Stochastic Fractional Models of the Diffusion of Covid-19

El-Borai, Mahmoud M.; El-Nadi, Khairia El-Said

doi:10.37418/amsj.9.12.19

Cited by 5 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An observer‐based output feedback control for a fractional reaction diffusion system was designed in Reference 26. Recently, fractional order PDEs have been used to model the diffusion and spread of the COVID‐19 27 . A backstepping boundary feedback controller for an fractional reaction diffusion system with a space‐dependent (nonconstant) diffusion coefficient was designed by Chen et al, 28 in which a generalized result on backstepping boundary feedback controller.…”

Section: Fractional Order Casementioning

confidence: 99%

Observer and output feedback control for nonlinear ordinary differential equation coupled to an under‐actuated transport partial differential equation

Mathiyalagan

Nidhi

2022

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

In this article, the under‐actuation problem for a class of first order hyperbolic partial differential equation system coupled to a nonlinear ordinary differential equation is considered. An anticollocated observer design and an appropriate output feedback control is developed based on the backstepping methodology. The stability conditions for the nonlinear coupled system are proposed using the Lyapunov theory and are formulated in terms of the LMI constraints. Further, we have extended the stability results and backstepping control design for the fractional‐order coupled system. The stability conditions and the control law proposed in the work are evaluated considering a numerical simulation.

show abstract

Section: Fractional Order Casementioning

confidence: 99%

Observer and output feedback control for nonlinear ordinary differential equation coupled to an under‐actuated transport partial differential equation

Mathiyalagan

Nidhi

2022

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…an IC, and C = [c ij ] ∈ R n×n will be chosen to ensure the asymptotic stability of system ( 10)- (13).…”

Section: Backstepping Mappingmentioning

confidence: 99%

“…Relation ( 26) depends on W (1, t) which is given by ( 10)- (13). And the discontinuous boundary controller (26) will enable to make the target system ( 10)-( 13) asymptotically stable.…”

Section: Control Strategymentioning

confidence: 99%

“…Consider the target system (10)- (13). Similar to the integer order PDE boundary control problem in [11,Theorem 3.3.3], we introduce the variable…”

Section: Well Posedness Of Closed-loop Systemsmentioning

confidence: 99%

“…Examples include transport dynamics in systems governed by anomalous diffusion [23], combustion processes [36], biological systems [33], etc. Especially, fractional diffusion models has been used for modeling of the diffusion of COVID-19 [13,14], and the optimal vaccination and treatment policies of time fractional diffusion susceptible-infected-recovered (SIR) epidemic systems [17] could play a role in COVID-19. Additionally, the control problem of time FRD systems has been reported recently (see e.g.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Backstepping sliding mode control for coupled delayed time fractional reaction diffusion systems subject to boundary input disturbances

Chen

Zhuang

Chen

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper we develop backstepping-based boundary sliding mode controllers for coupled time fractional reaction diffusion (FRD) systems governed by time fractional partial differential equations (PDEs) with time varying delay and input disturbances. Here, the diffusion coefficients are spatially varying (nonconstant) and can be same or different. To asymptotically stabilize the system, we first use a backstepping transformation to convert the original dynamics into a target dynamics with a new manipulable input and the perturbation. Then, the sliding mode algorithm is employed to design this discontinuous controller to suppress disturbances. In this case, we obtain the combined backstepping/sliding mode controller of the original dynamics, with which the closed-loop asymptotic stability is proved by the fractional Halanay's inequality. Fractional numerical examples are given to demonstrate the efficiency of the proposed synthesis.

show abstract

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Santra,

Mahapatra,

Basu

2024

Phys. Scr.

View full text Add to dashboard Cite

This article presents an epidemic disease propagation mathematical model in fractional order. The epidemiological characteristics are presented based on the susceptible, exposed, unknown infected, known infected, hospitalized population and the population in the secure zone. Both the disease endemic equilibrium and the disease-free equilibrium's stability characteristics have been examined using the basic reproduction number. Variation of basic reproduction number based on the different sensitive parameters has been discussed. It has been disputed whether the fractional model provides a uniform, reliable solution. An analysis of the time history of unknown and known infected populations, hospitalized populations and recovered populations at different values of various sensitive parameters has been carried out. To support the key theoretical conclusions, some numerical simulations are completed using MATLAB. The impact of various populations on the propagation of the illness has also been investigated, as well as how specific state variables change over time for various fractional order values.

show abstract

Stochastic Fractional Models of the Diffusion of Covid-19

Cited by 5 publications

References 0 publications

Observer and output feedback control for nonlinear ordinary differential equation coupled to an under‐actuated transport partial differential equation

Observer and output feedback control for nonlinear ordinary differential equation coupled to an under‐actuated transport partial differential equation

Backstepping sliding mode control for coupled delayed time fractional reaction diffusion systems subject to boundary input disturbances

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Contact Info

Product

Resources

About