Contagious Criminal Career Models Showing Backward Bifurcations: Implications for Crime Control Policies


Eduardo Massad


Praia de Botafogo, 190 - sala 537


17 de Maio de 2018 às 16h

In this work we provide a theoretical framework to study how criminal behaviors can be treated as an infectious phenomenon. Two mathematical models inspired in the models of the spreading of infectious diseases that mimic two situations describing the contagion of susceptible individuals not yet engaged in criminal career by convicted prisoners from inside the jails. Equilibrium analyses of each model arestudied in details. The models proposed in this work include the social, economic,personal and pressure from peers aspects that can, theoretically, determine the probability with which a susceptible individual with criminal propensity engage in a criminal career. These crime-inducing parameters are treated mathematically and their inclusion in the model aims to help policy makers design crime control strategies. We propose, to the best of our knowledge by the first time in quantitative criminology, the existence of thresholds for the stability of crime-endemic equilibrium that are the equivalent to the ’basic reproduction number’ widely used in the mathematical epidemiology literature. Both models presented the phenomena of backward bifurcation and breaking-point when the contact rates are chosen as bifurcation parameters. The finding of backward bifurcation in both models implies that there is an endemic equilibrium of criminality even when the threshold parameter for contagion is below unit which, in turn, implies that control strategies are more difficult to achieve considerable impact on crime control.

*Texto informado pelo autor. 


Eduardo Massad is a Full Professor of Applied Mathematics, School of Applied Mathematics, Fundação Getúlio Vargas, Rio de Janeiro, Brazil. Last Job: Full Professor and Head of the Department of Legal Medicine, Medical Ethics and Occupational Medicine, School of Medicine, University of São Paulo, Brazil.

Brief Background Information: Medical Doctor, Professor of Medical Informatics and Tropical Medicine, B.Sc. Physics, B.Sc.(Honors) Psychology, FIMA, Chartered Mathematician (IMA-UK), Chartered Scientist (SciCoun-UK), FRSM.; Full Professor of Medical Informatics, University of Sao Paulo; Head of the Department of Legal Medcine, University of Sao Paulo; Honorary Professor of Infectious Diseases, London School of Hygiene and Tropical Medicine; Courage Fund Visiting Professor of Medicine, National University of Singapore; Visiting Professor of Statistics and Psychology, University of Derby, UK; Fellow of the Institute of Mathematics and Its Applications (FIMA); Fellow of The Royal Society of Medicine (FRSM).

Current Research Grant: Co-PI with Professor Annelies Wilder-Smith of the €12.5 million European Community Consortium Project ZIKAPlan and the $999,781 project Assessing ZIKV transmission dynamics and mitigation strategies. A multidisciplinary approach, funded by the Canadian Institute of Health