Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives

Abstract

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior of such problems. In the case of Ebola, we observe spread that follows a fading memory process and also shows crossover behavior. Therefore, to capture this kind of spread one needs to use differential operators that posses crossover properties and fading memory. We analyze the Ebola disease model by considering three differential operators, that is the Caputo, Caputo–Fabrizio, and the Atangana–Baleanu operators. We present brief detail and some mathematical analysis for each operator applied to the Ebola model. We present a numerical approach for the solution of each operator. Further, numerical results for each operator with various values of the fractional order parameter α are presented. A comparison of the suggested operators on the Ebola disease model in the form of graphics is presented. We show that by decreasing the value of the fractional order parameter α , the number of individuals infected by Ebola decreases efficiently and conclude that for disease elimination, the Atangana–Baleanu operator is more useful than the other two.

Parallel Implementation of Modeling of Fractional-Order State-Space Systems Using the Fixed-Step Euler Method

“…By using Equation 1, we can present fractional-order differential equations in a simple, matrix/vector form. Therefore, we can find many uses of the state-space system (1) in practical applications, e.g., in electrical circuits [4,6], in modeling of thermal and diffusion processes [12,13,15], in medicine [8,16], etc. The fractional-order derivative is often described by using one of three definitions, that is, the Riemman-Liouville (RL), Caputo, or Grünwald-Letnikov (GL) definitions.…”

“…Fractional-order systems incorporating fractional-order derivatives (or differences) have attracted considerable research interest as their specific nature can be more adequate to describe some complex physical phenomena [1][2][3][4][5][6][7][8][9][10][11][12][13]. Since the fractional-order derivative is not defined at a point as in the case of its integer-order counterpart, impulse responses of fractional-order systems are not, in general, a class of exponential functions.…”

“…This is due to the fact that the modulus characteristic of a derivative of the fractional order α is increased by 20α dB per decade instead of 20 dB per decade for the integer-order derivative, whereas the phase characteristic is equal to πα/2. Therefore, the dynamic properties of the fractional-order system are more adjustable than for integer-order systems and can be more accurate in modeling various physical processes involving electrical circuits [4,6], thermal and diffusion processes [14,15], medicine [8,16], and others [17][18][19][20]. Among them, a lot of interest has been devoted to fractional-order generalizations of various entropy definitions and functions, i.e., Rényi entropy [11,21], Tsallis entropy [11,22], etc.…”

Projections and fractional dynamics of COVID-19 with optimal control analysis

“…Since last few decades, there are so many epidemic models have been solved by non-integer order derivatives. Recently some applications of non-integer order derivatives in mathematical epidemiology can be seen from [7,8,9,10,11]. There are so many research papers have been come to study the outbreaks of coronavirus, in which some are [12,13,14,15,16,17,18,19,20,21].…”

MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

“…Atangana and Alqahtani [42] studied the Caputo fractional derivative for analysis of the spread of river blindness disease. Furthermore, the idea of fractional derivatives was examined by Gomez and Atangana [43] with the power law and the Mittag-Leffler kernel applied to the non-linear Baggs-Freedman model, while Muhammad and Atangana [44] examined for dynamics of Ebola disease, and Khan et al [45] studied the analytical solution of the hyperbolic telegraph equation, using the natural transform decomposition method. Some other related references dealing with fluid motion, heat transfer, or fractional derivatives are given in [46][47][48][49][50][51][52][53].…”