01 تیر 1403
خسرو سايوند

خسرو سایوند

مرتبه علمی: استاد
نشانی: ملایر گروه ریاضی دانشگاه ملایر
تحصیلات: دکترای تخصصی / ریاضی
تلفن: 081-33398981
دانشکده: دانشکده علوم ریاضی و آمار

مشخصات پژوهش

عنوان
On epidemiological transition model of the Ebola virus in fractional sense
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
‎Ebola virus nonlinear equation‎, ‎Caputo's fractional-order derivative‎, ‎Dual Bernstein polynomials‎, ‎Operational matrix‎.
سال
2023
مجله Journal of Applied Analysis and Computation
پژوهشگران خسرو سایوند

چکیده

‎Recently‎, ‎many researchers have focused on modeling and analyzing various problems in biological phenomena and life sciences such as viruses and nervous system‎. ‎One of these cases can be seen in the modeling of the Ebola virus‎. ‎In this paper‎, ‎we present an efficient method based on properties of Bernstein's operational matrices as well as dual Bernstein for the system of nonlinear equations of Ebola virus in the Caputo fractional sense‎. ‎The operational matrix of the fractional derivative of order $v$ is obtained based on the dual Bernstein‎. ‎The proposed dual Bernstein method reduces the solution of the Ebola virus in fractional sense to the solution of a system of nonlinear algebraic equations‎. ‎The unknown coefficients are obtained by solving the final system of nonlinear equations using the Newton-Raphson method‎. ‎Another feature of this method is that a reasonable approximate solution can be found with a small number of bases‎. ‎Moreover‎, ‎some numerical treatments of fractional models of Ebola Virus are examined‎. ‎The existence‎, ‎uniqueness and stability of the suggested methodologies are discussed and proven‎. ‎Numerical simulations are reported for various fractional orders and by using comparisons between the simulated and measured data‎, ‎we find the best value of the fractional order‎. ‎Finally‎, ‎we will use the data provided by the World Health Organization (WHO) and we compare the fractional Mellin transform‎, ‎real data‎, ‎Caputo's derivative‎, ‎and the classical model‎. ‎According to the obtained results‎, ‎the ordinary derivative is less accurate than the fractional order model‎. ‎In other words‎, ‎the results showed that fractional order derivatives are superior to classical orders‎, ‎more reliable and effective in describing biological processes‎.