Spreading of COVID-19 in Brazil: Impacts and uncertainties in social distancing strategies

Abstract

Brazil's continental dimension poses a challenge to the control of the spread of COVID-19. Due to the country specific scenario of high social and demographic heterogeneity, combined with limited testing capacity, lack of reliable data, under-reporting of cases, and restricted testing policy, the focus of this study is twofold: (i) to develop a generalized SEIRD model that implicitly takes into account the quarantine measures, and (ii) to estimate the response of the COVID-19 spread dynamics to perturbations/uncertainties. By investigating the projections of cumulative numbers of confirmed and death cases, as well as the effective reproduction number, we show that the model parameter related to social distancing measures is one of the most influential along all stages of the disease spread and the most influential after the infection peak. Due to such importance in the outcomes, different relaxation strategies of social distancing measures are investigated in order to determine which strategies are viable and less hazardous to the population. The results highlight the need of keeping social distancing policies to control the disease spread. Specifically, the considered scenario of abrupt social distancing relaxation implemented after the occurrence of the peak of positively diagnosed cases can prolong the epidemic, with a significant increase of the projected numbers of confirmed and death cases. An even worse scenario could occur if the quarantine relaxation policy is implemented before evidence of the epidemiological control, indicating the importance of the proper choice of when to start relaxing social distancing measures.

Framework for enhancing the estimation of model parameters for data with a high level of uncertainty

“…In order to understand the model response to noisy data, we adopt an extension of the compartmental SEIR model, termed SEIRPD-Q model, which encompasses concepts of the models proposed by Jia et al [26] and Vol-patto et al [27]. Initially, consider a population susceptible to a viral outbreak, whose rate of transmission per contact is given by β .…”

“… The model adopted presents some fundamental differences in relation to those on which we are based: first, Jia et al [26] consider that only susceptible individuals are subject to quarantine measures, which is modeled using an explicit compartment and also considering an additional parameter that controls the social distancing relaxation; second, we disregard the asymptomatic compartment due to the uncertainties regarding the reported data, and in-corporate the dynamics related to positively diagnosed individuals, of which data are more reliable (as proposed by Volpatto et al [27]); third, we consider only the mortality rate of positively diagnosed individuals, unlike Vol-patto et al [27]. Additionally, we also compute the cumulative number of infected and dead individuals, which are respectively given by These quantities are used in the estimation of the model parameters and the term cumulative number of infected individuals is often used interchangeably with confirmed cases throughout the text.…”

Mathematical Parameters of the COVID-19 Epidemic in Brazil and Evaluation of the Impact of Different Public Health Measures

“…Finally, in case 4, the model was redefined for the second stage of the epidemy evolution in Brazil, through estimation of five parameters associated with new time-variable functions for the transmission rate and partition coefficient along this second phase. The statistical inversion approach here implemented falls within the Bayesian statistical framework [8][9][10][11][12], in which (probability distribution) models for the measurements and the unknowns are constructed separately and explicitly, as shall be briefly reviewed in what follows.…”

“…If the proposed jump is rejected, the current value is tally again. For more details on theoretical aspects of the Metropolis-Hastings algorithm and MCMC methods and its application, the reader should refer to References [8][9][10][11][12].…”

“…However, a Bayesian inference approach is here adopted for parametric estimations, complementing these analytical estimates obtained through the hypothesis of exponential growth in the early stage of the epidemy, before any public health intervention. Other recent contributions have successfully combined phenomenological deterministic compartmental models with Bayesian inference approaches for state estimation and parameter estimation [12][13][14][15][16]. For the present purposes, the Markov Chain Monte Carlo method with the Metropolis-Hastings sampling algorithm has been employed [17][18][19][20][21].…”