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SEIR Mathematical Model for Influenza-Corona Co-Infection with Treatment and Hospitalization Compartments and Optimal Control Strategies

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Computer Modeling in Engineering & Sciences 2025年第2期142卷 1899-1931页

作者： Muhammad Imran Brett McKinney Azhar Iqbal Kashif Butt Tandy school of Computer Science University of TulsaTulsaOK 74104USA Department of mathematics and statistics College of ScienceKing Faisal UniversityAl-Ahsa31982Saudi Arabia

The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical *** article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR(Susceptible-Exposed-Infectious-Recovered)framework to incorporate treatment and hospitalization *** population is divided into eight compartments,with infectious individuals further categorized into influenza infectious,corona infectious,and co-infection *** proposed mathematical model is constrained to adhere to fundamental epidemiological properties,such as non-negativity and boundedness within a feasible ***,the model is demonstrated to be well-posed with a unique *** points,including the disease-free and endemic equilibria,are identified,and various properties related to these equilibrium points,such as the basic reproduction number,are *** and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction *** the most influential parameters is crucial for understanding their impact on the co-infection’s spread and ***,an optimal control problem is defined to minimize disease transmission and to control strategy *** purpose of our study is to identify the most effective(optimal)control strategies for mitigating the spread of the co-infection with minimum cost of the *** results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s *** mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection,helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.

关键词： Influenza-corona co-infection stability analysis sensitivity analysis treatment self-precaution optimal control

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Global Dynamics of a Kawasaki Disease Vascular Endothelial Cell Injury Model with Backward Bifurcation and Hopf Bifurcation

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Acta Mathematicae Applicatae Sinica 2025年第1期41卷 200-233页

作者： Ke GUO Wan-biao MA school of mathematics and Physics University of Science and Technology BeijingBeijing 100083China

Kawasaki disease(KD)is an acute,febrile,systemic vasculitis that mainly affects children under five years of *** this paper,we propose and study a class of 5-dimensional ordinary differential equation model describing the vascular endothelial cell injury in the lesion area of *** model exhibits forward/backward *** is shown that the vascular injury-free equilibrium is locally asymptotically stable if the basic reproduction number R_(0)1,and some explicit analytic expressions of ultimate lower bounds of the solutions of the model are *** results suggest that the control of vascular injury in the lesion area of KD is not only correlated with the basic reproduction number R_(0),but also with the growth rate of normal vascular endothelial cells promoted by the vascular endothelial growth factor.

关键词： Kawasaki disease model backward bifurcation Hopf bifurcation global stability permanence

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Rough singular integrals associated to surfaces of revolution on product spaces

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Acta Mathematica Sinica,English Series 2025年

作者： Hussain AL-QASSEM Leslie CHENG Yibiao PAN mathematics Program Department of Mathematics Statistics and Physics College of Arts and Sciences Qatar University Department of mathematics Bryn Mawr College Department of mathematics University of Pittsburgh

We study the Lpboundedness of singular integral operators along surfaces of revolution on product spaces. The Lpboundedness for these operators are obtained under very weak conditions on kernels. Our results are new and they improve several previously known results. Furthermore, they are natural extensions of many known results on singular integrals in the one-parameter setting and they subsume many other corresponding results on the product space setting.

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ECHOS OF THE STEINER-LEHMUS EQUAL BISECTORSSTHEOREM

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Acta Mathematica Scientia 2025年第1期45卷 257-263页

作者： Christoph BÖRGERS Eric L.GRINBERG Mehmet ORHON Junhao SHEN Department of mathematics Tufts UniversityMedfordMA02155USA Department of mathematics University of Massachusetts BostonBostonMA02125USA Department of mathematics&statistics University of New HampshireDurhamNH03824USA

The Steiner-Lehmus equal bisectors theorem originated in the mid 19th *** its age,it would have been accessible to Euclid and his *** theorem remains evergreen,with new proofs continuing to appear *** theorem has fostered discussion about the nature of proof itself,direct and *** we continue the momentum by providing a trigonometric proof,relatively short,based on an analytic estimate that leverages algebraic trigonometric *** proofs of the theorem exist in the *** of these contain key ideas that already appeared in ***’1850 proofs,not always with *** the aim of increasing awareness of and making more accessible Lehmus’proofs,we provide an annotated *** conclude with remarks on different proofs and relations among them.

关键词： Steiner-Lehmus theorem equal bisectors

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Impact of Pollutant Concentration and Particle Deposition on the Radiative Flow of Casson-Micropolar Fluid between Parallel Plates

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Computer Modeling in Engineering & Sciences 2025年第1期142卷 665-690页

作者： Ghaliah Alhamzi Badr Saad T.Alkahtani Ravi Shanker Dubey Vinutha Kalleshachar Neelima Nizampatnam Department of mathematics and statistics College of ScienceImam Mohammad Ibn Saud Islamic University(IMSIU)Riyadh11564Saudi Arabia Department of mathematics College of ScienceKing Saud UniversityRiyadh11989Saudi Arabia Department of mathematics Amity School of Applied SciencesAmity University RajasthanJaipur302002RajasthanIndia Department of Studies in mathematics Davangere UniversityDavangere577002India Department of Electronics and Communication Engineering Amrita School of EngineeringAmrita Vishwa VidyapeethamBengaluru560035India

Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental *** the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge *** waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution *** study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle *** explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are *** governing equations are transformed into ordinary differential equations with the help of suitable similarity *** Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary *** integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of *** outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current *** reveal that concentration upsurges as the micropolar parameter *** concentration reduces with an upsurge in the thermophoretic *** upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass *** surface drag force declines for improved values of porosity and micropolar parameters.

关键词： Micropolar fluid thermal radiation porous medium thermophoretic particle deposition waste discharge concentration

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Finite-Time Stability of Impulsive and Switched Hybrid Systems With Delay-Dependent Impulses

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IEEE/CAA Journal of Automatica Sinica 2025年第2期12卷 466-468页

作者： Taixiang Zhang Jinde Cao Mahmoud Abdel-Aty Ardak Kashkynbayev the school of mathematics Southeast University IEEE the Deanship of Graduate Studies and Scientific Research Ahlia University the Jadara Research Center Jadara University the Department of mathematics Nazarbayev University

Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid *** switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.

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Finite Volume Element Method for Fractional Order Neutral Time-Delay Differential Equations

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Engineering(科研) 2025年第1期17卷 30-52页

作者： Zicheng Wei Qing Yang school of mathematics and statistics Shandong Normal University Jinan China

Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, etc. Therefore, it is of great significance to study fractional-order time-delay differential equations. In this paper, we discuss a finite volume element method for a class of fractional-order neutral time-delay differential equations. By introducing an intermediate variable, the fourth-order problem is transformed into a system of equations consisting of two second-order partial differential equations. The L1 formula is used to approximate the time fractional order derivative terms, and the finite volume element method is used in space. A fully discrete format of the equations is established, and we prove the existence, uniqueness, convergence and stability of the solution. Finally, the validity of the format is verified by numerical examples.

关键词： Fractional Order Time-Delay Differential Equation Finite Volume Element Method L1 Approximation Error Estimation Numerical Simulation

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The Finite Volume Element Method for Time-Fractional Nonlinear Fourth-Order Diffusion Equation with Time Delay

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Engineering(科研) 2025年第1期17卷 53-72页

作者： Anran Li Qing Yang school of mathematics and statistics Shandong Normal University Jinan China

In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.

关键词： Time-Fractional Nonlinear Fourth-Order Diffusion Equation with Time Delay Finite Volume Element Method Caputo-Fractional Derivative Optimal Priori Error Analysis

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Mechanisms and Efficacy of Chinese Herbal Medicines in Benign Prostatic Hyperplasia

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Chinese Journal of Integrative Medicine 2025年第1期31卷 73-82页

作者： WANG Fu MA Dong-yue YANG Jiu-tian LYU Dong-fang GAO Qing-he LI Chun-lei ZHONG Chong-fu Department of Andrology Xiyuan Hospital of China Academy of Chinese Medical SciencesBeijing100091China Graduate school Beijing University of Chinese MedicineBeijing100029China Department of Andrology The Affiliated Hospital of Shandong University of Traditional Chinese MedicineJinan250014China Faculty of Medicine Linyi UniversityLinyiShandong Province276000China

Benign prostatic hyperplasia(BPH) is one of the most common diseases in elderly men, the incidence of which gradually increases with age and leads to lower urinary tract symptoms(LUTS), which seriously affects the quality of life of patients. Chinese herbal medicines(CHMs) are widely used for the treatment of BPH in China and some other countries. To explore the molecular mechanisms of CHMs for BPH, we conducted a review based on peer-reviewed English-language publications in Pub Med and Web of Science databases from inception to December 31, 2023. This article primarily reviewed 32 papers on the use of CHMs and its active compounds in the treatment of BPH, covering animal and cell experiments, and identified relevant mechanisms of action. The results suggest that the mechanisms of action of CHMs in treating BPH may involve the regulation of sex hormones,downregulation of cell growth factors, anti-inflammatory and antioxidative effects, inhibition of cell proliferation, and promotion of apoptosis. CHMs also exhibit α-blocker-like effects, with the potential to relax urethral smooth muscle and alleviate LUTS. Additionally, we also reviewed 4 clinical trials and meta-analyses of CHMs for the treatment of BPH patients, which provided initial evidence of the safety and effectiveness of CHMs treatment. CHMs treatment for BPH shows advantages as a multi-component, multi-target, and multi-pathway therapy, which can mitigate the severity of the disease, improve LUTS, and may become a reliable treatment option in the future.

关键词： herbal treatment promotion

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Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus

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Science China mathematics 2025年

作者： Xin Lü Shengli Tan Kang Zuo school of Mathematical Sciences Key Laboratory of Mathematics and Engineering Applications(Ministry of Education) Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal University school of mathematics and statistics Wuhan University Institut für Mathematik Universit?t Mainz

We show that there does not exist any Shimura curve with a strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus g≥4. In particular, Shimura curves of Mumford type are not...

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