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ON THE QUASI-STATIONARY DISTRIBUTION OF SIS MODELS

Published online by Cambridge University Press:  16 September 2016

Gaofeng Da ,
Maochao Xu  and
Shouhuai Xu
Gaofeng Da
Affiliation:
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu Province, China E-mail: [email protected]
Maochao Xu
Affiliation:
Department of Mathematics, Illinois State University, Illinois, USA E-mail: [email protected]
Shouhuai Xu
Affiliation:
Department of Computer Science, University of Texas at San Antonio, San Antonio, Texas, USA
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Abstract

In this paper, we propose a novel method for constructing upper bounds of the quasi-stationary distribution of SIS processes. Using this method, we obtain an upper bound that is better than the state-of-the-art upper bound. Moreover, we prove that the fixed point map Φ [7] actually preserves the equilibrium reversed hazard rate order under a certain condition. This allows us to further improve the upper bound. Some numerical results are presented to illustrate the results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 4 , October 2016 , pp. 622 - 639
Copyright
Copyright © Cambridge University Press 2016 

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