Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19.

An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics-the World, Israel, The United States of America, and Japan.

Inverse problem for adaptive SIR model: Application to COVID-19 in Latin America.

This work presents a method for solving an Adaptive Susceptible-Infected-Removed (A-SIR) epidemic model with time-dependent transmission and removal rates. Available COVID-19 data as of March 2021 are used for identifying the rates from an inverse problem. The estimated rates are used to solve the adaptive SIR system for the spread of the infectious disease. This method simultaneously solves the problem for the time-dependent rates and the unknown functions of the A-SIR system. Presented results show the spread of COVID-19 in the World, Argentina, Brazil, Colombia, Dominican Republic, and Honduras. Comparisons of the reported affected by the disease individuals from the available real data and the values obtained with the A-SIR model demonstrate how well the model simulates the dynamic of the infectious disease.

Dynamics of COVID-19 Using Inverse Problem for Coefficient Identification in SIR Epidemic Models

This work deals with the inverse problem in epidemiology based on a SIR model with time-dependent infectivity and recovery rates, allowing for a better prediction of the long term evolution of a pandemic. The method is used for investigating the COVID-19 spread by first solving an inverse problem for estimating the infectivity and recovery rates from real data. Then, the estimated rates are used to compute the evolution of the disease. The time-depended parameters are estimated for the World and several countries (The United States of America, Canada, Italy, France, Germany, Sweden, Russia, Brazil, Bulgaria, Japan, South Korea, New Zealand) and used for investigating the COVID-19 spread in these countries.