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

Abstract

A SIRU-type epidemic model is employed for the prediction of the COVID-19 epidemy evolution in Brazil, and analyze the influence of public health measures on simulating the control of this infectious disease. The proposed model allows for a time variable functional form of both the transmission rate and the fraction of asymptomatic infectious individuals that become reported symptomatic individuals, to reflect public health interventions, towards the epidemy control. An exponential analytical behavior for the accumulated reported cases evolution is assumed at the onset of the epidemy, for explicitly estimating initial conditions, while a Bayesian inference approach is adopted for the estimation of parameters by employing the direct problem model with the data from the first phase of the epidemy evolution, represented by the time series for the reported cases of infected individuals. The evolution of the COVID-19 epidemy in China is considered for validation purposes, by taking the first part of the dataset of accumulated reported infectious individuals to estimate the related parameters, and retaining the rest of the evolution data for direct comparison with the predicted results. Then, the available data on reported cases in Brazil from February 15th until March 29th, is used for estimating parameters and then predicting the first phase of the epidemy evolution from these initial conditions. The data for the reported cases in Brazil from March 30th until April 23rd are reserved for validation of the model. Then, public health interventions are simulated, aimed at evaluating the effects on the disease spreading, by acting on both the transmission rate and the fraction of the total number of the symptomatic infectious individuals, considering time variable exponential behaviors for these two parameters. This first constructed model provides fairly accurate predictions up to day 65 below 5% relative deviation, when the data starts detaching from the theoretical curve. From the simulated public health intervention measures through five different scenarios, it was observed that a combination of careful control of the social distancing relaxation and improved sanitary habits, together with more intensive testing for isolation of symptomatic cases, is essential to achieve the overall control of the disease and avoid a second more strict social distancing intervention. Finally, the full dataset available by the completion of the present work is employed in redefining the model to yield updated epidemy evolution estimates.

Non-pharmaceutical interventions during the COVID-19 pandemic: A review

“…The first column describes the main categories, the second the sub-categories, the last the country/countries focus of each study and the references. Category Subcategory Country/countries of study and reference Compartmental SIR-like Brazil, China [48] ; China [49] , [50] , [51] ; China, Italy [52] ; China, France, Iran, Italy, South Korea, USA [53] ; France, Iran, Italy [54] ; Germany [55] ; India [56] ; Italy [57] ; USA [58] ; 187 countries [45] ; several European countries [44] , [59] SIR-like age structured China [60] , Italy [61] , 143 countries [47] SEIR-like Argentina, Japan, Indonesia, New Zealand, Spain, USA [62] ; Canada [63] , [64] ; Canada, Germany, Italy [65] ; China [66] , [67] , [68] , [69] ; China, Italy [70] ; China, UK [71] ; Germany [72] ; India [73] , [74] ; Indonesia [75] ; Ireland [76] ; Mexico [77] ; Pakistan [78] ; South Korea [79] , [80] ; Switzerland [81] ; USA [82] , [83] ...…”

“…We start considering the body of modeling work based on SIR-like models. This subset of papers studies the effects of isolation and quarantine policies [49] , models NPIs as effective changes of the parameters [44] , [45] , [48] , [50] , [52] , [54] , [55] , [56] , [57] , [59] , investigates the impact of different policies [53] , [58] , and defines the conditions for the optimal control of the spreading [51] . In the following, I will highlight some of these approaches.…”

“…Interestingly, they observed that only the compound effects of NPIs, put in place at different moments, was enough to bring the reproductive number below one. A similar estimation framework has been used to model the pandemic in Brazil and China [48] . In this paper however, authors impose a precise functional form of the variation of the transmission rate: for where is the value in absence of any interventions, is the modulation introduced by NPIs and is the time in which the interventions are put in place.…”

A Modelization of the Propagation of COVID-19 in Regions of Spain and Italy with Evaluation of the Transmission Rates Related to the Intervention Measures

“…The advance of the disease caused by the corona virus SARS-CoV-2 (COVID-19) surprised world population in the early 2020 as its rapid spread and virulence affected the lives of millions of people and caused thousands of deaths. Given the importance of this situation, a great number of mathematical models explaining the spread of the disease have been proposed [ 1 , 2 , 3 ], with a set of prescribed characteristic parameters defining the infection over time in a given population. While there is a great number of different models we can use to describe a disease like this [ 4 , 5 , 6 ], due to the limited data at the time of writing this paper, we have chosen a SIR model, which fits better the available data.…”

Epidemic Dynamics via Wavelet Theory and Machine Learning with Applications to Covid-19

“…However, while those use single waves coming from solutions differential equations, we use general wavelet functions such as Gaussian functions, log-normal functions, Gompertz density functions and Beta prime density functions, which all satisfy our general condition of being epidemic-fitted in the sense of Definition 2. We also refer to the works in [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 ] for other approaches on modelling and forecasting the spread of Covid-19 epidemic using deep learning, machine learning, time series analysis, network model, stochastic model and deterministic compartmental framework.…”