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 (preprint)

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.

Quarantine, relaxation and mutation explaining the CoViD-19 epidemic in Sao Paulo State (Brazil) (preprint)

BackgroundThe continuous SARS-CoV-2 transmission in several countries could contribute to the mutations appearance. The circulation of more virulent variants may increase the number of severe CoViD-19 needing hospital care and fatalities hugely. MethodsThe partial quarantine in Sao Paulo State and further relaxation associated with the mutations are explained by a mathematical model based on the CoViD-19 natural history encompassing the age-dependent fatality. The model parameters were fitted considering the observed data from Sao Paulo State. ResultsThe partial quarantine was explained by the less virulent SARS-CoV-2 transmission, but the relaxation alone could not explain the epidemic observed in Sao Paulo State. However, more virulent variants plus the transmission among isolated individuals explained the increased CoViD-19 fatalities. ConclusionsThe model described the CoViD-19 epidemic in Sao Paulo State by considering the partial quarantine, relaxation and mutations. The model provided a potential epidemiological scenario in the absence of mass vaccination.

Evaluating the trade-off between transmissibility and virulence of SARS-CoV-2 by mathematical modeling (preprint)

BackgroundAt the beginning of 2020, SARS-CoV-2 spread to all continents, and since then, mutations have appeared in different regions of the world. The appearance of more virulent mutations leads to asseverate that they are also more transmissible. We analyzed the lower and higher virulent SARS-CoV-2 epidemics to establish a relationship between transmissibility and virulence based on a mathematical model. MethodsA compartmental mathematical model based on the CoViD-19 natural history encompassing the age-dependent fatality was applied to evaluate the SARS-CoV-2 transmissibility and virulence. The transmissibility was measured by the basic reproduction number R0 and the virulence by the proportion of asymptomatic individuals. The model parameters were fitted considering the observed data from Sao Paulo State. ResultsThe numbers of severe CoViD-19 and deaths are three times higher, but R0 is 25% lower in more virulent SARS-CoV-2 transmission than in a less virulent one. However, the number of more virulent SARS-CoV-2 transmitting individuals is 25% lower, mainly due to symptomatic individuals isolation, explaining the increased transmission in lower virulence. ConclusionsThe quarantine study in Sao Paulo State showed that the more virulent SARS-CoV-2 resulted in a higher number of fatalities but less transmissible than the less virulent one. One possible explanation for the number of deaths surpassing that predicted by the low virulent SARS-CoV-2 infection could be the transmission of more virulent variant(s).

The SIR model estimates incorrectly the basic reproduction number for the covid-19 epidemic (preprint)

The transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) becomes pandemic, but presents different patterns in the world. To characterize the epi- demic of coronavirus disease 2019 (covid-19) in each countries and regions, mathematical models were formulated aiming the estimation of the basic reproduction number R0. Simple mathematical model, the SIR model, provided lower estimation for R0, ranging from 1.5 to 3.0. However, more elaborate model presented here estimated higher value for R0, 9.24 and 8.0 respectively, for Sao Paulo State (Brazil) and Spain. Additionally, SIR model estimated R0 using the severe covid-19 cases, which are not participating in the SARS-CoV-2 transmission chain.

Evaluating the impacts of release in Sao Paulo State (Brazil) on the epidemic of covid-19 based on mathematical model (preprint)

To flatten the curve of the natural epidemic of covid-19, many countries adopted lockdown or isolation resulting in the containment of the SARS-CoV-2 transmission. However, an important question arises about the strategies of release of isolated persons to avoid overloaded hospitals and increased deaths. Sao Paulo State (Brazil) implemented the isolation of the population in non- essential activities on March 24, and the progressive flexibilization considering the characteristics of each location (release of the isolated population) initiated on June 15. A mathematical model based on the natural history of covid-19 was applied to describe the epidemiological scenario with isolation in Sao Paulo State, and assess the impact of release on the covid-19 epidemic. Using data collected from Sao Paulo State, we estimated the model parameters to obtain the curves of the epidemic, the number of deaths, and the clinical evolution of covid-19. The epidemic under isolation was the framework to evaluate the strategies of the release, that is, how these curves are changed with the release of isolated persons. We evaluated three strategies of release. First two strategies considered four releases in the isolated population in four equal proportions, but successive releases elapsed by 14 and 21 days. In each strategy the beginning of the release was on June 29 and July 13, when the effective reproduction number Ref was evaluated. The third strategy aimed at the protection of the elder subpopulation. We observed that the delay to begin the release and the increased elapse between successive releases resulted in a better scenario by decreasing severe covid-19 cases and, consequently, to avoid overloaded hospitals. We also observed that the release delayed to achieve lower values for Ref and infectious persons retarded in several months the quick increasing phase of the forthcoming epidemic. However, this epidemic can be flattened or even suppressed by isolation of infectious persons by mass testing and/or by rigid adoption of protective measures and social distancing.

Mathematical modeling of the transmission of SARS-CoV-2 '' Evaluating the impact of isolation in Sao Paulo State (Brazil) and lockdown in Spain associated with protective measures on the epidemic of covid-19 (preprint)

Coronavirus disease 2019 (covid-19), with the fatality rate in elder (60 years old or more) being much higher than young (60 years old or less) patients, was declared a pandemic by the World Health Organization on March 11, 2020. Taking into account this age-dependent fatality rate, a mathematical model considering young and elder subpopulations was formulated based on the natural history of covid-19 to study the transmission of the SARS-CoV-2. This model can be applied to study the epidemiological scenario resulting from the adoption of isolation or lockdown in many countries to control the rapid propagation of covid-19. We chose as examples the isolation adopted in Sao Paulo State (Brazil) in the early phase but not at the beginning of the epidemic, and the lockdown implemented in Spain when the number of severe covid-19 cases was increasing rapidly. Based on the data collected from Sao Paulo State and Spain, the model parameters were evaluated and we obtained higher estimation for the basic reproduction number R0 (9.24 for Sao Paulo State, and 8 for Spain) compared to the currently accepted estimation of R0 around 3. The model allowed to explain the flattening of the epidemic curves by isolation in Sao Paulo State and lockdown in Spain when associated with the protective measures (face mask and social distancing) adopted by the population. However, a simplified mathematical model providing lower estimation for R0 did not explain the flattening of the epidemic curves. The implementation of the isolation in Sao Paulo State before the rapidly increasing phase of the epidemic enlarged the period of the first wave of the epidemic and delayed its peak, which are the desirable results of isolation to avoid the overloading in the health care system.

Evaluating epidemiological scenarios of isolation and further releases considering protection actions to control transmission of CoViD-19 in Sao Paulo State, Brazil. (preprint)

Sao Paulo State registered the first case of CoViD-19 on 26 February, the first death due to CoViD-19 on 16 March, and implemented the isolation of the population in non- essential activities on 24 March, which is programmed to end on 1 June. A mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations was formulated based on the natural history of CoViD-19 to study the transmission of the new coronavirus in Sao Paulo State, Brazil. This deterministic model used the data collected in Sao Paulo State to estimate the model parameters and to evaluate the effects of herd protection, that is, isolation and personal and collective protective measures. Based on the estimated parameters, we evaluated the scenarios of three releases divided in equal proportions elapsed by 14 days between releases, but beginning in three different times (the first release occurring on 1 and 23 June, and 6 July). We concluded that these three strategies of release are equivalent (little difference) in reducing the number of severe CoViD-19 if social behaviour does not change. However, if protective measures as using face mask and hygiene (washing hands, for instance) and social distancing could be massively disseminated in the population to decrease the transmission of CoViD-19 by 80%, we concluded that the health care system may not collapse with release.

Mathematical model describing CoViD-19 in Sao Paulo State, Brazil - Evaluating isolation as control mechanism and forecasting epidemiological scenarios of release (preprint)

We formulated a mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations to describe the introduction and dissemination of new coronavirus epidemics in the Sao Paulo State, Brazil. From the data collected in Sao Paulo State, we estimated the model parameters and calculated the basic reproduction number as R0 = 6.828. Considering isolation as a control mechanism, we varied the releasing proportions of young and elder persons to assess their epidemiological impacts. The best scenarios were release of young persons, but maintaining elder persons isolated. To avoid the collapse of the health care system, the isolation must be at least 80%.

Modeling the transmission of new coronavirus in São Paulo State, Brazil -- Assessing epidemiological impacts of isolating young and elder persons (preprint)

We developed a mathematical model to describe the transmission of new coronavirus in the S\~ao Paulo State, Brazil. The model divided a community in subpopulations comprised by young and elder persons, in order to take into account higher risk of fatality among elder persons with severe CoViD-19. From data collected in the S\~ao Paulo State, we estimated the transmission and additional mortality rates, from which we calculated the basic reproduction number R0. From estimated parameters, estimation of the deaths due to CoViD-19 was three times lower than those found in literature. Considering isolation as a control mechanism, we varied isolation rates of young and elder persons in order to assess their epidemiological impacts. The epidemiological scenarios focused mainly on evaluating the number of severe CoViD-19 cases and deaths due to this disease when isolation is introduced in a population.