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    Author Correction: Novel insights for a nonlinear deterministic-stochastic class of fractional-order Lassa fever model with varying kernels (Scientific Reports, (2023), 13, 1, (15320), 10.1038/s41598-023-42106-0)
    (Nature Research, 2023) Rashid, Saima; Karim, Shazia; Akgül, Ali; Bariq, Abdul; Elagan, S.K.
    Correction to: Scientific Reports, published online 15 September 2023 The original version of this Article contained an error. In the original version of this article, the Acknowledgements section was missing. The Acknowledgements section now reads: “The researchers would like to acknowledge the Deanship of Scientific Research at Taif University for funding this work.” The original Article has been corrected. © 2023, Springer Nature Limited.
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    Novel insights for a nonlinear deterministic-stochastic class of fractional-order Lassa fever model with varying kernels
    (Nature Portfolio, 2023) Rashid, Saima; Karim, Shazia; Akguel, Ali; Bariq, Abdul; Elagan, S. K.
    Lassa fever is a hemorrhagic virus infection that is usually spread by rodents. It is a fatal infection that is prevalent in certain West African countries. We created an analytical deterministic-stochastic framework for the epidemics of Lassa fever employing a collection of ordinary differential equations with nonlinear solutions to identify the influence of propagation processes on infected development in individuals and rodents, which include channels that are commonly overlooked, such as ecological emergent and aerosol pathways. The findings shed light on the role of both immediate and subsequent infectiousness via the power law, exponential decay and generalized Mittag-Leffler kernels. The scenario involves the presence of a steady state and an endemic equilibrium regardless of the fundamental reproduction number, R-0 < 1 , making Lassa fever influence challenging and dependent on the severity of the initial sub-populations. Meanwhile, we demonstrate that the stochastic structure has an exclusive global positive solution via a positive starting point. The stochastic Lyapunov candidate approach is subsequently employed to determine sufficient requirements for the existence and uniqueness of an ergodic stationary distribution of non-negative stochastic simulation approaches. We acquire the particular configuration of the random perturbation associated with the model's equilibrium R-0(s) < 1 according to identical environments as the presence of a stationary distribution. Ultimately, modeling techniques are used to verify the mathematical conclusions. Our fractional and stochastic findings exhibit that when all modes of transmission are included, the impact of Lassa fever disease increases. The majority of single dissemination pathways are less detrimental with fractional findings; however, when combined with additional spread pathways, they boost the Lassa fever stress.
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    Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects
    (Elsevier, 2023) Rashid, Saima; El-Deeb, Ahmed A.; Inc, Mustafa; Akgul, Ali; Zakarya, Mohammed; Weera, Wajaree
    In this paper, we suggest and assess a stochastic model for pneumonia-typhoid co -infection to investigate their distinctive correlation under the impact of preventative techniques con-sidering environmental noise and piecewise fractional derivative operators. Initially, we conducted a descriptive investigation of the model, and the basic reproductive number is defined in terms of the existence and stability of dynamic equilibrium. Then, we obtain the sufficient requirements for the existence of an ergodic stationary distribution by utilizing a novel methodology for constructing stochastic Lyapunov candidates. Besides that, the basic stochastic reproductive Rs0 as a threshold that will examine the extinction and persistence of the disease. Through a rigorous analysis, this study presents the concept of piecewise derivative with the goal of modelling the co-dynamics of pneumonia and typhoid fever with varying kernels. We viewed various possibilities and described numerical strategies for addressing difficulties. Visual observations, such as chaotic and dynamical behaviour patterns, are provided to demonstrate the efficacy of the proposed notion. Thus, the innovative considerations of fractional calculus include more versatile configurations, allowing us to more effectively acclimate to the dynamic system behaviours of real-world manifestations. Finally, we discovered that treating pneumonia with typhoid fever preventative measures is the least expensive. As a result, for advantageous and cost-effective regulation of both pathogens, legislators must prioritize preventative measures while not overlooking treatment of affected patients.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).