Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order

Titanium dioxide is a compound of oxygen and titanium with the formula TiO2 present in nature and manufactured on an industrial scale. It is used in several fields and applications such as cosmetics, paint, food, photocatalyst, electrodes in lithium batteries, dye solar cells (DSSC), biosensors, etc., given its importance and its various fields of application, there are several methods of synthesis of TiO2 such as the sol–gel method widely used to obtain nanoparticles. In our study, on the one hand we synthesized titanium dioxide nanopowders crystallized in the anatase phase at a crystal size of 49.25 nm with success using titanium tetraisopropoxide (TTIP) as precursor by the sol–gel method. The powders obtained were analyzed by X-ray diffraction (XRD) with CuKα radiation (λ=0.15406 nm) and Fourier transform infrared spectroscopy (FTIR) in the wave number range 4000−400 cm−1, and on the other hand we present a mathematical model for the prediction of the TiO2 concentration as a function of time and the concentration of reactants by using the fractional order derivative more precise than the whole order derivative, we study the existence and the uniqueness of the solutions. In addition, we determine the points of equilibrium. Numerical simulations and their graphical representations are made to visualize the efficiency of this model.

Section: Fractional Order Modelmentioning

confidence: 99%

The mathematical fractional modeling of TiO_2 nanopowder synthesis by sol–gel method at low temperature

Sadek¹,

Sadek²,

Touhtouh³

et al. 2022

“…Drawing on the ideas of Roland Ross, Kermack and McKrndrick in 1927 proposed the classic model SIR [5] which represents three classes (compartments), class S for healthy individuals, class I for infected individuals and class R for recovered ones. An extension of SIR models was set up based on the remark that for certain diseases, a certain part of the infected population does not present any symptoms, which gave rise to the SEIR model, with E represents the exposed individuals [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Global dynamic of spatio-temporal fractional order SEIR model

Bounkaicha¹,

Allali²,

Tabit³

et al. 2023

The global analysis of a spatio-temporal fractional order SEIR infection epidemic model is studied and analyzed in this paper. The dynamics of the infection is described by four partial differential equations with a fractional derivative order and with diffusion. The equations of our model describe the evolution of the susceptible, the exposed, the infected and the recovered individuals with taking into account the spatial diffusion for each compartment. At first, we will prove the existence and uniqueness of the solution using the results of the fixed point theorem, and the equilibrium points are established and presented according to R0. Next, the bornitude and the positivity of the solutions of the proposed model are established. Using the Lyapunov direct method it has been proved that the global stability of the each equilibrium depends mainly on the basic reproduction number R0. Finally, numerical simulations are performed to validate the theoretical results.

“…Fractional optimal control problems (FOCPs) are the generalization of classical optimal control problems (OCPs), in which the differential equations are fractional differential equations (FDEs) representing generalizations of the ordinary differential equations (ODEs) and which have become one of the appropriate mathematical tools to describe the dynamics of phenomena with memory that exists in most biological systems systems [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional optimal control HBV infection model with capsids and CTL immune response

Ichou¹,

Bachraoui²,

Hattaf³

et al. 2023

This paper deals with a fractional optimal control problem model that describes the interactions between hepatitis B virus (HBV) with HBV DNA-containing capsids, liver cells (hepatocytes), and the cytotoxic T-cell immune response. Optimal controls represent the effectiveness of drug therapy in inhibiting viral production and preventing new infections. The optimality system is derived and solved numerically. Our results also show that optimal treatment strategies reduce viral load and increase the number of uninfected cells, which improves the patient's quality of life.