A model-based assessment of the cost-benefit balance and the plea bargain in criminality -- A qualitative case study of the Covid-19 epidemic shedding light on the "car wash operation" in Brazil

We developed a simple mathematical model to describe criminality and the justice system composed of the police investigation and court trial. The model assessed two features of organized crime -- the cost-benefit analysis done by the crime-susceptible to commit a crime and the whistleblowing of the law offenders. The model was formulated considering the mass action law commonly used in the disease propagation modelings, which can shed light on the model's analysis. The crime-susceptible individuals analyze two opposing forces -- committing crime influenced by the law offenders not caught by police neither imprisonment by the court trial (benefit of enjoying the corruption incoming), and the refraction to commit crime influenced by those caught by police or condemned by a court (cost of incarceration). Moreover, we assessed the dilemma for those captured by police investigation to participate in the rewarding whistleblowing program. The model was applied to analyze the "car wash operation" against corruption in Brazil. The model analysis showed that the cost-benefit analysis of crime-susceptible individuals whether the act of bribery is worth or not determined the basic crime reproduction number (threshold); however, the rewarding whistleblowing policies improved the combat to corruption arising a sub-threshold. Some adopted mechanisms to control the Covid-19 pandemic shed light on understanding the "car wash peration" and threatens to the fight against corruption. Appropriate coverage of corruption by media, enhancement of laws against white-collar crimes, well-functioning police investigation and court trial, and the rewarding whistleblowing policies inhibited and decreased the corruption.