International Scientific Collaboration on Modeling and Analytical Solutions for Epidemic Diseases International

by Ramazan Özgür İridere | Dec 12, 2024

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

İTÜ Faculty of Civil Engineering

It can be accepted that the history of ITU Civil Engineering Faculty was commenced in 1727 by the establishment of Humbarahane during the era of Damat İbrahim Paşa. However, this attempt was to no avail due to the martyrization of the studwents of this school by the Janissaries.

In 1734, during the grand viziership of Topal Osman Paşa, classes related to Civil Engineering was being taught in Hendesehane, which was founded in Üsküdar. Similarly, this school was also closed after three years due to the opposition of the Janissaries. The reasons of the tragedy that occured in Battle of Chesma, 1770 were inadequacy of the ships and the ignorance of the Ottoman Navy.

Although the Atlantic Map (1513) and the Map of Europe and the Mediterranean Sea (1523) by Piri Reis were the leading pieces of the era, Ottoman viziers were so ignorant that they claimed it was impossible for the Russian Baltic Fleet to reach the Mediterranean Sea assuming that there were no sea connection. With the proposal from Gazi Hasan Paşa and Baron de Tott, Mühendishane-i Bahri-i Humayun was established during the time of Sultan Mustafa III, aiming to train naval construction engineers. Since Ottoman Empire did not have any engineering schools at the time, military engineering classes were taught by French engineers beginning from 1784. French lecturers had to return to their country in 1788 with the increasing suppression from Austria and Russia, which were unwilling for the development and thriving of Ottoman Empire. In 1759, during the Grand Viziership of Koca Ragıp Paşa, Humbarahane was reopened in Karaağaç, Haliç (Golden Horn) and continued to teach even though it was incompetent. In 1792, Lağımcı Ocağı and Humbaracı Ocağı (Guild of Sappers) were established.