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  1. Article: Fractional order mathematical modeling of COVID-19 transmission.

    Ahmad, Shabir / Ullah, Aman / Al-Mdallal, Qasem M / Khan, Hasib / Shah, Kamal / Khan, Aziz

    Chaos, solitons, and fractals

    2020  Volume 139, Page(s) 110256

    Abstract: ... of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding ... In this article, the mathematical model with different compartments for the transmission dynamics ... approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is ...

    Abstract In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.
    Keywords covid19
    Language English
    Publishing date 2020-09-02
    Publishing country England
    Document type Journal Article
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110256
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  2. Article ; Online: Fractional order mathematical modeling of COVID-19 transmission

    Ahmad, Shabir / Ullah, Aman / Al-Mdallal, Qasem M. / Khan, Hasib / Shah, Kamal / Khan, Aziz

    Chaos, Solitons & Fractals

    2020  Volume 139, Page(s) 110256

    Keywords General Mathematics ; covid19
    Language English
    Publisher Elsevier BV
    Publishing country us
    Document type Article ; Online
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110256
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Article: Fractional Order Mathematical Modeling of COVID-19 Transmission

    Ahmad, Shabir / Ullah, Aman / Al-Madlal, Qasem M / Khan, Hasib / Shah, Kamal / Khan, Aziz

    Chaos Solitons Fractals

    Abstract: ... of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding ... In this article, the mathematical model with different compartments for the transmission dynamics ... approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is ...

    Abstract In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.
    Keywords covid19
    Publisher WHO
    Document type Article
    Note WHO #Covidence: #739791
    Database COVID19

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  4. Article: Fractional-order backstepping strategy for fractional-order model of COVID-19 outbreak.

    Veisi, Amir / Delavari, Hadi

    Mathematical methods in the applied sciences

    2021  Volume 45, Issue 7, Page(s) 3479–3496

    Abstract: ... the transmission patterns of this new infection. In this paper, we utilized the fractional-order dynamics of COVID ... The coronavirus disease (COVID-19) pandemic has impacted many nations around the world. Recently ... of transmission, so finally the effectiveness of the proposed controller in the presence of new variant of COVID ...

    Abstract The coronavirus disease (COVID-19) pandemic has impacted many nations around the world. Recently, new variant of this virus has been identified that have a much higher rate of transmission. Although vaccine production and distribution are currently underway, non-pharmacological interventions are still being implemented as an important and fundamental strategy to control the spread of the virus in countries around the world. To realize and forecast the transmission dynamics of this disease, mathematical models can be very effective. Various mathematical modeling methods have been proposed to investigate the transmission patterns of this new infection. In this paper, we utilized the fractional-order dynamics of COVID-19. The goal is to control the prevalence of the disease using non-pharmacological interventions. In this paper, a novel fractional-order backstepping sliding mode control (FOBSMC) is proposed for non-pharmacological decisions. Recently, new variant of this virus have been identified that have a much higher rate of transmission, so finally the effectiveness of the proposed controller in the presence of new variant of COVID-19 is investigated.
    Language English
    Publishing date 2021-11-28
    Publishing country Germany
    Document type Journal Article
    ZDB-ID 1478610-2
    ISSN 1099-1476 ; 0170-4214
    ISSN (online) 1099-1476
    ISSN 0170-4214
    DOI 10.1002/mma.7994
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  5. Article ; Online: Modeling the impact of the vaccine on the COVID-19 epidemic transmission via fractional derivative.

    Arshad, Sadia / Khalid, Sadia / Javed, Sana / Amin, Naima / Nawaz, Fariha

    European physical journal plus

    2022  Volume 137, Issue 7, Page(s) 802

    Abstract: ... deterministic modeling, stochastic modeling or fractional order modeling etc. Fractional order derivative ... To achieve the goal of ceasing the spread of COVID-19 entirely it is essential to understand ... beneficial and economical to understand the key factors involved in the spread of COVID-19. As there are ...

    Abstract To achieve the goal of ceasing the spread of COVID-19 entirely it is essential to understand the dynamical behavior of the proliferation of the virus at an intense level. Studying this disease simply based on experimental analysis is very time consuming and expensive. Mathematical modeling might play a worthy role in this regard. By incorporating the mathematical frameworks with the available disease data it will be beneficial and economical to understand the key factors involved in the spread of COVID-19. As there are many vaccines available globally at present, henceforth, by including the effect of vaccination into the model will also support to understand the visible influence of the vaccine on the spread of COVID-19 virus. There are several ways to mathematically formulate the effect of disease on the population like deterministic modeling, stochastic modeling or fractional order modeling etc. Fractional order derivative modeling is one of the fundamental methods to understand real-world problems and evaluate accurate situations. In this article, a fractional order epidemic model
    Language English
    Publishing date 2022-07-11
    Publishing country Germany
    Document type Journal Article
    ISSN 2190-5444
    ISSN (online) 2190-5444
    DOI 10.1140/epjp/s13360-022-02988-x
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  6. Article ; Online: Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data.

    Zarin, Rahat / Humphries, Usa Wannasingha / Khan, Amir / Raezah, Aeshah A

    Mathematical biosciences and engineering : MBE

    2023  Volume 20, Issue 6, Page(s) 11281–11312

    Abstract: ... The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar ... of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods ... of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and ...

    Abstract This study explores the use of numerical simulations to model the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods. The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar wavelet collocation method offers a precise and efficient solution to the fractional derivatives used in the model. The simulation results yield crucial insights into the Omicron variant's spread, providing valuable information to public health policies and strategies designed to mitigate its impact. This study marks a significant advancement in comprehending the COVID-19 pandemic's dynamics and the emergence of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and the model's existence and uniqueness are established by considering fixed point theory results. Sensitivity analysis is conducted on the model to identify the parameter with the highest sensitivity. For numerical treatment and simulations, we apply the Haar wavelet collocation method. Parameter estimation for the recorded COVID-19 cases in India from 13 July 2021 to 25 August 2021 has been presented.
    MeSH term(s) Humans ; COVID-19/epidemiology ; SARS-CoV-2 ; Pandemics ; Computer Simulation
    Language English
    Publishing date 2023-06-15
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2265126-3
    ISSN 1551-0018 ; 1551-0018
    ISSN (online) 1551-0018
    ISSN 1551-0018
    DOI 10.3934/mbe.2023500
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  7. Article: A fractional-order mathematical model for analyzing the pandemic trend of COVID-19.

    Agarwal, Praveen / Ramadan, Mohamed A / Rageh, Abdulqawi A M / Hadhoud, Adel R

    Mathematical methods in the applied sciences

    2021  Volume 45, Issue 8, Page(s) 4625–4642

    Abstract: ... mathematical model to examine the COVID-19 disease outbreak. This model outlines the multiple mechanisms ... fractional-order derivative-based modeling can be beneficial. We propose in this paper a fractional-order ... Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID-19 ...

    Abstract Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID-19) that was first reported in China. To understand and forecast the transmission dynamics of this disease, fractional-order derivative-based modeling can be beneficial. We propose in this paper a fractional-order mathematical model to examine the COVID-19 disease outbreak. This model outlines the multiple mechanisms of transmission within the dynamics of infection. The basic reproduction number and the equilibrium points are calculated from the model to assess the transmissibility of the COVID-19. Sensitivity analysis is discussed to explain the significance of the epidemic parameters. The existence and uniqueness of the solution to the proposed model have been proven using the fixed-point theorem and by helping the Arzela-Ascoli theorem. Using the predictor-corrector algorithm, we approximated the solution of the proposed model. The results obtained are represented by using figures that illustrate the behavior of the predicted model classes. Finally, the study of the stability of the numerical method is carried out using some results and primary lemmas.
    Language English
    Publishing date 2021-12-29
    Publishing country Germany
    Document type Journal Article
    ZDB-ID 1478610-2
    ISSN 1099-1476 ; 0170-4214
    ISSN (online) 1099-1476
    ISSN 0170-4214
    DOI 10.1002/mma.8057
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  8. Article ; Online: Dynamics of fractional order COVID-19 model with a case study of Saudi Arabia.

    Chu, Yu-Ming / Ali, Aatif / Khan, Muhammad Altaf / Islam, Saeed / Ullah, Saif

    Results in physics

    2021  Volume 21, Page(s) 103787

    Abstract: ... a useful tool and gains much interest in this regard. In this paper, a fractional-order transmission model ... The novel coronavirus disease or COVID-19 is still posing an alarming situation around the globe ... The classical Caputo type derivative of fractional order is used in order to formulate the model ...

    Abstract The novel coronavirus disease or COVID-19 is still posing an alarming situation around the globe. The whole world is facing the second wave of this novel pandemic. Recently, the researchers are focused to study the complex dynamics and possible control of this global infection. Mathematical modeling is a useful tool and gains much interest in this regard. In this paper, a fractional-order transmission model is considered to study its dynamical behavior using the real cases reported in Saudia Arabia. The classical Caputo type derivative of fractional order is used in order to formulate the model. The transmission of the infection through the environment is taken into consideration. The documented data since March 02, 2020 up to July 31, 2020 are considered for estimation of parameters of system. We have the estimated basic reproduction number
    Language English
    Publishing date 2021-01-02
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2631798-9
    ISSN 2211-3797 ; 2211-3797
    ISSN (online) 2211-3797
    ISSN 2211-3797
    DOI 10.1016/j.rinp.2020.103787
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  9. Article ; Online: A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus.

    Omame, Andrew / Abbas, Mujahid / Onyenegecha, Chibueze P

    Results in physics

    2022  Volume 37, Page(s) 105498

    Abstract: ... a mathematical model for COVID-19 and Hepatitis B Virus (HBV) co-interaction is developed and studied using ... biological processes. It is worth mentioning that the standard mathematical models of integer-order derivatives ... on the proposed model is also highlighted. The results proven in this paper illustrate that HBV and COVID-19 ...

    Abstract Fractional differential equations are beginning to gain widespread usage in modeling physical and biological processes. It is worth mentioning that the standard mathematical models of integer-order derivatives, including nonlinear models, do not constitute suitable framework in many cases. In this work, a mathematical model for COVID-19 and Hepatitis B Virus (HBV) co-interaction is developed and studied using the Atangana-Baleanu fractional derivative. The necessary conditions of the existence and uniqueness of the solution of the proposed model are studied. The local stability analysis is carried out when the reproduction number is less than one. Using well constructed Lyapunov functions, the disease free and endemic equilibria are proven to be globally asymptotically stable under certain conditions. Employing fixed point theory, the stability of the iterative scheme to approximate the solution of the model is discussed. The model is fitted to real data from the city of Wuhan, China, and important parameters relating to each disease and their co-infection, are estimated from the fitting. The approximate solutions of the model are compared using the integer and fractional order derivatives. The impact of the fractional derivative on the proposed model is also highlighted. The results proven in this paper illustrate that HBV and COVID-19 transmission rates can greatly impact the dynamics of the co-infection of both diseases. It is concluded that to control the co-circulation of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.
    Language English
    Publishing date 2022-04-21
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2631798-9
    ISSN 2211-3797 ; 2211-3797
    ISSN (online) 2211-3797
    ISSN 2211-3797
    DOI 10.1016/j.rinp.2022.105498
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  10. Article: Effect of an antiviral drug control and its variable order fractional network in host COVID-19 kinetics.

    Wang, Bo / Mondal, Jayanta / Samui, Piu / Chatterjee, Amar Nath / Yusuf, Abdullahi

    The European physical journal. Special topics

    2022  Volume 231, Issue 10, Page(s) 1915–1929

    Abstract: ... order calculus in the modeling of systems and processes, the proposed variable-order fractional model ... In December 2019, a novel coronavirus disease (COVID-19) appeared in Wuhan, China. After ... of our throat and lungs are the main target area of the SARS-CoV-2 virus which leads to COVID-19 disease ...

    Abstract In December 2019, a novel coronavirus disease (COVID-19) appeared in Wuhan, China. After that, it spread rapidly all over the world. Novel coronavirus belongs to the family of Coronaviridae and this new strain is called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epithelial cells of our throat and lungs are the main target area of the SARS-CoV-2 virus which leads to COVID-19 disease. In this article, we propose a mathematical model for examining the effects of antiviral treatment over viral mutation to control disease transmission. We have considered here three populations namely uninfected epithelial cells, infected epithelial cells, and SARS-CoV-2 virus. To explore the model in light of the optimal control-theoretic strategy, we use Pontryagin's maximum principle. We also illustrate the existence of the optimal control and the effectiveness of the optimal control is studied here. Cost-effectiveness and efficiency analysis confirms that time-dependent antiviral controlled drug therapy can reduce the viral load and infection process at a low cost. Numerical simulations have been done to illustrate our analytical findings. In addition, a new variable-order fractional model is proposed to investigate the effect of antiviral treatment over viral mutation to control disease transmission. Considering the superiority of fractional order calculus in the modeling of systems and processes, the proposed variable-order fractional model can provide more accurate insight for the modeling of the disease. Then through the genetic algorithm, optimal treatment is presented, and its numerical simulations are illustrated.
    Language English
    Publishing date 2022-02-01
    Publishing country France
    Document type Journal Article
    ZDB-ID 2267176-6
    ISSN 1951-6401 ; 1951-6355
    ISSN (online) 1951-6401
    ISSN 1951-6355
    DOI 10.1140/epjs/s11734-022-00454-4
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