Trends in Incidence and Transmission Patterns of COVID-19 in Valencia, Spain

Key Points Question How does SARS-CoV-2 spread within a city, and are there instrumental neighborhoods that might modulate the spread? Findings This epidemiological cohort study of 2646 patients with COVID-19 conducted in the third most populated city in Spain found that the neighborhood where the COVID-19 testing facility was located also had the highest number of total connections (both inbound and outbound). The mean income and population density had a direct correlation with the number of cases. Meaning These findings suggest that a selective and strategic lockdown of specific neighborhoods could help reduce the spread of SARS-CoV-2.


Spatial Model
In the Besag 1 model the risk associated with a region is modelled as the sum of a heterogeneity and a clustering effect. For the temporal effect we want a smooth and flexible evolution, thus we consider a structured random effect in order to make sure that periods close in time are expected to be similar and also allowing for flexible forms for the temporal evolution curves.
For this study, we assumed O ij to be the number of observed cases and E ij the expected number of cases for the ith neighborhood and jth day within the period. Hence, the number of observed cases was modelled as O ij ∼ Poisson (r ij E ij ), where r ij is the underlying relative risk for COVID-19 infection. The relative risk represents the ratio between the number of estimated cases provided by the model and the expected number of cases in ith neighborhood on day jth. E ij was calculated as the total number of cases observed on day j multiplied by the fraction of the population that neighborhood i represents. The following equation shows the general definition of the additive spatiotemporal model: where is the global intercept of the model; ′ represent covariate ( ) effects; and are two spatial effects adopting the standard model 2 with structured and unstructured components, respectively; and and represent the structured and distribution was chosen to model the spatially-structured random effect. The usual contiguity matrix which considers that two areas are neighbors if they share a geographical border was considered to define this prior. An independent zero-mean normal prior was used for the temporal effect . In contrast, the parameter displays a temporal structure. We considered a second-order random walk (RW2) for , with a prior in which effects for neighboring time points tend to be alike. The parameter represents space-time interaction. The spatio-temporal interaction term was modeled through a Gaussian prior, which corresponds to the type I interaction in the context of the Knorr-Held models. Specific constraints on the random effects have been considered to avoid identifiability issues. 3 The following covariates were studied: population density ( 1 , in inhabitants/km 2 ); average income per household ( 2 , in euro); and three meteorological variables, namely average temperature ( 3 , in °C), average wind speed ( 4 , in km/h), and number of sunlight hours ( 5 , number of hours in which solar irradiance is >120 W/m 2 ). Population density and income data were obtained from the National Statistics Institute. The effect of the meteorological covariates was considered on a daily basis and with a 7-day lag. An ordinary kriging model 4 was used to estimate the covariate values. Daily measurements were collected from the meteorological stations of the National Weather Service (AEMET).

Functional Networks
Propagation Assessment The Granger´s causality test 5 is based on two intuitive concepts: causes must precede the corresponding effects and the prediction of the caused time series should be improved when using information from the causes. It has been extensively applied to economic 6 and biomedical data. 7,8 If the propagation of COVID-19 occurs from neighborhood B to neighborhood A, a forecast of the number of cases in A should be more precise when information from the past of B is also included. Reversing the argument, such forecast can then be used to infer the presence of a propagation process, without the need of a priori information as mobility data, but only relying on the local evolution of the pandemics. present. Before applying it, time series have been checked for stationarity, i.e. for the absence of linear and periodic trends; note that the presence of such trends is known to lead to spurious results in a Granger test. Stationarity has been assessed using an augmented Dickey-Fuller unit root test. 9 While half of them, the presence of a unit root could not be discarded (for = 0.01), an autocorrelation analysis showed that this was mainly due to a periodicity of 7 days. This, nevertheless, did not affect the results, as most of the causality relationships were found for shorter time lags (Fig. 1a).
The associations detected by the Granger test were on a shorter time scale than the trends, thus the impact of the latter ones is negligible. The forecast of the time series was then performed through an autoregressive-moving-average model, 10 in which the time series of the causing element was shifted a number of time steps back in time. An F-test was finally applied to assess the statistical significance of this inequality of Eq (2) and to obtain a corresponding p-value.

Propagation Network Reconstruction
The network', in which the dynamics of nodes is expected to be a function of the connectivity; the latter (the unknown part) is then reconstructed through the former (the known data). 13 We further calculated a weight matrix , encoding how strong the propagation was between pairs of neighborhoods. For each pair ( , ) with , = 1, , was defined as − 10 , , where , is the p-value obtained by the Granger test for neighborhoods and . Therefore, the larger the value , , the clearer the propagation process from a Granger point of view.
Note that the adjacency matrix and the weight matrix represent complementary views of the same information. Each element ( , ) in them is derived from the same Granger test, and specifically from the corresponding p-value. , yields a binarized view of the p-value, i.e. whether a statistically significant association exists; on the other hand, , indicates the strength of such association. This dual view of the connectivity structure is customary in network science, and each matrix is used to characterize different aspects of it.
The resulting network was analyzed in terms of the following metrics 14 : • Out-degree: number of outbound links from a given node, or number of neighborhoods the vector is propagating. This value corresponds to the row-sum of the adjacency matrix .
• In-degree: number of inbound links at a given node, or number of neighborhoods propagating to it.
• Total degree: sum of inbound and outbound links of a node.
• Betweenness centrality: how instrumental or strategical a neighborhood was in propagating the disease throughout the whole network, defined the sum of the fractions of all-pair shortest paths that pass through that node. 15 In other words, this centrality assesses how many times a neighborhood has mediated the propagation between two other regions. The distance between pairs of nodes, which corresponds to the dissimilarity between the corresponding neighborhoods, is defined as the inverse of , . The resulting values were normalized such that the most central node has a betweenness centrality of 1.