MOESM1 of Unveiling patterns of international communities in a global city using mobile phone data

Supplementary information. Correlation between entropy and points of interest. Entropy outliers during the football match Ajax-Milan. Mathematical details of the persistent homology. Sensitivity analysis on the clustering of international communities

Pattern of Tick Aggregation on Mice: Larger Than Expected Distribution Tail Enhances the Spread of Tick-Borne Pathogens

<div><p>The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of <i>Ixodes ricinus</i> ticks feeding on <i>Apodemus flavicollis</i> mice (main reservoir-competent host for tick-borne encephalitis, TBE) sampled in Trentino (Northern Italy). The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB), Poisson-LogNormal (PoiLN), and Power-Law (PL). The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.</p></div

Nymphs to total ticks ratio for observed feeding ticks on mice.

<p>Percentage of feeding nymphs on the total feeding ticks observed on mice in different years (2000–2008) and grids (<i>A</i>-<i>I</i>).</p><p>Nymphs to total ticks ratio for observed feeding ticks on mice.</p

Estimated parameters of different distributions (NB on left and PL on right) obtained inside (blue) and outside (red) of the mice peak abundance time window.

<p>Time windows are defined by (from left to right for each subsets). Vertical bars indicate best model fits (central horizontal lines) with their uncertainties that are confidence interval for NB models while standard deviations for PL models.</p

Median of the final prevalence as a function of the transmission probability.

<p>A PL distribution of vectors-per-host has been considered in all scenarios. Simulations that consider different aggregation behaviours according to the temporal window of mice abundance (red) are compared with others with a fixed distribution (blue). Other parameters are , , and .</p

Detection of seasonal abundance time-windows.

<p>The time series of captured mice has been interpolated by a quadratic polynomial curve. By normalising the obtained parabola to unity and setting a threshold ( in the example), we identify mice captured in high abundance season, those above the threshold (triangles), and mice captured in low abundance period, those below the threshold (circles).</p

Basic descriptive statistics for empirical data.

<p>Number of trapping grids, trapping sessions, total number of <i>A. flavicollis</i> captures for different years, sum of feeding ticks, median and ranges of the number of ticks per rodent, and mean number of nymphs fraction among feeding ticks.</p><p>Basic descriptive statistics for empirical data.</p

Median (line), interquartile (darker area) and confidence intervals (lighter area) of the final prevalence as a function of the transmission probability, for different fitting distributions (PL, NB and PoiLN).

<p>Other parameters are , , and .</p

Complementary cumulative functions of number of ticks per host (real-data) with the best power-law (PL), negative binomial (NB), and Poisson LogNormal (PoiLN) fit.

<p>The PL fitting model shows high proximity to the tail of the real data distribution while the NB and the PoiLN fits appropriately describe the initial part of the distribution they describe the tail improperly.</p

Temporal variation of <i>A. flavicollis</i> mice abundance recorded in different grids (labelled in different colours from A to I).

<p>Temporal variation of <i>A. flavicollis</i> mice abundance recorded in different grids (labelled in different colours from A to I).</p