Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19.

This paper presents a novel numerical technique for the identification of effective and basic reproduction numbers, Re and R0, for long-term epidemics, using an inverse problem approach. The method is based on the direct integration of the SIR (Susceptible-Infectious-Removed) system of ordinary differential equations and the least-squares method. Simulations were conducted using official COVID-19 data for the United States and Canada, and for the states of Georgia, Texas, and Louisiana, for a period of two years and ten months.

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.

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.