Dynamics of COVID-19 using inverse problem for coefficient identification in SIR epidemic models

Abstract

Highlights The inverse problem for estimating the time-dependent transmission and removal rates in the SIR epidemic model is derived and solved. The minimization problem uses the entire dataset with data available on June 21, 2020 for estimating the non-constant rates. The obtained numerical results demonstrate that the transmission and removal rates and the unknown functions are accurately estimated. The numerically computed rates are used for forecasting the COVID-19 pandemic for the world and a number of countries. The results of this research give insight of the pandemic in parts of the world and could help in determining policy. The SIR model is a good choice for the short period of time of this epidemic; however, it possesses known limitations in case of a long term infectious disease. In future, we plan to use other models. Depending on future developments of the disease, we may consider models addressing non-constant population, latency, reinfection, and vaccine.

Two Inverse Problems Solution by Feedback Tracking Control

“…, based on the feedback strategy (15), and u α (•) given by ( 10), solve the input restoration problem. However, a feedback solution is simpler from the computational point of view and it is more stable numerically.…”

“…The problems of restoration of a system input and coefficients arise in various applications such as metrology [1][2][3][4], image processing [5,6], spectroscopy [7], geophysics [8,9], process control [10], engineering [11,12], medicine [13,14], and many others. The identification of the virus spread models, i.e., the restoration of the coefficients of the corresponding differential equations, became crucial in the period of coronavirus pandemic (see, e.g., [15,16]) for constructing reliable forecasts of the pandemic evolution. These problems belong to a wide class of ill-posed (inverse) problems [17][18][19].…”

Dynamics of an SIR-Based COVID-19 Model With Linear Incidence Rate, Nonlinear Removal Rate, and Public Awareness

“…Various approaches were used in the literature for this purpose. These include least squares method that minimizes the sum of squared residuals [2] and variational method applied to time-depended model parameters [18]. Comunian et al [19] provided a critical analysis of the inverse problem.…”

Adaptive SIR model for propagation of SARS-CoV-2 in Brazil

“…In this work we further investigate the dynamics of the SARS-CoV-2 epidemic within the Brazilian territory from March to December, covering the second wave as well. To achieve this task, we resort to an adaptive susceptible–infected–removed (SIR) model [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , which also allows us to predict epidemic evolution within 10–20 days ahead. The calculations employ dynamic recuperation and propagation rates (namely and parameters in the SIR model) and we are able to reproduce the time series of the number of confirmed cases with less than 5% error.…”