Temporal percolation of a susceptible adaptive network

• Published in: Physica A Vol. 392; no. 18; pp. 4172 - 4180
• Main Authors: Valdez, L.D., Macri, P.A., Braunstein, L.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.09.2013
• Subjects: Adaptive networks; Dynamic tests; Epidemic models; Evolution; Mathematical analysis; Networks; Percolation; Simulation; Spreading; Temporal logic; Adaptive networks; Epidemic models; Percolation
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2013.05.003

In the past decades, many authors have used the susceptible–infected–recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the susceptible individuals. In this paper, we study the dynamic of the susceptible–infected–recovered model in an adaptive network that mimics the transitory deactivation of permanent social contacts, such as friendship and work-ship ties. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations for the fraction susceptible individuals in the susceptible biggest component. In particular, we focus on how the individual’s behavior impacts on the dilution of the susceptible network. We show that, as a consequence, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time at which the giant susceptible component is destroyed. Our theoretical results are fully supported by extensive simulations. •We focus on the temporal unfolding of the susceptible individuals in an adaptive susceptible network.•Using a temporal percolation approach we derive the relevant magnitudes of this model.•The functional susceptible network is protected longer than in the case without strategy.