Fig 1.
Timeline of main COVID-19-related events in India, Israel and Mexico (January 2020-December 2020).
Fig 2.
Event type distribution across India, Israel and Mexico as tallied from January 3rd to December 12th, 2020.
“Violence a.c.” stands for “Violence against civilians”. The majority of events are protests, followed in smaller percentage by riots, violence against civilians, and battles respectively. ACLED also lists explosions, which are not reported in any of the countries under investigation.
Table 1.
Distribution of disorder events (violence against civilians, riots, protests, battles) across the top 10 countries as tallied by ACLED between January 3rd and December 12th 2020.
The countries considered in this study, India, Israel and Mexico are italicized, and account for almost 40% of the world total. At this time of writing, ACLED does not report data for the US.
Fig 3.
Time series of nationwide disorder events (protests, riots, violence against civilians, battles) in India, Israel and Mexico, from January 3rd to December 12th 2020.
Note the relatively more uniform distribution in Mexico, compared to the more structured ones in India and especially in Israel.
Fig 4.
COVID-19 disorder events in India.
The four detected clusters, C1-C4, host approximately equal numbers of residents, with a maximum of about 27% of the total population in C1 and a minimum of about 18% in C2. Clusters however are very heterogeneous in terms of population density and territorial extent. Two of the most densely inhabited states in the area, Uttar Pradesh and Bihar, are located in C1 and C2, respectively. This map has been generated via rnaturalearth in R, a package built using Natural Earth map data.
Fig 5.
Weekly time series of disorder events {nj} visualized by cluster, in India.
Weeks are marked from week j = 1 (December 29th 2019 to January 4th 2020) to week j = 50 (December 6th to December 12th 2020).
Fig 6.
Cluster dynamics in India: (left) Pearson’s correlation of weekly eventsnj across pairs of clusters.
(right) Pearson’s correlation of differentiated weekly events Δnj = nj − nj−1. The color scale is restricted to positive values as as no negative relationships are found. The left panel reveals a substantial level of correlation, however, when first-order differences are considered all coefficients decrease, implying that the rate of change in the occurrence of events is less correlated.
Table 2.
Statistical outcomes of the Hawkes process applied to data from India.
The Hawkes process outperforms the baseline Poisson process both nationwide and in each cluster, since the Hawkes AIC is always less than the Poisson AIC. The Hawkes process passes the KS test at the 95% significance level in all cases, with .
Fig 7.
COVID-19 disorder events in Israel.
Clusters C1, C3, C4 host the most densely populated areas located around the cities of Haifa, Tel Aviv and Jerusalem, respectively, Events in cluster C2, the least dense region, are the most sparse and emerge mostly at the border with Jordan. This map has been generated via rnaturalearth in R, a package built using Natural Earth map data.
Fig 8.
Weekly time series of disorder events {nj} visualized by cluster, in Israel.
Weeks are marked from week j = 1 (December 29th 2019 to January 4th 2020) to week j = 50 (December 6th to December 12th 2020).
Fig 9.
Cluster dynamics in Israel: (left) Pearson’s correlation of weekly events nj across pairs of clusters.
(right) Pearson’s correlation of differentiated weekly events Δnj = nj − nj−1 across pairs of clusters. The left panel shows almost perfect correlation between weekly-based streams of events for all cluster pairs. The synchrony remains almost perfect when considering first-order differences in the right. The nationwide correlation that is much more visible than in India or Mexico may be due to Israel’s more compact geographical extension, linguistic unity, tighter virtual connectivity, and/or due to the nationwide engagement of the Flag movement. Note that correlation coefficients between clusters in Israel are very large (r ≥ 0.95 in all cases) compared to those computed for India (and Mexico). Thus, if we kept the same scale as in Figs 6 and 12 (-1 ≤ r ≤ 1) the correlation plots for Israel would be colored uniformly. Instead, for a more nuanced view we use instead a more restricted scale (0.95 ≤ r ≤ 1).
Table 3.
Statistical outcomes of the Hawkes process applied to data from Israel.
The Hawkes process outperforms the baseline Poisson process both nationwide and in each cluster, since the Hawkes AIC is always less than the Poisson AIC. The Hawkes process passes the KS test at the 95% significance level in all cases except for C4, where , indicating that the hypothesis that the data can be fit to a Hawkes process with a decaying exponential should not be accepted. Given the nature of the data, a more steeply decaying function than the decaying exponential should be used in C4.
Fig 10.
COVID-19 disorder events in Mexico.
Of all clusters, C4 carries the largest population as it includes the capital city and the state of Mexico. The two are respectively the most populated city and state in the country. The state of Mexico is also the most dense nationwide. This map has been generated via rnaturalearth in R, a package built using Natural Earth map data.
Fig 11.
Weekly time series of disorder events {nj} visualized by cluster, in Mexico.
Weeks are marked from week j = 1 (December 29th 2019 to January 4th 2020) to week j = 50 (December 6th to December 12th 2020).
Fig 12.
Cluster dynamics in Mexico: (left) Pearson’s correlation of weekly events nj across pairs of clusters.
(right) Pearson’s correlation of differentiated weekly events Δnj = nj − nj−1. The left panel shows a high level of correlation between clusters; however, contrary to what observed in India and Israel, dramatic decreases are observed when computing coefficients between first order differences implying a low level of synchrony in the rate of change of events.
Table 4.
Statistical outcomes of the Hawkes process applied to data from Mexico.
The Hawkes process outperforms the baseline Poisson process both nationwide and in each cluster, since the Hawkes AIC is always less than the Poisson AIC. The Hawkes process passes the KS test at the 95% significance level in all cases, with .