Article
Computer Science, Interdisciplinary Applications
Lan Meng, Wei Zhu
Summary: This paper presents an SEIR epidemic patch model with nonlinear incidence rate, vaccination, and quarantine strategies, and investigates the effects of vaccination, quarantine strategies, and population migration on disease transmission through numerical simulations.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Lian Duan, Lihong Huang
Summary: In this study, a vector-host epidemic model with spatial heterogeneity and general incidence rate was formulated and analyzed. The results show that the disease extinction is determined by the basic reproduction number R-0.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Interdisciplinary Applications
Deguo Sun, Qing Li, Wencai Zhao
Summary: In this paper, a fractional SEQIR epidemic model with saturated incidence and vaccination is constructed. Stability analysis and threshold conditions are derived for the deterministic fractional system. The stochastic stability near the positive equilibrium point is discussed for the stochastic system of integer order. The optimal control solution is obtained for the fractional control system using the maximum principle, and the theoretical derivations are verified by numerical simulation.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematical & Computational Biology
Jianpeng Wang, Binxiang Dai
Summary: This paper proposes a reaction-diffusion SEI epidemic model with nonlinear incidence rate and studies the well-posedness of solutions, including the existence of positive and unique classical solution and the boundedness of global solutions. The effects of basic reproduction numbers in spatially heterogeneous and homogeneous environments are analyzed, showing different stability and persistence scenarios. Examples and control strategies are provided through numerical simulations and sensitivity analysis.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2021)
Article
Mathematics, Applied
M. L. Diagne, H. Rwezaura, S. A. Pedro, J. M. Tchuenche
Summary: In this study, a mathematical model was used to evaluate the dynamics of measles transmission and the effectiveness of control strategies. The results indicate that vaccination and the inhibitory effect of infected individuals play significant roles in disease spread.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Physics, Multidisciplinary
Afeez Abidemi, Kolade M. Owolabi, Edson Pindza
Summary: In this paper, a seven-dimensional nonlinear mathematical model is formulated to describe the dynamics of Lassa fever transmission between human and rodent populations. The model is analyzed to investigate the behavior of its solutions and to gain insights into the impact of model parameters on disease transmission dynamics.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Mathematics, Applied
Xuan Tian, Shangjiang Guo
Summary: This paper mainly investigates the existence and nonexistence of traveling waves for a diffusive epidemic model with a general nonlinear incidence rate and infection-age structure. The results show that the spread of the disease depends on the basic reproduction number and critical wave speed, and the infection-age structure can reduce the speed of disappearance of infectious diseases.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Pegah Taghiei Karaji, Nemat Nyamoradi, Bashir Ahmad
Summary: In this paper, the SIR model with a nonlinear incidence rate is studied. The disease-free equilibrium E0, the endemic equilibrium E1, and the basic reproduction number R0 of the model are obtained. The local asymptotic stability of E0 is established when R0<1, and the local asymptotic stability of E1 is proved when R0>1. The global stability of the model is studied using Barbalat's lemma. The transcritical bifurcation analysis is investigated by the Sotomayor theorem. The existence of Hopf bifurcation and the sensitivity analysis of the basic reproduction number are checked. Numerical simulations are conducted to support the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Yi Wang, Junling Ma, Jinde Cao
Summary: The basic reproduction number R-0 is an important indicator of the severity of an epidemic outbreak. Assortative and disassortative mixing have different effects on virus transmission, and the results in degree correlated networks may not be universal but hold true for bimodal degree distribution and assortative mixing networks.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Veterinary Sciences
Woo-Hyun Kim, Seongbeom Cho
Summary: This study estimated the basic reproduction number and generation time of H5N1, H5N8, and H5N6 subtypes of avian influenza, finding differences in transmission characteristics among the subtypes.
FRONTIERS IN VETERINARY SCIENCE
(2021)
Article
Multidisciplinary Sciences
Jan Brink Valentin, Henrik Moller, Soren Paaske Johnsen
Summary: Early identification of the basic reproduction number (BRN) is crucial for political decision making during an epidemic. In this study, the BRN in Denmark during the early stage of the COVID-19 epidemic was estimated using a SEIR dynamical system. The model provided valuable insights for decision makers on the effect of a politically determined lockdown.
Article
Mathematics, Applied
Xiaodan Chen, Renhao Cui
Summary: This paper focuses on a diffusive cholera epidemic model with a nonlinear incidence rate. By constructing suitable Lyapunov functionals, the global stability of the disease free equilibrium and the endemic equilibrium are investigated.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Baba Seidu, Oluwole D. Makinde, Joshua Kiddy K. Asamoah
Summary: This paper presents a novel algebraic method, named as Jacobian-Determinant method, for constructing Lyapunov functions to study the global stability of disease-free equilibrium points in deterministic epidemic ordinary differential equation models. The method relies on a direct algebraic procedure and determines a threshold quantity, R'0, which is analogous to the basic reproduction number, R0. The method is applied to various models and reveals that the threshold quantity is related to the basic reproduction numbers obtained using the next-generation matrix method, even for models that do not use standard or mass action incidence.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Xiaolan Liu, Cheng-Cheng Zhu, Hari Mohan Srivastava, Hongyan Xu
Summary: The first purpose of this article is to establish and analyze the incidence rate of system 4 under homogeneous Neumann boundary conditions, which models the dynamics of interactions between pathogens and the host immune system and has important applications in HIV-1, HCV, flu, etc. The globally asymptotic stability of the equilibria is obtained using the Lyapunov-LaSalle method. The results show that the infection-free equilibrium is stable when the reproductive number R-0 is less than or equal to 1, while the CTL-inactivated infection equilibrium is stable when R-1 is less than or equal to 1 but greater than R-0, and the CTL-activated equilibrium is stable when R-1 is greater than 1. The discretization of the model using a non-standard finite difference scheme is also investigated, and it is found that the global stability of the equilibria is consistent between the continuous and discrete models. Numerical simulations are performed to illustrate the theoretical results.
Article
Mathematics, Applied
Pan Zhou, Jianpeng Wang, Zhidong Teng, Kai Wang
Summary: This article focuses on a diffusive SVEIR epidemic model with nonlinear incidences. The well-posedness of solutions for the model is obtained. The basic reproduction number R0 and the local basic reproduction number (R0) over bar (x) are then calculated, defined as the spectral radii of the next-generation operators. The relationship between R0 and (R0) over bar (x), as well as the asymptotic properties of R0 when the diffusive rates tend to infinity or zero, is investigated using compact linear operators L-1 and L-2. Using the theory of monotone dynamical systems and the persistence theory of dynamical systems, it is shown that the disease-free equilibrium is globally asymptotically stable when R0 < 1, while the disease is uniformly persistent when R0 > 1. Furthermore, in the spatially homogeneous case, it is proven that the disease-free equilibrium is globally asymptotically stable if R-0 <= 1, and the endemic equilibrium is globally asymptotically stable if R0 > 1 and an additional condition is satisfied.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics, Applied
Xinzhi Liu, Peter Stechlinski
APPLIED MATHEMATICS AND COMPUTATION
(2016)
Article
Operations Research & Management Science
Peter G. Stechlinski, Paul I. Barton
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2016)
Article
Biology
Xinzhi Liu, Peter Stechlinski
JOURNAL OF BIOLOGICAL SYSTEMS
(2017)
Article
Mathematics
Peter G. Stechlinski, Paul I. Barton
JOURNAL OF DIFFERENTIAL EQUATIONS
(2017)
Article
Computer Science, Software Engineering
Paul I. Barton, Kamil A. Khan, Peter Stechlinski, Harry A. J. Watson
OPTIMIZATION METHODS & SOFTWARE
(2018)
Article
Computer Science, Interdisciplinary Applications
Peter Stechlinski, Michael Patrascu, Paul Barton
COMPUTERS & CHEMICAL ENGINEERING
(2018)
Article
Mathematics, Applied
Peter Stechlinski, Kamil A. Khan, Paul I. Barton
SIAM JOURNAL ON OPTIMIZATION
(2018)
Article
Automation & Control Systems
Xinzhi Liu, Peter Stechlinski
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2018)
Article
Operations Research & Management Science
Peter Stechlinski, Johannes Jaschke, Paul I. Barton
Article
Operations Research & Management Science
Peter Stechlinski
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2020)
Article
Mathematics, Applied
Peter Stechlinski, Paul Barton
Summary: This article investigates Hessenberg differential-algebraic equations with nonsmooth right-hand side functions, focusing on consistent initialization robust to parametric perturbations and local existence and uniqueness of solutions. The results are derived from the regularity of initial data and the Lipschitz homeomorphism determined by participating functions. Consequently, the theory lays a rigorous foundation for smooth Hessenberg DAEs with classical differentiation index nu.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Sameh A. Eisa, Peter Stechlinski
Summary: This paper focuses on dynamic sensitivities of nonsmooth power control systems, using recent advances in nonsmooth sensitivity theory to provide new insights on design and implementation for large-scale practical problems. The dynamic simulations of sensitivities give valuable information for system control limits and improvements.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics
Peter Stechlinski
Summary: In this study, generalized differentiation index-one nonlinear complementarity systems (NCSs) are mathematically regularized. It is shown that strong regularity of solutions implies generalized differentiation index one holding and Lipschitzian parametric dependence. By relating strong regularity to orientation from piecewise continuously differentiable functions and utilizing an extended nonsmooth implicit function theorem, well-posedness of NCSs is established.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Jon Donnelly, Peter Stechlinski
Summary: Graph centrality measures are widely used to rank agents in networks based on their importance for predicting and managing network outcomes. However, malicious agents can potentially impact the reliability of schemes like EigenTrust, even if they have low centrality themselves.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Matthew Ackley, Peter Stechlinski
Summary: This article investigates the parametric sensitivities of rioting activity using a model of the 2005 French riots. It concludes that the exit/removal rate from rioting activity and geographic proximity have the greatest impact on the dynamics of social contagion.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2021)
Article
Engineering, Multidisciplinary
A. A. Aganin, A. I. Davletshin
Summary: A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed in this paper. The model equations are more accurate and compact compared to existing analogs. Five problems are considered for validation, and the results show good agreement with experimental data and numerical solutions. The model is also used to analyze the behavior of bubbles in different clusters, providing meaningful insights.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Hao Wu, Jie Sun, Wen Peng, Lei Jin, Dianhua Zhang
Summary: This study establishes an analytical model for the coupling of temperature, deformation, and residual stress to explore the mechanism of residual stress formation in hot-rolled strip and how to control it. The accuracy of the model is verified by comparing it with a finite element model, and a method to calculate the critical exit crown ratio to maintain strip flatness is proposed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shengwen Tu, Naoki Morita, Tsutomu Fukui, Kazuki Shibanuma
Summary: This study aimed to extend the finite element method to cope with elastic-plastic problems by introducing the s-version FEM. The s-version FEM, which overlays a set of local mesh with fine element size on the conventional FE mesh, simplifies domain discretisation and provides accurate numerical predictions. Previous applications of the s-version FEM were limited to elastic problems, lacking instructions for stress update in plasticity. This study presents detailed instructions and formulations for addressing plasticity problems with the s-version FEM and analyzes a stress concentration problem with linear/nonlinear material properties.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bo Fan, Zhongmin Wang
Summary: A 3D rotating hyperelastic composite REF model was proposed to analyze the influence of tread structure and rotating angular speed on the vibration characteristics of radial tire. Nonlinear dynamic differential equations and modal equations were established to study the effects of internal pressure, tread pressure sharing ratio, belt structure, and rotating angular speed on the vibration characteristics.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
X. W. Chen, Z. Q. Yue, Wendal Victor Yue
Summary: This paper examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modeled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The analytical solutions of the stress intensity factors are obtained and numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xumin Guo, Jianfei Gu, Hui Li, Kaihua Sun, Xin Wang, Bingjie Zhang, Rangwei Zhang, Dongwu Gao, Junzhe Lin, Bo Wang, Zhong Luo, Wei Sun, Hui Ma
Summary: In this study, a novel approach combining the transfer matrix method and lumped parameter method is proposed to analyze the vibration response of aero-engine pipelines under base harmonic and random excitations. The characteristics of the pipelines are investigated through simulation and experiments, validating the effectiveness of the proposed method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xiangyu Sha, Aizhong Lu, Ning Zhang
Summary: This paper investigates the stress and displacement of a layered soil with a fractional-order viscoelastic model under time-varying loads. The correctness of the solutions is validated using numerical methods and comparison with existing literature. The research findings are of significant importance for exploring soil behavior and its engineering applications under time-varying loads.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Thuy Dong Dang, Thi Kieu My Do, Minh Duc Vu, Ngoc Ly Le, Tho Hung Vu, Hoai Nam Vu
Summary: This paper investigates the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change using the Ritz energy method. The results show the significant beneficial effects of FG-GRC laminated coatings and corrugated core on the nonlinear buckling responses of structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Zhihao Zhai, Chengbiao Cai, Qinglai Zhang, Shengyang Zhu
Summary: This paper investigates the effect of localized cracks induced by environmental factors on the dynamic performance and service life of ballastless track in high-speed railways. A mathematical approach for forced vibrations of Mindlin plates with a side crack is derived and implemented into a train-track coupled dynamic system. The accuracy of this approach is verified by comparing with simulation and experimental results, and the dynamic behavior of the side crack under different conditions is analyzed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
James Vidler, Andrei Kotousov, Ching-Tai Ng
Summary: The far-field methodology, developed by J.C. Maxwell, is utilized to estimate the effective third order elastic constants of composite media containing random distribution of spherical particles. The results agree with previous studies and can be applied to homogenization problems in other fields.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Kim Q. Tran, Tien-Dat Hoang, Jaehong Lee, H. Nguyen-Xuan
Summary: This study presents novel frameworks for graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates and investigates their performance through static and free vibration analyses. The results show that the mass density framework has potential for comparing different porous cores and provides a low weight and high stiffness-to-weight ratio. Primitive plates exhibit superior performance among thick plates.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bence Hauck, Andras Szekrenyes
Summary: This study explores several methods for computing the J-integral in laminated composite plate structures with delamination. It introduces two special types of plate finite elements and a numerical algorithm. The study presents compact formulations for calculating the J-integral and applies matrix multiplication to take advantage of plate transition elements. The models and algorithms are applied to case studies and compared with analytical and previously used finite element solutions.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Wu Ce Xing, Jiaxing Wang, Yan Qing Wang
Summary: This paper proposes an effective mathematical model for bolted flange joints to study their vibration characteristics. By modeling the flange and bolted joints, governing equations are derived. Experimental studies confirm that the model can accurately predict the vibration characteristics of multiple-plate structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Pingchao Yu, Li Hou, Ke Jiang, Zihan Jiang, Xuanjun Tao
Summary: This paper investigates the imbalance problem in rotating machinery and finds that mass imbalance can induce lateral-torsional coupling vibration. By developing a model and conducting detailed analysis, it is discovered that mass imbalance leads to nonlinear time-varying characteristics and there is no steady-state torsional vibration in small unbalanced rotors. Under largely unbalanced conditions, both resonant and unstable behavior can be observed, and increasing lateral damping can suppress instability and reduce lateral amplitude in the resonance region.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Yong Cao, Ziwen Guo, Yilin Qu
Summary: This paper investigates the mechanically induced electric potential and charge redistribution in a piezoelectric semiconductor cylindrical shell. The results show that doping levels can affect the electric potentials and mechanical displacements, and alter the peak position of the zeroth-order electric potential. The doping level also has an inhibiting effect on the first natural frequency. These findings are crucial for optimizing the design and performance of cylindrical shell-shaped sensors and energy harvesters.
APPLIED MATHEMATICAL MODELLING
(2024)
