Disease-induced resource constraints can trigger explosive epidemics

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into "explosive" spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.Comment: 24 pages, 6 figure

Saving Human Lives: What Complexity Science and Information Systems can Contribute

We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are often not effective and sufficient to contain them. Many common approaches do not provide a good picture of the actual system behavior, because they neglect feedback loops, instabilities and cascade effects. The complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be better understood by means of complexity science. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives.Comment: 67 pages, 25 figures; accepted for publication in Journal of Statistical Physics [for related work see http://www.futurict.eu/

Temporal dynamics of online petitions

Online petitions are an important avenue for direct political action, yet the dynamics that determine when a petition will be successful are not well understood. Here we analyze the temporal characteristics of online-petition signing behavior in order to identify systematic differences between popular petitions, which receive a high volume of signatures, and unpopular ones. We find that, in line with other temporal characterizations of human activity, the signing process is typically non-Poissonian and non-homogeneous in time. However, this process exhibits anomalously high memory for human activity, possibly indicating that synchronized external influence or contagion play and important role. More interestingly, we find clear differences in the characteristics of the inter-event time distributions depending on the total number of signatures that petitions receive, independently of the total duration of the petitions. Specifically, popular petitions that attract a large volume of signatures exhibit more variance in the distribution of inter-event times than unpopular petitions with only a few signatures, which could be considered an indication that the former are more bursty. However, petitions with large signature volume are less bursty according to measures that consider the time ordering of inter-event times. Our results, therefore, emphasize the importance of accounting for time ordering to characterize human activity

Temporal dynamics of online petitions

<div><p>Online petitions are an important avenue for direct political action, yet the dynamics that determine when a petition will be successful are not well understood. Here we analyze the temporal characteristics of online-petition signing behavior in order to identify systematic differences between popular petitions, which receive a high volume of signatures, and unpopular ones. We find that, in line with other temporal characterizations of human activity, the signing process is typically non-Poissonian and non-homogeneous in time. However, this process exhibits anomalously high memory for human activity, possibly indicating that synchronized external influence or contagion play and important role. More interestingly, we find clear differences in the characteristics of the inter-event time distributions depending on the total number of signatures that petitions receive, independently of the total duration of the petitions. Specifically, popular petitions that attract a large volume of signatures exhibit more variance in the distribution of inter-event times than unpopular petitions with only a few signatures, which could be considered an indication that the former are more bursty. However, petitions with large signature volume are less bursty according to measures that consider the time ordering of inter-event times. Our results, therefore, emphasize the importance of accounting for time ordering to characterize human activity.</p></div

Characterizing the distribution of the number of signatures a petition accrues.

<p>(left) Number of signatures as function of their rank (Zipf plot) in the <i>openPetition</i> data set. The red lines are guides to the eye with slopes −0.9 and −8.0 respectively. (right) Relative frequency of petitions in the <i>openPetition</i> data set with a certain number of signatures. The inset shows the distribution of the petitions’ signatures first digit (green bars) and the corresponding Benford distribution data (red dots).</p

Signing time series and time evolution of total number of signatures.

<p>(left) Time series of the largest petition’s signing activity per hour. The inset shows the superimposed circadian pattern. (right) The corresponding total number of signatures as a function of time.</p

Local variation analysis of petition signing spike trains for different classes of numbers of signatures.

<p>All petitions are divided into four different classes based on the number of signatures <i>N</i>. (upper left) Distribution of the local variation for the real signing activity spike train data. (upper right) Same as the latter for randomized spike trains (null model), showing behavior that is more clearly Poissonian and the same for all classes. (lower left) The mean <i>μ</i>(<i>L</i>_<i>V</i>) of real and randomized spike trains for different classes of numbers of signatures. (lower right) The z-values of real and randomized data for different classes of numbers of signatures, showing that the classes with only a few signatures deviate from the Poissonian assumption according to the <i>L</i>_<i>V</i> measure.</p