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.

No abstract

No abstract

a b s t r a c tA method for solving the inverse problem for coefficient identification in the EulerBernoulli equation from over-posed data is presented. The original inverse problem is replaced by a minimization problem. The method is applied to the problem for identifying the coefficient in the case when it is a piece-wise polynomial function. Several examples are elaborated and the numerical results confirm that the solution of the imbedding problem coincides with the direct simulation of the original problem within the second order of approximation.Published by Elsevier B.V.

No abstract