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Browsing by Author "Bozkurt, Fatma"

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    Citation - WoS: 28
    Citation - Scopus: 29
    A Mathematical Model of the Evolution and Spread of Pathogenic Coronaviruses From Natural Host To Human Host
    (Pergamon-elsevier Science Ltd, 2020) Baleanu, Dumitru; Alzabut, Jehad; Bozkurt, Fatma; Yousef, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents. At the same time, the transmission of the infection to the human host is caused by domestic animals that represent in the habitat the intermediate host. In this study, we review the currently collected information about coronaviruses and establish a model of differential equations with piecewise constant arguments to discuss the spread of the infection from the natural host to the intermediate, and from them to the human host, while we focus on the potential spillover of bat-borne coronaviruses. The local stability of the positive equilibrium point of the model is considered via the Linearized Stability Theorem. Besides, we discuss global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time t and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates the Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings. (C) 2020 Elsevier Ltd. All rights reserved.
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    Citation - WoS: 14
    Citation - Scopus: 17
    A Mathematical Model With Piecewise Constant Arguments of Colorectal Cancer With Chemo-Immunotherapy
    (Pergamon-elsevier Science Ltd, 2023) Yousef, Ali; Bilgil, Halis; Baleanu, Dumitru; Bozkurt, Fatma; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    We propose a new mathematical model with piecewise constant arguments of a system of ODEs to investigate the growth of colorectal cancer and its response to chemo-immunotherapy. Our main target in this paper is to analyze and represent the I.S.'s (immune system) efficiency during the chemotherapeutic process. Therefore, we proved and illustrated the necessity of IL-2 that supports the immune system, especially in early-detected cases of tumor density. Thus, the constructed model has been divided into sub-systems: the cell populations, the effects of the medications doxorubicin, and IL-2 concentration.Firstly, we analyze the stability of the equilibrium points (disease-free and co-existing) using the RouthHurwitz criteria. In addition, our study has shown that the system undergoes period-doubling, stationary and Neimark-Sacker bifurcations based on specific conditions. In the end, we illustrate some simulations to assist the theory of the manuscript.