Figure 1.
Observed civil unrest event count distributions.
The incidence of civil unrest events per year is measured by summing over the reported country-level number of anti-government demonstrations, riots, and general strikes (see the section Domestic Conflict Data), for all countries within a particular subregion of the world (see the section Countries and Geographical Regions Included in the Study). The figure shows the log-log plot of the complementary cumulative distribution of civil unrest event count, .(A) Unrest event count distributions for geographical subregions of Asia: Western Asia (○); South-Eastern Asia (□); Eastern Asia (▵); Southern Central Asia (▿). (B) Unrest event count distributions for geographical subregions of Africa: Western Africa (○); Southern Africa (□); Middle Africa (▵); Eastern Africa (▿). (C) Unrest event count distributions for geographical subregions of Europe: Western Europe (○); Southern Europe (□); Northern Europe (▵); Eastern Europe (▿). (D) Unrest event count distributions for geographical subregions of America: Caribbean, Central, and South America (○); North America (□).
Figure 2.
Social unrest spatial contagion model.
The model is defined on a square grid of sites, which represents the division of a country into urban clusters (see the section Parameter Estimation for details). Each site of the grid can be in one of three different states: empty (“white”), susceptible to social unrest (“red”), and involved in social unrest (“crowd”). Sites are one grid step apart if they are directly adjacent to each other in either the horizontal or vertical direction, or are connected through weak links (e.g., site E4 is connected to site F2). The weak links are formed by associating with each site, with probability
, a single link to a site selected uniformly at random from the grid. The grid is updated synchronously according to the following rules: at each time step, empty sites become susceptible with probability
, and susceptible sites become involved in social unrest with probability
. Unrest contagion occurs on a short time scale as follows. If a site is involved in social unrest (e.g., sites B2 and E4), the unrest activity spreads with probability
to susceptible sites that are one grid step apart (e.g., sites C2, B3, or D5), which in turn can lead (with probability
) to further instabilities of susceptible sites that are two grid steps apart, three grid steps apart, and so on. Each of the sites involved in social unrest during a time step contributes to the size of the unrest contagion.
Figure 3.
Observed data and best-fit curves for civil unrest event count distributions.
Observed values are denoted by circles. Solid best-fit lines denote average distributions calculated from 500 realizations of the social unrest contagion model. The goodness of fit of the model relative to the empirically observed unrest event count distributions was determined by measuring the distance between the observed and simulated distributions. Here, the tail-weighted Kolmogorov–Smirnov (wKS) statistic is used (see the section Assessing the Goodness of Fit of the Model). The fit of the model is very good for all regions. Goodness-of-fit (wKS) and fitted parameters for all regions: Western Asia = 0.1269
, South-Eastern Asia = 0.1581
, Eastern Asia = 0.1492
, Southern Central Asia = 0.1078
, Western Africa = 0.1749
, Southern Africa = 0.2513
, Middle Africa = 0.1856
, Eastern Africa = 0.1191
, Western Europe = 0.1436
, Southern Europe = 0.11220
, Northern Europe = 0.16
, Eastern Europe = 0.1634
, Caribbean, Central, and South America = 0.0707
, North America = 0.2349
. Values of wKS that are less than 0.3 represent good fits (see the section Assessing the Goodness of Fit of the Model).
Figure 4.
Calculated size of the grid over time based on an average urban cluster of 26250 people.
Figure 5.
Goodness-of-fit (average wKS statistics) and simulated event count distributions for various grid sizes.
Observed values for each sub-region of Asia are denoted by circles. Solid best-fit lines denote average distributions calculated from 500 realizations of the social unrest contagion model by using a grid size . Simulated count distributions for grid sizes
use the fitted parameters obtained for
(see Fig. 3). Goodness-of-fit (wKS) for all regions and grid sizes: Western Asia: 0.1269
, 0.1254
, 0.1265
; South-Eastern Asia: 0.1581
, 0.1682
, 0.1692
; Eastern Asia: 0.1492
, 0.1521
, 0.1598
; Southern Central Asia: 0.1078
, 0.1161
, 0.1199
. The differences between the curves are too small to be visually noticeable. Running time on an Intel i7 Core processor was approximately 6.6 hours
, 21 hours
, 50.56 hours
.
Figure 6.
Effect of mass media on civil unrest activity.
(A) Change in the total number of radios, television receivers, and phones, owned or operated per capita: 1919 to 2008. Widespread use of telecommunication technologies started around 1950. (B) The empirically observed distributions of the number of unrest incidents in the world: for the entire period of 1919–2008, and for pre- and post-1950.
Figure 7.
Effect of network structure on civil unrest activity.
Observed values for each sub-region of Asia are denoted by red circles. Black points denote best-fit average distributions calculated from 500 realizations of the social unrest contagion model by using a grid size and a uniform distribution of long-range links (fitted parameters
for all regions are given in Figure 3). In all cases, a scale-free overlay network was generated with roughly the same number of directed links,
, as in the corresponding uniform overlay network. Here,
is the expected number of long-range links on a square grid of
sites when the uniform distribution is used.