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(searched for: doi:10.53391/mmnsa.2021.01.008)
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Published: 14 September 2022
Applied Mathematics in Science and Engineering, Volume 30, pp 635-660; https://doi.org/10.1080/27690911.2022.2121823

Abstract:
The paper's main aim is to investigate the 2019 coronavirus disease in Ethiopia using a fractional-order mathematical model. It would also focus on the importance of fractional-order derivatives that may help us in modelling the system and understanding the effect of model parameters and fractional derivative orders on the approximate solutions of our model. A SELAIQHCR model is constructed using nonlinear differential equations in the Atangana–Baleanu non-integer operator in the Caputo sense. After that, the Chebyshev fourth kind spectral collocation method is used to change a fractional system to an algebraic system. Newton iterative technique is used to solve the converted system. The next-generation matrix technique is used to obtain the effective reproduction number. The COVID-19-free equilibrium point and endemic equilibrium point, solution positivity and boundedness, and their stability are all carefully done. The sensitivity of the effective reproduction value with respect to the key model parameters is discussed. The beginning values provided for our system were obtained using reports from the Ethiopian Public Health Institute from 29 February 2021 to 7 June 2021. The fundamental reproduction number is obtained with R0=1.4331. The model's numerical solutions are represented graphically.
Published: 1 April 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10071125

Abstract:
This work proposes a qualitative study for the fractional second-grade fluid described by a fractional operator. The classical Caputo fractional operator is used in the investigations. The exact analytical solutions of the constructed problems for the proposed model are determined by using the Laplace transform method, which particularly includes the Laplace transform of the Caputo derivative. The impact of the used fractional operator is presented; especially, the acceleration effect is noticed in the paper. The parameters’ influences are focused on the dynamics such as the Prandtl number (Pr), the Grashof numbers (Gr), and the parameter η when the fractional-order derivative is used in modeling the second-grade fluid model. Their impacts are also analyzed from a physical point of view besides mathematical calculations. The impact of the fractional parameter α is also provided. Finally, it is concluded that the graphical representations support the theoretical observations of the paper.
Qiulin Huang, , Chuanjun Dai, Zengling Ma, Qi Wang, Min Zhao
Mathematical Biosciences and Engineering, Volume 20, pp 930-954; https://doi.org/10.3934/mbe.2023043

Abstract:
Within the framework of physical and ecological integrated control of cyanobacteria bloom, because the outbreak of cyanobacteria bloom can form cyanobacteria clustering phenomenon, so a new aquatic ecological model with clustering behavior is proposed to describe the dynamic relationship between cyanobacteria and potential grazers. The biggest advantage of the model is that it depicts physical spraying treatment technology into the existence pattern of cyanobacteria, then integrates the physical and ecological integrated control with the aggregation of cyanobacteria. Mathematical theory works mainly investigate some key threshold conditions to induce Transcritical bifurcation and Hopf bifurcation of the model $ (2.1) $, which can force cyanobacteria and potential grazers to form steady-state coexistence mode and periodic oscillation coexistence mode respectively. Numerical simulation works not only explore the influence of clustering on the dynamic relationship between cyanobacteria and potential grazers, but also dynamically show the evolution process of Transcritical bifurcation and Hopf bifurcation, which can be clearly seen that the density of cyanobacteria decreases gradually with the evolution of bifurcation dynamics. Furthermore, it should be worth explaining that the most important role of physical spraying treatment technology can break up clumps of cyanobacteria in the process of controlling cyanobacteria bloom, but cannot change the dynamic essential characteristics of cyanobacteria and potential grazers represented by the model $ (2.1) $, this result implies that the physical spraying treatment technology cannot fundamentally eliminate cyanobacteria bloom. In a word, it is hoped that the results of this paper can provide some theoretical support for the physical and ecological integrated control of cyanobacteria bloom.
Hardik Joshi, Brajesh Kumar Jha,
Mathematical Biosciences and Engineering, Volume 20, pp 213-240; https://doi.org/10.3934/mbe.2023010

Abstract:
In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.
M Kumaresan, M Senthil Kumar, Nehal Muthukumar
Mathematical Biosciences and Engineering, Volume 19, pp 9983-10005; https://doi.org/10.3934/mbe.2022466

Abstract:
Aggregating a massive amount of disease-related data from heterogeneous devices, a distributed learning framework called Federated Learning(FL) is employed. But, FL suffers in distributing the global model, due to the heterogeneity of local data distributions. To overcome this issue, personalized models can be learned by using Federated multitask learning(FMTL). Due to the heterogeneous data from distributed environment, we propose a personalized model learned by federated multitask learning (FMTL) to predict the updated infection rate of COVID-19 in the USA using a mobility-based SEIR model. Furthermore, using a mobility-based SEIR model with an additional constraint we can analyze the availability of beds. We have used the real-time mobility data sets in various states of the USA during the years 2020 and 2021. We have chosen five states for the study and we observe that there exists a correlation among the number of COVID-19 infected cases even though the rate of spread in each case is different. We have considered each US state as a node in the federated learning environment and a linear regression model is built at each node. Our experimental results show that the root-mean-square percentage error for the actual and prediction of COVID-19 cases is low for Colorado state and high for Minnesota state. Using a mobility-based SEIR simulation model, we conclude that it will take at least 400 days to reach extinction when there is no proper vaccination or social distance.
, Billel Semmar, Kamal Al Nasr
Published: 1 January 2022
Nonlinear Engineering, Volume 11, pp 100-111; https://doi.org/10.1515/nleng-2022-0013

Abstract:
In this article, a prey–predator system is considered in Caputo-conformable fractional-order derivatives. First, a discretization process, making use of the piecewise-constant approximation, is performed to secure discrete-time versions of the two fractional-order systems. Local dynamic behaviors of the two discretized fractional-order systems are investigated. Numerical simulations are executed to assert the outcome of the current work. Finally, a discussion is conducted to compare the impacts of the Caputo and conformable fractional derivatives on the discretized model.
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