Spatiotemporal evolution of COVID-19 in Portugal’s Mainland with self-organizing maps

In December of 2019, multiple cases of a highly transmittable virus, the SARS-CoV-2 virus, were identified in China’s Wuhan city, Hubei province [1]. The World Health Organization (WHO) named the disease itself as the Coronavirus Disease-2019 (COVID-19) [2]. The initial measures and strategies to combat and mitigate the propagation of the virus in China were ineffective, resulting in propagation of the virus worldwide. What was originally a local epidemic event, rapidly escalated into a global pandemic phenomenon [3]. This pandemic had serious implications in the stress of the national health systems and in terms of fatalities, which resulted directly from the virus propagation [4].

To fight and delay the propagation of the virus, and before the generalization of the vaccination, lockdowns were one of the strategies adopted by governments worldwide. The reduced economic activity during lockdown periods exacerbated existing economic and social inequalities in countries around the globe [5,6,7]. Portugal was not exception and in the first year of pandemic several local (i.e., per municipality or group of municipalities) and national periods of lockdown were implemented aiming to deaccelerate the growth of the COVID-19 incidence curves. Besides, these mitigation actions also comprised those aiming to reduce social gatherings, the concentration of people in closed spaces and restrict people’s mobility to their main residency area (or municipality) [8]. However, the impact of these measures in effectively preventing the virus transmission varied depending on the socio-economic and demographic characteristics of the region where they were applied [9]. Therefore, the dynamics of the virus depends simultaneously on space and time domains and consequently its modelling should be jointly performed.

Several numerical modelling tools were applied to this end. Initially, contagion risk models (e.g., SIR models [10, 11]) provided a relevant source of information for public health authorities and governments and for the strategies developed to minimize the impact of the pandemic on health systems. However, these models are difficult to calibrate locally with field data at the small-scale (e.g., per municipality or parish) as the disease spreading depends simultaneously on the individual and social behaviors [12, 13]. Along with these models, geo-spatial mapping tools were also developed and made available to the community. This set of tools included information dashboards at local and national levels, infection risk maps produce with geostatistical tools (e.g., [14]), spatiotemporal modeling and forecasting with machine learning methods based on neural networks and deep learning (e.g., [15,16,17]) and spatial analysis tools based on spatial correlation indices [18].

Since the outbreak of the disease large amounts of data regarding the evolution of COVID-19 were produced. These data have the potential to provide insights into the dynamics of the spatiotemporal evolution of the pandemic allowing to devise better mitigation strategies for new pandemic or epidemic events. Under this scope, we leverage machine learning methods (i.e., self-organizing maps (SOM)) to explore, analyze and classify local 14-days cumulative incidence curves of COVID-19 for each the 278 municipalities in mainland Portugal along with key socio-economic and demographic characteristics of these municipalities. We use data from the first year of the pandemic in mainland Portugal between March 15th, 2020, and February 6th, 2021 (i.e., a total of 326 days).

Self-Organizing Maps are an artificial-neural network used as a dimensionality reduction technique or as an unsupervised clustering method [19]. This algorithm performs both vector quantization and vector projection and uses a neighborhood function to preserve the topological properties of the input space [20], being a powerful dimensionality reduction algorithm, while keeping the notion of neighbor, which is important for data with a spatial continuity pattern. When applied to data spatially distributed, SOM can explain complex elements associations in a spatial perspective [21]. Besides, as similar inputs in the original high-dimension space tend to be mapped together in its low-dimension output space, SOM can represent the probability distribution of inputs patterns and encode their associations and nonlinear relationships [22].

SOM have been applied in different scientific fields, but its use in health-related studies is still limited (e.g., [23, 24]). Melin et al. [25] used SOM to spatially group countries worldwide and then all the 32 states of Mexico, according to their COVID-19 incidence rates and mortality data. Similarly, Galvan et al. [26] analyzed the evolution of the disease in regions, states, and major cities of Brazil. Galvan et al. [27] used SOM to cluster together the Brazilian Sates according to their incidence rates and death numbers along with other health indicators into the model, having concluded that the states with higher ICU beds, ventilators, physicians and nurses per 100,000 inhabitants are clustered together and less affected by COVID-19. Resta [28] used SOM as an early warning system for pandemic events in Italy considering simultaneously demographic, healthcare, and political data.

Recently, the temporal behavior of COVID-19 incidence ratio has been related to the socio-economic and demographic variables. Da Costa and Costa [29], concluded that municipalities in mainland Portugal with more elderly people in nursing homes and with a higher number of immigrants were at a higher incidence risk of COVID-19. Lewis et al. [30] proposed the Area-Level Deprivation index for the Utah state (USA) and concluded that the odds of infection by COVID-19 were two times greater in high-deprivation areas and three times greater in very high-deprivation areas. Additionally, de Lusignan et al. [31] in a cross-sectional study, analyzed the risk factors influencing the infection by SARS-CoV-2 in the United Kingdom and concluded that people living in more deprived, densely populated areas and of Black ethnicity were at higher risk of contracting the disease.

We propose herein the use of SOM to spatially explore, at the municipality level, the first year of pandemic in mainland Portugal and the influence of local socio-economic and demographic variables in the spread of the disease. We use SOM due to the ability of this algorithm to model data with different temporal resolution (i.e., 14-days incidence curves and socio-demographic indicators) while preserving the spatial nature of the data (i.e., the geographical location of the municipalities). This unique characteristic makes SOM suitable to model natural phenomena with both temporal and spatial components, like the spread of a contagious disease. The results shown herein represent one of the first attempts to interpret at the municipality level, and from a geo-spatial perspective, the influence of local socio-economic and demographic characteristics in the spread of COVID-19 in mainland Portugal.

Next, we briefly describe the theoretical background of SOM, followed by a description of the data set used in this study. Then, we present the main results of the spatiotemporal modelling of COVID-19 evolution with SOM in mainland Portugal. The last section draws the main conclusions.

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