Topics of Research

The adoption of new technology and the speed with which it happens is a subject of study since the sixties, particularly from Rogers' book. Very slow adoption can impede the growth of the new technology or lead to its stagnation and demise, as was the case with the Concorde supersonic aircraft. In our first contribution, we studied the dynamics of the adoption of innovations, taking into account the cost of innovation, an influence of advertising and a resistance to technology change. To these factors is added social influence, which can be an attractive factor for some agents and negative for others who do not want to follow the majority. We have shown that the role of agents who resist as changes is an important factor, they can not only influence the adoption of new technologies, but also determine when that technology will finally be adopted. We also demonstrate that the interaction with small groups is very important, accelerating the adoption process.

We are interested in topological fragility or resilience of graphs and real complex networks (biological, social, infrastructure, etc), in general, and, in particular, criminal networks. For this purpose, the correct identification of the organization of relationships, whether in community structure or in nested hierarchical organizations or in a mixture of both is a basic and essential subject. One of the project's objectives, of potential practical utility, is to identify and attack communities in real criminal networks. The more abstract objective consists of the analysis, identification, and modeling of hierarchical structures that can mask the true modular structure of social or criminal networks.

We study the dynamics of disease propagation using the SIR model (Susceptible-Infected-Removed) and variants such as SEIR, SAIR, etc in networks and paradigmatic structured meta-populations, or adapted from available data. The objective is to determine epidemic thresholds, characterize steady states, and determine periods of epidemic fluctuations. Our goal is the realistic modeling of disease spreading, through the dynamic construction of networks and the use of realistic distribution of typical disease times. We have used real data to analyze the spread of the COVID-19 pandemic. We have analyzed the trend of the COVID-19 pandemic in China, in Brazil and in the rest of the world. We have also studied the spreading-rate related measure of COVID-19 as a function of population density and population size for all US counties, Brazilian cities and German cities. Contrary to what is the common hypothesis, we observed a higher per-capita contact rate for higher city’s population density and population size, with population size having a more explanatory effect than the population density.