Emrah Haspolat

RESEARCH, TEACHING, or OTHER INTERESTS

Applied Mathematics, Computational Mathematics, Modeling and Simulation, Numerical Analysis

Scopus Publications

Stability analysis and numerical simulation of dynamic and fractional SEIRD models for spread of nCOVID-19 in Turkey
B. Yildiz, E. Haspolat, A. Yilmaz, Z. Önes
Asian European Journal of Mathematics, 2022
There are various mathematical models that have been designed for forecasting the future behavior of coronavirus spreading, which helps to rapidly control the process while there is no treatment and vaccines. The main aim of this study is to describe COVID-19 dynamics in Turkey by using a Susceptible–Exposed–Infected–Recovered–Deceased (SEIRD) model. For this purpose, a new SEIRD model of nCOVID-19 and its fractional-order version are designed. The basic reproduction number is calculated with the generation operator method. All possible equilibria of the dynamic model are investigated in terms of the basic reproduction number. Further, stability conditions are obtained through the Routh–Hurwitz and Lyapunov stability theories. Finally, some numerical simulations of the dynamic system and its fractional version are given based on the data from the number of nCOVID-19 cases in Turkey. These results provide to implicate the theoretical findings corresponding to the model.
Fractional Order of a New 7D Hyperchaotic Lorenz-like System
Konuralp Journal of Mathematics, 2021
Deterministic and Stochastic Models of Arabidopsis thaliana Flowering
E. Haspolat, B. Huard, M. Angelova
Bulletin of Mathematical Biology, 2019
Experimental studies of the flowering of Arabidopsis thaliana have shown that a large complex gene regulatory network (GRN) is responsible for its regulation. This process has been mathematically modelled with deterministic differential equations by considering the interactions between gene activators and inhibitors (Valentim et al. in PLoS ONE 10(2):e0116973, 2015; van Mourik et al. in BMC Syst Biol 4(1):1, 2010). However, due to complexity of the model, the properties of the network and the roles of the individual genes cannot be deducted from the numerical solution the published work offers. Here, we propose simplifications of the model, based on decoupling of the original GRN to motifs, described with three and two differential equations. A stable solution of the original model is sought by linearisation of the original model which contributes to further investigation of the role of the individual genes to the flowering. Furthermore, we study the role of noise by introducing and investigating two types of stochastic elements into the model. The deterministic and stochastic nonlinear dynamic models of Arabidopsis flowering time are considered by following the deterministic delayed model introduced in Valentim et al. (2015). Steady-state regimes and stability of the deterministic original model are investigated analytically and numerically. By decoupling some concentrations, the system was reduced to emphasise the role played by the transcription factor Suppressor of Overexpression of Constants1 ( $$\textit{SOC}1$$ ) and the important floral meristem identity genes, Leafy ( $$\textit{LFY}$$ ) and Apetala1 ( $$\textit{AP}1$$ ). Two-dimensional motifs, based on the dynamics of $$\textit{LFY}$$ and $$\textit{AP}1$$ , are obtained from the reduced network and parameter ranges ensuring flowering are determined. Their stability analysis shows that $$\textit{LFY}$$ and $$\textit{AP}1$$ are regulating each other for flowering, matching experimental findings. New sufficient conditions of mean square stability in the stochastic model are obtained using a stochastic Lyapunov approach. Our numerical simulations demonstrate that the reduced models of Arabidopsis flowering time, describing specific motifs of the GRN, can capture the essential behaviour of the full system and also introduce the conditions of flowering initiation. Additionally, they show that stochastic effects can change the behaviour of the stability region through a stability switch. This study thus contributes to a better understanding of the role of $$\textit{LFY}$$ and $$\textit{AP}1$$ in Arabidopsis flowering.

RECENT SCHOLAR PUBLICATIONS

Predator-prey dynamics of four fish species in the Black Sea with analytical and numerical analysis
E Haspolat, M Yücel
Bulletin of Biomathematics 4 (1), 131-159 , 2026
2026.0
Modeling the impact of reinfected infectious diseases vaccination using a nonlinear SVEIRD framework: A case study from Alberta, Canada
E Haspolat, B Yildiz, V Yildirim
Discrete and Continuous Dynamical Systems-S, 0-0 , 2026
2026.0
Citations: 1
Temperature-dependent parameters in enzyme kinetics: impacts on enzyme denaturation
Hİ Eğilmez, E Haspolat
Fundamental Journal of Mathematics and Applications 7 (4), 226-235 , 2024
2024.0
Citations: 13
REKABETÇİ OLMAYAN ENZİM İNHİBİTÖRLERİ İÇİN MATEMATİKSEL MODEL ANALİZİ
E Haspolat, S Yıldırım
4. Uluslara Arası Trakya Bilimsel Araştırmalar Kongresi , 2024
2024.0
Stability analysis and numerical simulation of dynamic and fractional SEIRD models for spread of nCOVID-19 in Turkey
B Yildiz, E Haspolat, A Yilmaz, Z Önes
Asian-European Journal of Mathematics 15 (12), 2250226 , 2022
2022.0
Citations: 3
Fractional Order of a New 7D Hyperchaotic Lorenz-like System
E Haspolat, B YILDIZ
Konuralp Journal of Mathematics (KJM) 9 (1), 76-89 , 2021
2021.0
Citations: 6
Deterministic and Stochastic Models of Arabidopsis thaliana Flowering
E Haspolat, B Huard, M Angelova
Bulletin of Mathematical Biology 81 (1), 277-311 , 2019
2019.0
Citations: 7
Mathematical modelling of arabidopsis flowering time
E Haspolat
2018.0
Mathematical Modelling of Arabidopsis Flowering Time Gene Regulatory Network
E Haspolat
PQDT-UK & Ireland , 2018
2018.0
A Delay Differential Equation Model for Predator-Prey Dynamics of Four Commercial Fish Species in the Black Sea with Analytical and Numerical Analysis
E Haspolat

MOST CITED SCHOLAR PUBLICATIONS

Temperature-dependent parameters in enzyme kinetics: impacts on enzyme denaturation
Hİ Eğilmez, E Haspolat
Fundamental Journal of Mathematics and Applications 7 (4), 226-235 , 2024
2024.0
Citations: 13
Deterministic and Stochastic Models of Arabidopsis thaliana Flowering
E Haspolat, B Huard, M Angelova
Bulletin of Mathematical Biology 81 (1), 277-311 , 2019
2019.0
Citations: 7
Fractional Order of a New 7D Hyperchaotic Lorenz-like System
E Haspolat, B YILDIZ
Konuralp Journal of Mathematics (KJM) 9 (1), 76-89 , 2021
2021.0
Citations: 6
Stability analysis and numerical simulation of dynamic and fractional SEIRD models for spread of nCOVID-19 in Turkey
B Yildiz, E Haspolat, A Yilmaz, Z Önes
Asian-European Journal of Mathematics 15 (12), 2250226 , 2022
2022.0
Citations: 3
Modeling the impact of reinfected infectious diseases vaccination using a nonlinear SVEIRD framework: A case study from Alberta, Canada
E Haspolat, B Yildiz, V Yildirim
Discrete and Continuous Dynamical Systems-S, 0-0 , 2026
2026.0
Citations: 1
Predator-prey dynamics of four fish species in the Black Sea with analytical and numerical analysis
E Haspolat, M Yücel
Bulletin of Biomathematics 4 (1), 131-159 , 2026
2026.0
REKABETÇİ OLMAYAN ENZİM İNHİBİTÖRLERİ İÇİN MATEMATİKSEL MODEL ANALİZİ
E Haspolat, S Yıldırım
4. Uluslara Arası Trakya Bilimsel Araştırmalar Kongresi , 2024
2024.0
Mathematical modelling of arabidopsis flowering time
E Haspolat
2018.0
Mathematical Modelling of Arabidopsis Flowering Time Gene Regulatory Network
E Haspolat
PQDT-UK & Ireland , 2018
2018.0
A Delay Differential Equation Model for Predator-Prey Dynamics of Four Commercial Fish Species in the Black Sea with Analytical and Numerical Analysis
E Haspolat