Numerical Solution of the Spread Model of COVID-19 by Using Muntz Functions
محورهای موضوعی : فصلنامه ریاضیAfkar Kareem Mnahi 1 , Majid Tavassoli Kajani 2 , Mohammed Jasim Mohammed 3 , Masoud Allame 4
1 - .Department of Mathematics, Islamic Azad University, Isfahan (Khorasgan) Branch, Isfahan, Iran.
2 - Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.
3 - Department of Mathematics, University of Thi-Qar, Nasiriyah, 64001, Iraq.
4 - Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.
کلید واژه: Muntz function, Fractional Differential Equations, Collocation Method, Spread model of COVID- 19.,
چکیده مقاله :
The outbreak of COVID-19 has necessitated the development of various mathematical models to understand and predict its spread. Among these, fractional differential equations have gained attention for their ability to capture the complexity and dynamics of infectious disease transmission. However, obtaining analytical solutions for such models is often infeasible. In this paper, we present an approach to approximate solutions of a fractional differential equation that describes the spread of COVID-19. The fractional order in the model reflects the memory and hereditary properties of the disease transmission process, which are not adequately described by traditional integer-order models. To tackle the complexities of this equation, we utilize Muntz functions, which are a class of basis functions used in approximation theory. Muntz functions are particularly useful due to their flexible nature and ability to converge to various types of functions, making them suitable for approximating solutions to differential equations. We perform numerical simulations to evaluate the performance of the Muntz functions in approximating the solution of our model. The findings indicate that the Muntz function approach yields superior accuracy in modeling the spread of COVID-19 compared to these alternative methods.
The outbreak of COVID-19 has necessitated the development of various mathematical models to understand and predict its spread. Among these, fractional differential equations have gained attention for their ability to capture the complexity and dynamics of infectious disease transmission. However, obtaining analytical solutions for such models is often infeasible. In this paper, we present an approach to approximate solutions of a fractional differential equation that describes the spread of COVID-19. The fractional order in the model reflects the memory and hereditary properties of the disease transmission process, which are not adequately described by traditional integer-order models. To tackle the complexities of this equation, we utilize Muntz functions, which are a class of basis functions used in approximation theory. Muntz functions are particularly useful due to their flexible nature and ability to converge to various types of functions, making them suitable for approximating solutions to differential equations. We perform numerical simulations to evaluate the performance of the Muntz functions in approximating the solution of our model. The findings indicate that the Muntz function approach yields superior accuracy in modeling the spread of COVID-19 compared to these alternative methods.
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