A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs
Today, the socio-cultural lack of some countries with increased urbanization has led to the unconscious breeding of stray dogs. The failure to care for the offspring of possessive dogs or ignoring the responsibility to find a suitable family for the offspring increased the dog population on the str...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Balikesir University
2024-03-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
| Subjects: | |
| Online Access: | http://ijocta.org/index.php/files/article/view/1418 |
| _version_ | 1797234433747582976 |
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| author | Zafer Öztürk Ali Yousef Halis Bilgil Sezer Sorgun |
| author_facet | Zafer Öztürk Ali Yousef Halis Bilgil Sezer Sorgun |
| author_sort | Zafer Öztürk |
| collection | DOAJ |
| description |
Today, the socio-cultural lack of some countries with increased urbanization has led to the unconscious breeding of stray dogs. The failure to care for the offspring of possessive dogs or ignoring the responsibility to find a suitable family for the offspring increased the dog population on the streets and in the shelters. In this study, our main target is to analyze the habitat of stray dogs and the strategy of how to control the population without damaging the ecosystem of the species. For this aim, we establish a fractional-order differential equation system to investigate the fractal dimension with long-term memory that invovles two compartments; the non-sterilized dog population (x(t)) and the sterilized one (y(t)). Firstly, we analyze the stability of the equilibrium points using the Routh-Hurwitz criteria to discuss cases that should not affect the ecosystem of the dog population, but control the stray dog population in the habitat. Since the intervention to the stray dog population occurs at discrete time impulses, we use the Euler method's discretization process to analyse the local and global stability around the equilibrium points. Besides this, we show that the solutions of the system represent semi-cycle behaviors. At the end of the study, we use accurate data to demonstrate the sterilization rate of stray dogs in their habitat.
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| first_indexed | 2024-04-24T16:32:00Z |
| format | Article |
| id | doaj.art-c80d7dde46594154b31b54b776e339f3 |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-24T16:32:00Z |
| publishDate | 2024-03-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-c80d7dde46594154b31b54b776e339f32024-03-30T00:37:05ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032024-03-0114210.11121/ijocta.1418A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogsZafer Öztürk0Ali Yousef1Halis Bilgil2Sezer Sorgun3Institute of Science, Nevsehir Haci Bektas Veli University, 50300, Nevsehir, TurkiyeDepartment of Natural Sciences and Mathematics, College of Engineering, International University of Science and Technology in Kuwait, 92400 Al-Ardiya, KuwaitFaculty of Engineering, Architecture and Design, Kayseri University, 38280, Kayseri, TurkiyeDepartment of Mathematics, Nevsehir Haci Bektas Veli University, 50300, Nevsehir, Türkiye Today, the socio-cultural lack of some countries with increased urbanization has led to the unconscious breeding of stray dogs. The failure to care for the offspring of possessive dogs or ignoring the responsibility to find a suitable family for the offspring increased the dog population on the streets and in the shelters. In this study, our main target is to analyze the habitat of stray dogs and the strategy of how to control the population without damaging the ecosystem of the species. For this aim, we establish a fractional-order differential equation system to investigate the fractal dimension with long-term memory that invovles two compartments; the non-sterilized dog population (x(t)) and the sterilized one (y(t)). Firstly, we analyze the stability of the equilibrium points using the Routh-Hurwitz criteria to discuss cases that should not affect the ecosystem of the dog population, but control the stray dog population in the habitat. Since the intervention to the stray dog population occurs at discrete time impulses, we use the Euler method's discretization process to analyse the local and global stability around the equilibrium points. Besides this, we show that the solutions of the system represent semi-cycle behaviors. At the end of the study, we use accurate data to demonstrate the sterilization rate of stray dogs in their habitat. http://ijocta.org/index.php/files/article/view/1418Fractional-order Differential EquationEuler MethodStability AnalysisStray Dog Population and SterilizationStrategySemi-cycle Solution |
| spellingShingle | Zafer Öztürk Ali Yousef Halis Bilgil Sezer Sorgun A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs An International Journal of Optimization and Control: Theories & Applications Fractional-order Differential Equation Euler Method Stability Analysis Stray Dog Population and Sterilization Strategy Semi-cycle Solution |
| title | A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs |
| title_full | A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs |
| title_fullStr | A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs |
| title_full_unstemmed | A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs |
| title_short | A Fractional-order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs |
| title_sort | fractional order mathematical model to analyze the stability and develop a sterilization strategy for the habitat of stray dogs |
| topic | Fractional-order Differential Equation Euler Method Stability Analysis Stray Dog Population and Sterilization Strategy Semi-cycle Solution |
| url | http://ijocta.org/index.php/files/article/view/1418 |
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