The solution of fractional order epidemic model by implicit Adams methods

Abstract

We consider the numerical solution of the fractional order epidemic model on long time-intervals of a non-fatal disease in a population. Under\ud real-life initial conditions the problem needs to be treated by means of an implicit numerical scheme. Here we consider the use of implicit fractional\ud linear multistep methods of Adams type. Numerical results are presented

On the solution of fractional order SIS epidemic model

“…95 and α = 0 . 99 , we can see that the numerical solution's trajectory is approaching to the ordinary solution as where as when α is approaching to 1, this numerical analysis is often used in different papers see [4,7,9,12] and [13] , we conclude that the fractional model generalizes the ordinary one (19) , furthermore, from the same figures, we remark that if the fractional derivative order decreases, the disease takes more time to be eradicated (presence of memory effect). In Figs.…”

“…Moreover in 2014 the fractional order SIS model has been developed with a constant population size [4] and with a variable population size [5] , in both works the stability of equilibrium points of the model is studied, two years later mathematical model for the transmission of Ebola in human society has been presented [6] , in the same year Ameen I and Novati P proposed https://doi.org/10.1016/j.chaos.2018.10.023 0960-0779/© 2018 Elsevier Ltd. All rights reserved. numerical solution for fractional SIR model with constant population [7] by using discrete methods: Generalized Euler Method and Predictor Corrector Adams method, which is an implicit numerical scheme, also Okyere E et al studied a fractional order extension of the SIR and SIS model by replacing the ordinary derivative by the Caputo fractional derivative [8] , they used also Adams method to illustrate model solutions and Banerjee SK studied a fractional order SIS epidemic model with constant recruitment rate and variable population size [9] , in 2017 Sun GQ et al suggested a mathematical model to describe the transmission of cholera in the population of China [10] , what is particular in this model is the environment-to-human transmission of the disease, Li L presented a dynamical model on hemorrhagic fever with renal syndrome in China [11] , within the same frame Ahmed EM and El-Saka HA studied the transmission of a dangerous epidemic, called MERS-CoV using fractional order derivative [12] , recently in 2018 Sigh J et al considered a fractional epidemiological SIR model to describe the spread of computer virus [13] .…”

Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease

“…e implicit fractional Adams method of order 2 is a generalization of the classical trapezoidal rule (for more details, see [59][60][61]). For instance, consider the initial value problem:…”

On the Construction of Some Fractional Stochastic Gompertz Models

“…In such paper, the fractional derivative is used to study the Q-factor of some non-ferromagnetic solids, thus being introduced in an applicative context. From such moment, fractional calculus has been used to address a lot of different models: from epidemics [8] to osmosis [9], from neurophysiology [10] to viscoelasticity [11] and many others [12].…”