Reconstruction of the Temporal Correlation Network of All-Cause Mortality Fluctuation across Italian Regions: The Importance of Temperature and Among-Nodes Flux

Abstract

All-cause mortality is a very coarse grain, albeit very reliable, index to check the health implications of lifestyle determinants, systemic threats and socio-demographic factors. In this work, we adopt a statistical-mechanics approach to the analysis of temporal fluctuations of all-cause mortality, focusing on the correlation structure of this index across different regions of Italy. The correlation network among the 20 Italian regions was reconstructed using temperature oscillations and traveller flux (as a function of distance and region's attractiveness, based on GDP), allowing for a separation between infective and non-infective death causes. The proposed approach allows monitoring of emerging systemic threats in terms of anomalies of correlation network structure.

Keywords: complex networks; dynamical systems; epidemiology; time series.

Figure 1

Death rates in different regions are extremely correlated. (a) Actual time series for three regions, normalised to have an average value equal to one. The three lines present a strikingly similar course. (b) Pairwise between-region correlations (regions are ordered—left to right and top to bottom—according to decreasing GDP). A trend with GDP is appreciable, with smaller and less densely populated regions (i.e., Valle d’Aosta and Molise) endowed with lower (albeit still high) correlations.

Figure 2

(a) Normalised death rates for three regions as a function of the temperature. The continuous lines are the results of a fit (see Equations (1) and (3)). (b) Pairwise between-region correlations for the time series of the deaths when the fitted effect of the temperature is subtracted from the raw numbers. Correlations drastically decrease (colour scale as in Figure 1b) but remain large.

Figure 3

Determinants of the commuters flux. (a) The flux between two regions decays exponentially with the distance to travel (continuous line, exponential fit; see Equation (4)). The points at the bottom of the graph are zeros (not allowed in logarithmic scale and not considered in the fit). (b) The flux increases linearly with the GDP of the region of destination (continuous line, linear fit; see Equations (6) and (7)).

Figure 4

Actual commuters flux vs. the flux reconstructed by a fitted model that decays exponentially with the distance and grows linearly with the GDP of the region of destination (see Equation (8)). The continuous line is the identity line. Only non-zero entries of the commuters’ matrix are displayed and considered in the fitting procedure.

Figure 5

(a) Actual deaths vs. the deaths expected by the model (corr = 0.993; the continuous line is the identity). (b) Time-series of the deaths for three regions; dashed lines: data; continuous lines: model.

Figure 6

Between-region correlation: data vs. reconstructed from the model (corr = 0.841; the continuous line is the identity line).