<span style="font-family:Verdana;">In a short time, many illustrative studies have been conducted on the mathematical modeling and analysis of COVID-19. There are not enough studies taking into account...<span style="font-family:Verdana;">In a short time, many illustrative studies have been conducted on the mathematical modeling and analysis of COVID-19. There are not enough studies taking into account the vaccine campaign among these studies. In this context, a mathematical model is developed to reveal the effects of vaccine treatment, which has been performed recently, on COVID-19 in this study. In the proposed model, as well as the vaccinated individuals, a five-dimensional compartment system including the susceptible, infected, exposed and recovered population is constructed. Moreover, besides the positivity, existence and uniqueness of the solution, biologically feasible region are provided. The basic reproduction number</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">known as expected secondary infection which means that expected infection among the susceptible populations caused by this infection is evaluated. In the numerical simulations, the parameter values taken from the literature and estimated are used to perform the solutions of the proposed model. Fourth-order Runge-Kutta numerical scheme is applied to obtain the results.</span>展开更多
Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,w...Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,which we can obtain with this new fractional operator.The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions,polynomial functions,exponential functions,trigonometric functions,or Mittag-Leffler functions.For all the fractional differential equations,the obtained solutions are represented graphically.The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations.Finally,we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel.展开更多
文摘<span style="font-family:Verdana;">In a short time, many illustrative studies have been conducted on the mathematical modeling and analysis of COVID-19. There are not enough studies taking into account the vaccine campaign among these studies. In this context, a mathematical model is developed to reveal the effects of vaccine treatment, which has been performed recently, on COVID-19 in this study. In the proposed model, as well as the vaccinated individuals, a five-dimensional compartment system including the susceptible, infected, exposed and recovered population is constructed. Moreover, besides the positivity, existence and uniqueness of the solution, biologically feasible region are provided. The basic reproduction number</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">known as expected secondary infection which means that expected infection among the susceptible populations caused by this infection is evaluated. In the numerical simulations, the parameter values taken from the literature and estimated are used to perform the solutions of the proposed model. Fourth-order Runge-Kutta numerical scheme is applied to obtain the results.</span>
基金TUBITAK(The Scientific and Technological Research Council of Turkey).
文摘Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,which we can obtain with this new fractional operator.The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions,polynomial functions,exponential functions,trigonometric functions,or Mittag-Leffler functions.For all the fractional differential equations,the obtained solutions are represented graphically.The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations.Finally,we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel.
