Scaling effect in COVID-19 spreading: The role of heterogeneity in a hybrid ODE-network model with restrictions on the inter-cities flow.

The new Covid-19 pandemic has left traces of suffering and devastation to individuals of almost all countries worldwide and severe impact on the global economy. Understanding the clinical characteristics, interactions with the environment, and the variables that favor or hinder its dissemination help the public authorities in the fight and prevention, leading for a rapid response in society. Using models to estimate contamination scenarios in real time plays an important role. Population compartments models based on ordinary differential equations (ODE) for a given region assume two homogeneous premises, the contact mechanisms and diffusion rates, disregarding heterogeneous factors as different contact rates for each municipality and the flow of contaminated people among them. This work considers a hybrid model for covid-19, based on local SIR models and the population flow network among municipalities, responsible for a complex lag dynamic in their contagion curves. Based on actual infection data, local contact rates ( ß ) are evaluated. The epidemic evolution at each municipality depends on the local SIR parameters and on the inter-municipality transport flow. When heterogeneity of ß values and flow network are included, forecasts differ from those of the homogeneous ODE model. This effect is more relevant when more municipalities are considered, hinting that the latter overestimates new cases. In addition, mitigation scenarios are assessed to evaluate the effect of earlier interventions reducing the inter-municipality flux. Restricting the flow between municipalities in the initial stage of the epidemic is fundamental for flattening the contamination curve, highlighting advantages of a contamination lag between the capital curve and those of other municipalities in the territories.

Socio-economic urban scaling properties: Influence of regional geographic heterogeneities in Brazil.

The recent efforts dedicated to understanding important features and consequences of city growth have profited from the scaling approach to urban indicators. This kind of analysis can be conveniently used to investigate the impact of geo-economic transformations, like fast urbanization and industrial development, which occurred in continental size countries (e.g., India, China, and Brazil) during the past half-century. Profiting from high quality data, this work explores how scaling relationships among urban indicators are influenced by strong regional heterogeneities in Brazil. It is based on economic, infrastructure and violence related data sets for the time interval 2002-2016. Results indicate that regional specificities related to infrastructure, economic development, and geography have a larger influence on the absolute value of the urban indexes. Regional scaling similarities and differences among Brazilian regions were also uncovered. Interesting enough, the results indicate that the richest and poorest Brazilian regions share similar scaling behavior, despite all huge different local influences. By contrast, the results for the two richest regions, with similar average values of urban indexes and the same kind of local influences have rather different scaling properties. Thus, scaling analysis suggests that distinct political solutions might be necessary to improve life's quality, even for two regions with similar average values of urban indicators.

Evolutionary analysis of apolipoprotein E by Maximum Likelihood and complex network methods.

Apolipoprotein E (apo E) is a human glycoprotein with 299 amino acids, and it is a major component of very low density lipoproteins (VLDL) and a group of high-density lipoproteins (HDL). Phylogenetic studies are important to clarify how various apo E proteins are related in groups of organisms and whether they evolved from a common ancestor. Here, we aimed at performing a phylogenetic study on apo E carrying organisms. We employed a classical and robust method, such as Maximum Likelihood (ML), and compared the results using a more recent approach based on complex networks. Thirty-two apo E amino acid sequences were downloaded from NCBI. A clear separation could be observed among three major groups: mammals, fish and amphibians. The results obtained from ML method, as well as from the constructed networks showed two different groups: one with mammals only (C1) and another with fish (C2), and a single node with the single sequence available for an amphibian. The accordance in results from the different methods shows that the complex networks approach is effective in phylogenetic studies. Furthermore, our results revealed the conservation of apo E among animal groups.