ABSTRACT In this contribution, we present a predictive tool developed to help in the management of the evolution of the COVID-19 pandemic situation in Rio Grande do Sul (RS)-Brazil. This tool is the result of georeferenced data analysis, mathematical modeling, and parameter calibration for the dynamics of a SIR-type model defined on a spatial structure that allows distinct subpopulations to interact, similar to the controlled distancing (A l for l=1, ···, 21)) groupings proposed by the RS government and public health authorities. The predictive analysis, updated biweekly, provides three distinct scenarios per month (milder, average, and severe) and is made available as WebSIGs (Geographic Information System-GIS). The forecast of the average scenario for each A l group is the result of a simulation of the proposed SIR-type dynamics with calibrated parameters derived from an augmented Lagrangian maximum a posteriori estimation and data on the number of infected cases made available by the RS Health Secretariat. The milder and severe scenarios are obtained from the average scenario, with changes in the contagion rates of each A l group. When compared to the number of infections reported in each A l group, the modeling predictions for a biweekly time window (the first two weeks) were quite satisfactory, with errors ranging from 0% to 5.13%, gradually increasing over time. Therefore, we suggest a biweekly re-calibration of the parameters and corresponding forecasts as a wise strategy.

ABSTRACT In this contribution we analyze a discretized SIR (Susceptible, Infectious, and Removed) compartmental model, to investigate the role of individual interactions in the spread of diseases. The compartments S i,j , I i , j and R i , j ( i , j , = 1 , 2 , . . . , n ) are spatially distributed in a two-dimensional n × n network. We assume that the dynamics follow the well-known SIR-like iteration within the population in each (i, j) site. Moreover, the dynamics are enriched by considering a multi-population interaction following a Gaussian spatial distribution. Therefore, the mobility of individuals between distinct networks is measured from the width α of the Gaussian distribution. The interaction of individuals between distinct sites, responsible for the contagion between different populations, is assumed to occur in a time interval smaller than a fixed interval h so that, the total population in each site (i, j), given by N i , j = S i , j + I i , j + R i , j, remained constant (for example, individual leaves his home site (i, j) to work at a neighboring site and returns to his home in a time interval less than h). We numerically explore some scenarios of population interaction, based on distinct choices of width α, that include a hypothetically rapidly closedness and reopening of the economy. The results found show interesting dynamics in the infected population due to the interaction parameter α(t) between the populations. Finally, the model can be applied to evaluate the spread of diseases such as COVID-19 enabling decision making in different contexts.

A Análise de Parcimônia de Endemismo (PAE) é um método da biogeografia histórica que é usado para detectar e conectar áreas de endemismo. Baseando-se em dados de distribuição de primatas Neotropicais, construíram-se matrizes de dados utilizando-se quadrículas, regiões entre rios e áreas de endemismo pré-determinadas para aves como Unidades Geográficas Operacionais (OGUs). Codificou-se a ausência da espécie na OGU como 0 (zero) e a presença como 1 (um). Uma área hipotética com ausência total de espécies de primatas foi usada como grupo externo para polarização. Todas as três análises resultaram em grupos similares de áreas de endemismo, coincidindo com a distribuição de biomas na região Neotropical: uma área incluindo a América Central e o extremo Noroeste da América do Sul; outra, a Bacia Amazônica; e, uma terceira, a Mata Atlântica, Caatinga, Cerrado e Chaco.

The Parsimony Analysis of Endemicity (PAE) is a method of historical biogeography that is used for detecting and connecting areas of endemism. Based on data on the distribution of Neotropical primates, we constructed matrices using quadrats, interfluvial regions and pre-determinated areas of endemism described for avians as Operative Geographic Units (OGUs). We codified the absence of a species from an OGU as 0 (zero) and its presence as 1 (one). A hypothetical area with a complete absence of primate species was used as outgroup to root the trees. All three analyses resulted in similar groupings of areas of endemism, which match the distribution of biomes in the Neotropical region. One area includes Central America and the extreme Northwest of South America, other the Amazon basin, and another the Atlantic Forest, Caatinga, Cerrado and Chaco.