International Scientific Collaboration Title: Modeling and Analytical Solutions for Epidemic Diseases
Project Coordinator: Prof. Dr. Teoman Özer (Istanbul Technical University)
Investigators: Prof. Dr. Martin Kröger (ETH Zurich)
Ph. D. Student. Navid Amiri Babaei (Istanbul Technical University)
In this study, the analytical, integrability, and dynamic properties of an epidemic COVID-19 model called SEIARM, which is a system of coupled nonlinear ordinary differential equations in six dimensions from a mathematical point of view, were investigated by the artificial Hamilton method based on Lie symmetry groups. Using this method, the model's Lie symmetries, first integrals, and analytical solutions were analyzed using some constraint relations for the model parameters. By examining the basic factors such as how many people are susceptible, infected, or recovered, the "constraints" within the model were revealed. These "constraints" provide valuable information about the potential spread of COVID-19 and the effectiveness of control measures by showing us how the virus can spread under different conditions, especially when the critical model parameter is between 0 and 1. Analytical solutions and graphical representations for some real values of the model parameters obtained from China during the pandemic period were also provided.
In addition, in a second study, the integrability properties and analytical solutions of an initial-value problem in the form of a system of fourth-dimensional and first-order coupled nonlinear ordinary differential equations for a SIRD model (SIRD-CAAP) with a fixed population size were theoretically analyzed using the partial Hamilton method. This research presents a COVID-19 study as a real-world problem using the analytical results obtained in the study. The first integrals and associated complete analytical solutions of the model were examined in terms of algebraic relations between the model parameters. Then, for both cases, the dynamic behaviors of the model based on the analytical solutions were analyzed and graphical representations of the closed-form solutions were shown and compared. It was also shown that the SIRD-CAAP model can be decomposed based on its first integrals for all cases from a mathematical perspective. In addition, the periodicity properties and classification of the regimes of the solutions according to the model parameter restrictions were investigated. Finally, COVID-19 applications were given using data for different countries.
Babei N.A., Kröger M., Özer T., Physica D: Nonlinear Phenomena, 468, 134291, 2024
Babei N.A., Kröger M., Özer T., Applied Mathematical Modelling, 127, 237-258, 2024