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Development of a probabilistic model for quantitative risk assessment of Covid-19 in Brazil

Pesquisadores da UFPE desenvolveram um modelo probabilístico para quantificar os riscos de uma explosão de Covid-19 no Brasil, que é o epicentro da doença na América Latina. Isso significa dizer um número excessivo de novas infecções que sobrecarregariam o sistema público de saúde. As previsões vão de 12 de julho a 10 de outubro de 2020 para vários tipos de contenções estratégicas, incluindo manter os negócios como sempre foram, isolamento social em casa (stay at home - SAH) para jovens e/ou idosos, restrições de voos entre regiões, retomada gradual dos negócios e o uso obrigatório de máscaras.



Paulo G. S. C. Siqueirab , c ; Alexandre C. A. Oliveiraa ; Heitor O. Duartea ; Márcio J. C. Mourab,c 


aDepartment of Mechanical Engineering, Universidade Federal de Pernambuco, Av. Prof. Moraes Rego, 1235 - Cidade Universitária, Recife - PE, 50740-550

bCEERMA - Center for Risk Analysis, Reliability Engineering and Environmental Modeling, Universidade Federal de Pernambuco, Recife-PE, Brazil

cDepartment of Industrial Engineering, Universidade Federal de Pernambuco, Rua Acadêmico Hélio Ramos, s/n, Cidade Universitária, CEP: 50740-530 Recife-PE, Brazil Currently under review:





Pesquisadores da UFPE desenvolveram um modelo probabilístico para quantificar os riscos de uma explosão de Covid-19 no Brasil, que é o epicentro da doença na América Latina. Isso significa dizer um número excessivo de novas infecções que sobrecarregariam o sistema público de saúde. As previsões vão de 12 de julho a 10 de outubro de 2020 para vários tipos de contenções estratégicas, incluindo manter os negócios como sempre foram, isolamento social em casa (stay at home - SAH) para jovens e/ou idosos, restrições de voos entre regiões, retomada gradual dos negócios e o uso obrigatório de máscaras. Eles indicam que: se uma estratégia de SAH fosse mantida, haveria um risco negligível de explosão e o sistema público de saúde não ficaria sobrecarregado. Para as demais estratégias de contenção, o cenário que combina a retomada gradativa dos negócios com o uso obrigatório de máscaras seria o mais eficaz, reduzindo o risco a uma categoria mais baixa, mas ainda negligível. Caso esta estratégia seja aplicada em conjunto com o investimento em mais leitos de Unidade de Terapia Intensiva (UTI), o risco pode ser reduzido a níveis negligíveis. 




We have developed a probabilistic model to quantify the risks of COVID-19 explosion in Brazil, which is the epicenter of COVID-19 in Latin America. By explosion, we mean an excessive number of new infections that would overload the public health system. We made predictions from July 12th to October 10th, 2020 for various containment strategies, including business as usual, stay at home (SAH) for young and/or elderly, flight restrictions among regions, gradual resumption of business and the compulsory wearing of masks. They indicate that: if a SAH strategy was sustained, there would be a negligible risk of explosion and the public health system would not be overloaded. For the other containment strategies, the scenario that combines the gradual resumption of business with the mandatory wearing of masks would be the most effective, reducing risk to considerable category. Should this strategy is applied together with the investment in more Intensive Care Unit beds, risk could be reduced to negligible levels.


Currently under review:

SRA - Society For Risk Analysis 



Brazil is the epicenter of coronavirus disease (COVID-19) in Latin America and is the second hardest hit country, with almost 2,5 million confirmed cases and more than 88,000 deaths by end of July 2020 (worldometers, 2020). Indeed, infected people have been confirmed in all the 5 regions: North (N), Northeast (NE), Central-West (CW), Southeast (SE), and South (S). The lack of efficient risk management and poor risk communication to the public, linked to other environmental, socio-economic factors (e.g. high proportion of young population, who are more exposed, and thus virus spreadsfaster; high population density in urban centers and ‘favelas’; economical pressure to come back to business to avoid massive unemployment and starvation) make the perspectives for Brazil even more worrisome. In this context, this work provides useful results for developing more efficient risk management and communication in Brazil. 

Since late March, when reports about SARS-CoV-2 (hereinafter, the term virus without specification refers to SARS-CoV-2) transmission patterns in Brazil started to emerge, many containment strategies have been discussed and implemented to control its spread until a vaccine is developed, licensed and manufactured. These actions include social isolation (for the purposes of this work, this is equivalent to Stay At Home (SAH) measures), vertical isolation (when SAH is applied only to the elderly), restrictions on business/studies/social activities (hereinafter, the term business refers to all of these three types of activities), gradual resumption of business, national flights restrictions and wearing of face masks. This work simulates each of these strategies, keeping all other things the same (Ceteris paribus) in order to track their effectiveness.

To assist policymakers in making decisions, many mathematical models have been proposed to describe and predict the evolution of number of infections and deaths in Brazil either at regional or national level (Canabarro et al., 2020; Coelho et al., 2020; Costa et al., 2020; Crokidakis, 2020; Mellan et al., 2020; Savi et al., 2020). However, at the best of authors’ knowledge, all these models are deterministic, i.e. the model inputs and outputs are single-point estimates, usually expected values, without proper treatment about the uncertainty. This limits the application of these outcomes because actual values may greatly vary around the expected measures. Thus, deterministic predictions may lead to imprudent decisions and actions by managers and society, and thousands of deaths as a result. In fact, a recent study highlights the importance of acknowledging uncertainty as a main component of risk of COVID-19 pandemic (Aven & Bouder, 2020).

On the other hand, our model is probabilistic in nature. The great advantage of probabilistic over deterministic approaches is that results show not only what could happen, but how likely each outcome is. In this way, one can measure and communicate uncertainty in results. This is the main characteristic of our model. 

There are a few probabilistic COVID-19 models to predict cases in Brazil (Crokidakis, 2020; Martinez et al., 2020; Sousa et al., 2020). Similarly to our model, they structure the population in stages and have parameters that govern the transition from one stage to another, e.g. the infection rate governs the transition from susceptible to infected individuals (note: this rate should not be confused with the reproduction number (R), i.e. a dimensionless value that describes the number of secondary cases one case would produce; for more details see (Delamater et al., 2019)). In comparison to these models, another feature that makes ours innovative is how we treat the infection rate. In the aforementioned models, this parameter is assumed to be constant over time and, then, the number of infected grows exponentially and is unlimited until the end of the forecast, which causes results to be overestimated. To simulate containment scenarios, they (Crokidakis, 2020; Martinez et al., 2020; Sousa et al., 2020) manually alter the infection rate and generate predictions.

Conversely, the approach considered in this work is grounded on the concepts of population ecology (H Resit Akçakaya et al., 1999), in which the virus dynamics can be described not only in terms of the host parameters, but also of those inherent to the virus itself. We aggregate in the model the concept of Density-Dependence (DD), which is the modification in the influence of any factor that affects the population growth as the population density changes (H Resit Akçakaya et al., 1999). In this sense, the population density of exposed susceptible people (i.e. the carrying capacity of the virus) decreases over time as the virus spreads. This happens because the harder the virus finds susceptible people to infect, the lower the infection rate.

Thus, our model includes two realistic features that the aforementioned approaches do not. First, for any containment scenario, as more people become infected, the susceptible population density decreases, and then does the infection rate. Secondly, to simulate different containment measures, we do not manually alter the respective infection rate, because we consider that containment strategies do not instantly reduce the infection rate since the start of the simulation. Instead, we consider that each containment strategy causes a reduction in the carrying capacity and, thus, accelerates the decrease in the infection rate over time. We perform this through Contest type DD modelling (H Resit Akçakaya et al., 1999), as we explain further.

A few more contributions are: (i) our model is structured by age groups (young and elderly) with different probabilities of fatality and/or infection, which allows to simulate specific containment strategies; (ii) it is a metapopulation model structured by 5 subpopulations, representing each Brazilian region, with different probabilities of fatality and/or infection as well as different probabilities of dispersal between subpopulations; (iii) it is able to assess quantitatively the effectiveness of recent containment plans (e.g. (a) gradual resumption of economy; and (b) mass distribution and compulsory wearing of masks), no matter they are applied either in an isolated or integrated manner.

In this work, we use the well-known definition of risk as a measure of probability/frequency/likelihood and undesired consequences (CPR18E, 2005), PURPLE BOOK). More specifically, this work conducts a Quantitative Microbial Risk Assessment (QMRA), which is the formal process of estimating the probability of undesired consequences to humans due to exposure to one or more microbial pathogens (Duarte et al, 2019; Haas et al., 1999). The main objective of a QMRA is to predict relative risks for future scenarios and/or to evaluate the effectiveness of different containment measures. 

Therefore, the aim of this paper is to develop an epidemiological probabilistic model for COVID-19 that overcomes the aforementioned drawbacks of other models and is tailored for a QMRA. To the best of our knowledge, this works conducts the first QMRA of COVID-19 in Brazil. We set out to answer the following questions in order to steer Brazilian policymakers on how to prioritize resources for designing containment scenarios:

  • How many lives can we save and how many infections can we reduce until October 10th if we decide to implement a certain containment strategy?
  • What is the probability of having a collapse in the Brazilian health system by October 10th for each containment scenario? Would a gradual economic resumption plan be effective to reduce the risk of collapse? Is vertical isolation effective? What about Business as Usual (BAU) with the wearing of masks?
  • Which regions are most at risk in the future? Which ones deserve the most effort to control the disease? What is the order of prioritization?
  • What is the risk category for an integrated strategy where wearing of masks is mandatory for everyone out of home together with a gradual resumption of the economy? How many more Intensive Care Unit (ICUs) beds would it be necessary to invest, alongside with the integrated strategy, to reduce the risk to negligible levels?

The remainder of this work is structured as follows. First, we present the model structure and the assumptions, which is flexible in parameterization and can be used to simulate several containment scenarios. Next, we discuss the materials and methods to carry out a QMRA and explain how we consolidate and parameterize scenarios. Then, we present the model results for each scenario, compare them, answer the questions raised above, and discuss the advantages and limitations of the model. Finally, we draw some conclusions and propose suggestions for future works.


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Data da última modificação: 19/09/2020, 10:53