diffusive processes on the same individual interacting and affecting each other. We assume that there is a distributed time delay for an individual getting infected and no delay for an individual changing one’s status from unawareness to awareness. There are three possible equilibria E1, E2 and E3, called disease and information free equilibrium, disease free and information saturated equilibrium and endemic and information saturated equilibrium, in this model. Our main result contain the following. First, we prove the uniform persistence of the model for parameter region yielding E3. Second, it is shown that E1 is globally stable for any time delay. Third, we prove that E2 is globally stable for any time delay. Finally, With help of the uniform persistence, we shoe that there exists a H*>0 such that E3 is globally stable for time delay less than H*.