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(searched for: doi:10.53391/mmnsa.2021.01.007)
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K. Shiva Reddy, Kottakkaran Sooppy Nisar, N. Phani Kumar, Choonkil Park, Ibrahim S. Yahia
Published: 1 December 2022
Alexandria Engineering Journal, Volume 61, pp 12123-12128; https://doi.org/10.1016/j.aej.2022.06.019

Published: 10 October 2022
by MDPI
Fractal and Fractional, Volume 6; https://doi.org/10.3390/fractalfract6100578

Abstract:
Despite its high mortality rate of approximately 90%, the Ebola virus disease (EVD) has not received enough attention in terms of in-depth research. This illness has been responsible for over 40 years of epidemics throughout Central Africa. However, during 2014–2015, the Ebola-driven epidemic in West Africa became, and remains, the deadliest to date. Thus, Ebola has been declared one of the major public health issues. This paper aims at exploring the effects of external fluctuations on the prevalence of the Ebola virus. We begin by proposing a sophisticated biological system that takes into account vaccination and quarantine strategies as well as the effect of time lags. Due to some external perturbations, we extend our model to the probabilistic formulation with white noises. The perturbed model takes the form of a system of stochastic differential equations. Based on some non-standard analytical techniques, we demonstrate two main approach properties: intensity and elimination of Ebola virus. To better understand the impact of applied strategies, we deal with the stochastic control optimization approach by using some advanced theories. All of this theoretical arsenal has been numerically confirmed by employing some real statistical data of Ebola virus. Finally, we mention that this work could be a rich basis for further investigations aimed at understanding the complexity of Ebola virus propagation at pathophysiological and mathematics levels.
Asmat Batool, Imran Talib, Rym Bourguiba, Iyad Suwan, , Muhammad Bilal Riaz
International Journal of Nonlinear Sciences and Numerical Simulation; https://doi.org/10.1515/ijnsns-2021-0338

Abstract:
In this paper, we construct a new generalized result to study the existence of solutions of nonlinear fractional boundary value problems (FBVPs). The proposed results unify the existence criteria of certain FBVPs including periodic and antiperiodic as special cases that have been previously studied separately in the literature. The method we employ is topological in its nature and manifests themselves in the forms of differential inequalities (lower and upper solutions, and coupled lower and upper solutions (CLUSs)). Two examples are given to demonstrate the applicability of the developed theoretical results.
Published: 31 January 2022
by MDPI
Fractal and Fractional, Volume 6; https://doi.org/10.3390/fractalfract6020078

Abstract:
In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than the corresponding model of fractional ordinary differential equations (ODEs). The Caputo fractional derivative is considered. Linear stability analysis of the disease-free equilibrium state of the epidemic model (ODEs) is presented by employing Routh–Hurwitz stability criteria. In order to solve this model, a fractional numerical scheme is proposed. The proposed scheme can be used to find conditions for obtaining positive solutions for diffusive epidemic models. The stability of the scheme is given, and convergence conditions are found for the system of the linearized diffusive fractional epidemic model. In addition to this, the deficiencies of accuracy and consistency in the nonstandard finite difference method are also underlined by comparing the results with the standard fractional scheme and the MATLAB built-in solver pdepe. The proposed scheme shows an advantage over the fractional nonstandard finite difference method in terms of accuracy. In addition, numerical results are supplied to evaluate the proposed scheme’s performance.
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.
Yi Tian
Mathematical Modelling and Control, Volume 2, pp 75-80; https://doi.org/10.3934/mmc.2022009

Abstract:
Fractal ordinary differential equations are successfully established by He's fractal derivative in a fractal space, and their variational principles are obtained by semi-inverse transform method.Taylor series method is used to solve the given fractal equations with initial boundary value conditions, and sometimes Ying Buzu algorithm play an important role in this process. Examples show the Taylor series method and Ying Buzu algorithm are powerful and simple tools.
, 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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