Time scales of epidemic spread and risk perception on adaptive networks

¹ School of Finance, Zhejiang University of Finance and Economics - Hangzhou 310018, China
² School of Information Engineering, Nanchang Hangkong University - Nanchang 330063, China
³ School of Business, East China University of Science and Technology - Shanghai 200237, China
⁴ School of Physics and Electronic Information, Wenzhou University - Wenzhou 325027, China

^a zlxxwj@163.com

Received: 18 November 2010
Accepted: 7 March 2011

Abstract

Incorporating dynamic contact networks and delayed awareness into a contagion model with memory, we study the spreading patterns of infectious diseases in connected populations. It is found that the spread of an infectious disease is not only related to the past exposures of an individual to the infected but also the time scales of risk perception reflected in the social-network adaptation. The epidemic threshold p_c is found to decrease with the rise of the time scale parameter s and the memory length T, which satisfies the equation . Both the lifetime of the epidemic and the topological property of the evolved network are considered. The standard deviation σ_d of the degree distribution increases with the rise of the absorbing time t_c, a power-law relation σ_d=mt_c^γ is found.