A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19

Jahanshahi, Hadi; Muñoz‐Pacheco, Jesús M.; Bekiros, Stelios; Alotaibi, Naif D.

doi:10.1016/j.chaos.2020.110632

Cited by 80 publications

(51 citation statements)

References 54 publications

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“…We note that although the fractional models are capable of accounting for memory effects via non-local operators and their application has been motivated in the literature to a great extent, the crucial less-studied element is to develop a robust computational framework to implement the inverse problem of inferring the time-dependent fractional orders. For example, 19 suggests the use of time-dependent variables fractional orders, however, in their implementation the fractional orders are parameterized with a few constant parameters as piece-wise constant functions to render the inverse problem feasible in their formulation. The under-parametrization of fractional orders may lead to inaccurate results.…”

Section: Resultsmentioning

confidence: 99%

“…These results demonstrate that even in the case of access to data for all compartments, the inference of fractional orders is not very robust and still exhibits some uncertainties, which is a reflection of lack of identifiability of the model. The choice of piece-wise constant parameters in the work of 19 simplifies the problem but leads to erroneous results.…”

Section: Resultsmentioning

confidence: 99%

“…In B : we compare the piece-wise parameter r ( t ) and the fPINN inference of time-dependent parameter r ( t ). Here the piece-wise fractional orders and parameters are given by 19 . The other parameters of the model are fixed as a = 0.0215 and b = 0.0048 19 in the simulation.…”

Section: Resultsmentioning

confidence: 99%

“…The integer-order models use simple derivative operators that do not account for the effect of memory in the evolution of dynamics, but instead the model parameters are treated as time-varying variables. However, many works have confirmed the power-law scaling feature of the dynamics of COVID-19 transmission 19, 20 , which indicates the notion of memory effects in the spread dynamics. In the classical SIR model, the current number of infectious individuals has exponential distribution in the infectious period, i.e., .…”

Section: Model Pluralitymentioning

confidence: 99%

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Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Kharazmi

Cai

Zheng

et al. 2021

Preprint

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We analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify multiple time-dependent parameters and to discover new data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and delay in the dynamics described by integer-order, fractional-order, and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states, and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks (NNs). In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by NNs. We investigate the identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with NNs and with control measures in forecasting the pandemic.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Model Pluralitymentioning

confidence: 99%

See 2 more Smart Citations

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Kharazmi

Cai

Zheng

et al. 2021

Preprint

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“…Despite the long history of fractional calculus, its applications are only a new subject of interest. Fractional calculus has recently been utilized in various fields of study [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. Also, the modeling of HIV using fractional differential equations has started to attract some research attention.…”

Section: Introductionmentioning

confidence: 99%

A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

Wang

Jahanshahi

Wang

et al. 2021

Entropy

Self Cite

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Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated.

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A review on design and implementation of type‐2 fuzzy controllers

Jahanshahi

Alotaibi

Soradi‐Zeid

et al. 2022

Math Methods in App Sciences

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Nowadays, advances in different fields of technology have increased demands for reliable controllers. Uncertainty and disturbances, which are inevitable in most real‐world systems, as well as increasing complexity in the dynamics of many systems, are requiring the design and application of intelligent controllers. Fuzzy controllers, and specifically type‐2 fuzzy control techniques, could play a beneficial role in a variety of control purposes, since they are robust against uncertainties. Therefore, an immense body of research is devoted to these fuzzy control techniques. This paper introduces a comprehensive review about the most recent advances in the design and implementation of type‐2 fuzzy control schemes both for integer‐ and fractional‐order systems. Thus, in addition to the past and present achievements in this context, future trends are also delineated. Moreover, most important works dealing with type‐2 fuzzy controller are discussed, and their advantages and drawbacks are outlined. Consequently, we firmly believe the present paper will pave the way for future research in this area.

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A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19

Cited by 80 publications

References 54 publications

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

A review on design and implementation of type‐2 fuzzy controllers

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