Fractional Order SIR Model with Constant Population

Discrete-Time Fractional Optimal Control

“…Then substituting x(k) into Equation (26) we get the co-state vector λ(k). Once λ(k) is known, the control vector u(k) can be calculated using Equation (21). Solving the above equations we obtain the following results.…”

“…is known, the control vector ) (k u can be calculated using Equation (21). Solving the above equations we obtain the following results.…”

“…On the other hand the Caputo fractional derivative accepts initial conditions similar to the integer order systems. Therefore, Caputo fractional derivative is preferred for modeling physical systems [5,6,[14][15][16][17][18][19][20][21][22][23][24].…”

An epidemiological MSEIR model described by the Caputo fractional derivative

“…Recently, fractional derivatives have been used to describe epidemiological models and they have proven to be more accurate in some cases, when compared to the classical ones. We find in the literature different models described by fractional derivatives, like the SIR model [6,7,21,24,47,50,60,61], the SIR model with vaccination [17,36,58], the SIRC model [17], the SEIR model [23,51], the MSEIR model [8], etc. We also refer some applications to biomedical modelling [11,29,44,45,48].…”

On the solution of fractional order SIS epidemic model

“…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] .…”