Scrutinizing the heterogeneous spreading of COVID-19 outbreak in large territorial countries

Abstract

After the spread of COVID-19 out of China, the evolution of the pandemic has shown remarkable similarities and differences between countries around the world. Eventually, such characteristics are also observed between different regions of the same country. Herewith, we introduce a general method that allows us to compare the evolution of the pandemic in different localities inside a large territorial country: in the case of the present study, Brazil. To evaluate our method, we study the heterogeneous spreading of the COVID-19 outbreak until May 30th, 2020, in Brazil and its 27 federative units, which has been seen as the current epicenter of the pandemic in South America. Each one of the federative units may be considered a cluster of interacting people with similar habits and distributed to a highly heterogeneous demographic density over the entire country. Our first set of results regarding the time-series analysis shows that: (i) a power-law growth of the cumulative number of infected people is observed for federative units of the five regions of Brazil; and (ii) the distance correlation calculated between the time series of the most affected federative units and the curve that describes the evolution of the pandemic in Brazil remains about 1 over most of the time, while such quantity calculated for the federative units with a low incidence of newly infected people remains about 0.95. In the second set of results, we focus on the heterogeneous distribution of the confirmed cases and deaths. By applying the epidemiological susceptible-infected-recovered-dead model we estimated the effective reproduction number (ERN) R e during the pandemic evolution and found that: (i) the mean value of R e for the eight most affected federative units in Brazil is about 2; (ii) the current value of R e for Brazil is greater than 1, which indicates that the epidemic peak is far off; and (iii) Ceará was the only federative unit for which the current <?CDATA ${\mathcal{R}}_{\mathrm{e}}{ R e &lt; 1 . Based on these findings, we projected the effects of increase or decrease of the ERN and concluded that if the value of R e increases 20%, not only the peak might grow at least 40% but also its occurrence might be anticipated, which hastens the collapse of the public health-care system. In all cases, keeping the ERN 20% below the current value can save thousands of people in the long term.

Trends in COVID-19 prevalence and mortality: A year in review

“…Next, nonlinear dynamics researchers have proposed several sophisticated extensions to the classical predictive SIR model, including analytic techniques to find explicit solutions [18] , [19] , modifications to the SIR model with additional variables [20] , [21] , [22] , [23] , [24] , incorporation of Hamiltonian dynamics [25] or network models [26] and a closer analysis of uncertainty in the SIR approach [27] . Other mathematical approaches to prediction and analysis include power-law models [28] , [29] , [30] , distance analysis [31] , [32] , network models [33] , [34] , [35] , [36] , analyses of the dynamics of transmission and contact [37] , [38] , forecasting models [39] , Bayesian methods [40] , clustering [41] , [42] and many others [43] , [44] , [45] , [46] .…”

Data based model for predicting COVID-19 morbidity and mortality in metropolis

“…correlated to the disease and allows the prediction of its evolution in a coordinated and agile way with a high degree of accuracy. The scientific community has been working intensively to identify variables related to COVID-19 23 – 28 , 35 , 36 and to predict the evolution of the disease 11 – 22 however, these efforts have taken place separately. This article proposes an approach that integrates the prediction and characterization of explanatory variables quickly and contributes important information to managers.…”

A symbiosis between cellular automata and dynamic weighted multigraph with application on virus spread modeling

“…Modeling the dynamic of heterogeneous spaces using CA leads to defining the weights of neighborhood to reflect the varying impacts of nearby cells [34] , [35] , [36] . The weighted adjacency presentation can increase the modeling power of CA, especially in cases neighboring cells do not necessarily interact and influence each other similarly.…”