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 15 February until 29 March, 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 30 March until 23 April 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.
Highlights
A new human coronavirus started spreading in Wuhan, China, by the end of 2019, and turned into a pandemic disease called COVID-19 as declared by the World Health Organization on 11 March 2020.Since the affected countries and cities around the world have been reacting in different ways, towards locally controlling the disease evolution
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
A SIRU-type model is adopted, which inherently accounts for the unreported symptomatic infectious individuals
Summary
A new human coronavirus started spreading in Wuhan, China, by the end of 2019, and turned into a pandemic disease called COVID-19 as declared by the World Health Organization on 11 March 2020. The SIRU-type model in References [2,3,4,5,6,7,8,9,10,11] is implemented for the direct problem formulation of the COVID-19 epidemy evolution, adding a time variable parametrization for the fraction of asymptomatic infectious that become reported symptomatic individuals, a very important parameter in the public health measure associated with massive testing and consequent focused isolation. The goal of the inverse problem analysis was estimating the parameters associated with the transmission rate and the fraction of asymptomatic infectious that become reported symptomatic individuals, which can be quite different in the various regions and countries and may vary according to the public health measures. The full dataset of reported cases available by completion of this work, was employed in the redefinition of the model to provide predictions of the epidemy evolution based on more recent observations at that particular moment
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