Quarantine-generated phase transition in epidemic spreading

Abstract

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w c separating a phase (w < w c ) where the disease reaches a large fraction of the population, from a phase (w ≥ w c ) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that w c increases with the mean degree and heterogeneity of the network. We also find that w c is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.

Probing into the effectiveness of self-isolation policies in epidemic control

“…disease only disseminates through the network if we increase the infection probability λ. In other words, the final size of the epidemic may be reduced, as was observed in the 2009 H1N1 pandemic [11] and as also discussed in some works [31,32,33,34,52].…”

“…presented have been obtained averaging over 10 3 independent simulations, for each set values presented. Please observe we have only considered the epidemic spreading in the largest connected component of the network, i.e., the giant cluster [32].…”

“…Recently, some works have studied the effect of isolation in the physics and computer science literature [31,32,33,34,35,36,37]. It was therein argued that such policies can be effective in controlling the spread of an epidemic disease.…”

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks

“…However, the basic reproduction number (and thus the epidemic threshold) remained equal to those of random preventive vaccination, and this failed to contain epidemics in a highly heterogeneous network unless almost all individuals were vaccinated. There are also studies investigating dynamic reactions of individuals to the spread of epidemics [20][21][22][23][24][25], such as behavioral responses of individuals by reducing their contact rates [25], based on the number of infected neighbors or by rewiring connections (i.e., disconnecting their connections to infected neighbors and reconnecting others) [21].…”

Detecting and describing dynamic equilibria in adaptive networks

“…More recently, allowing for the coevolution of network structure and node-state dynamics has given rise to abundant literature on adaptive networks [5,6], capturing such diverse phenomena as the emergence of cooperation [7,8,9,10,11,12], opinion formation [13,14,15,16], disease spreading [17,18,19,20,21], speciation [22,23] and traffic flows [24,25,26]. While some contributions explore the respective phenomenology with individualbased simulations [8,10,27,28], others also focus on providing explanatory frameworks for observed dynamics [7,9,11,15,19,20,29].…”