Mathematics and Computers in Simulation最新文献

{"title":"The adiabatic exponential limits of Riemann solutions in the isentropic three-component model","authors":"Yiheng Jiang,&nbsp;Chun Shen","doi":"10.1016/j.matcom.2025.10.002","DOIUrl":"10.1016/j.matcom.2025.10.002","url":null,"abstract":"<div><div>The explicit construction of Riemann solutions is achieved for an ideally isentropic three-component model owning a unitary velocity and a collective pressure in one space dimension under the hypotheses without mass and heat transfer and also without viscosity. In addition, the asymptotic results of Riemann solutions are explored at length by sending the adiabatic exponent drop to one. On the one side, it reveals the concentration phenomenon, where the Riemann solution with a 1-shock, 2,3-contact and 4-shock waves converges to a delta shock solution. On the other side, it also exhibits the cavitation phenomenon, where all internal states in the 1-rarefaction and 4-rarefaction waves become vacuum ones by sending this limit. Finally, some representative numerical simulations are offered to observe the formation of delta shock wave and vacuum state in a more intuitive way as the adiabatic exponent tends to one, which is consistent with the theoretical analysis.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 48-70"},"PeriodicalIF":4.4,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145236240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A meshless structure-preserving quasi-interpolation method for solving Allen–Cahn equations on spheres","authors":"Zhengjie Sun ,&nbsp;Yuyan Gao","doi":"10.1016/j.matcom.2025.09.031","DOIUrl":"10.1016/j.matcom.2025.09.031","url":null,"abstract":"<div><div>This paper proposes a novel meshless structure-preserving scheme for solving Allen–Cahn equations on spheres. Within the scalar auxiliary variable (SAV) framework, we introduce a kernel-based spherical quasi-interpolation method for spatial discretization on scattered collocation points, complemented by appropriate time integration schemes. Our approach stands out by ensuring unconditional energy stability and overcoming the limitations of traditional mesh-based techniques. Quasi-interpolation methods are known for their simplicity and adaptability to various kernel properties, eliminating the need for large linear systems and making the scheme easy to implement. We provide rigorous theoretical analysis to validate the proposed spherical quasi-interpolation SAV scheme, including well-posedness, energy stability, and error estimates. Numerical examples further demonstrate the convergence of the quasi-interpolation method and the accuracy of simulating Allen–Cahn equations on the sphere.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 31-47"},"PeriodicalIF":4.4,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145236239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the heterogeneous susceptibility and infectivity: A nonlocal state-structured SIR epidemic model","authors":"Kailong Zhao,&nbsp;Zhijun Liu,&nbsp;Lianwen Wang","doi":"10.1016/j.matcom.2025.09.030","DOIUrl":"10.1016/j.matcom.2025.09.030","url":null,"abstract":"<div><div>This work develops and analytically investigate a nonlocal state-structured SIR epidemic model governed by integro-differential equations, which characterizes heterogeneous host susceptibility and variable infectivity of infected individuals. Constructing appropriate Lyapunov functionals, we show that the basic reproduction number exclusively determines global stability of both disease-free and endemic steady states. Numerical simulations corroborate our theoretical findings and demonstrate the substantial impact of nonlocal kernels on disease transmission dynamics, besides, some significantly effective strategies are identified, including immunization of susceptible populations, contact-reduction measures, mitigation of pathogen-specific infectivity and retardation of disease progression. Furthermore, we apply an SVELITR model derived by discretizing the nonlocal state-structured model to project tuberculosis prevalence trends in China, providing quantitative insights into the efficacy of several interventions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 1-30"},"PeriodicalIF":4.4,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145236157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enhanced FIR system identification: Empirical copula delay estimation method and variable stacking length multi-gradient algorithm","authors":"Shaoxue Jing","doi":"10.1016/j.matcom.2025.09.029","DOIUrl":"10.1016/j.matcom.2025.09.029","url":null,"abstract":"<div><div>This study offers an improved strategy for identifying finite impulse response (FIR) systems. To begin with, a modified time delay estimation method, rooted in empirical copula, is applied, creating a robust framework for parameter estimation. Following this, an innovative stochastic gradient algorithm that incorporates a flexible stacking length is presented to enhance the accuracy of parameter estimates. This algorithm adapts stacking length dynamically according to the optimization progress, which enhances both convergence and accuracy. Additionally, a criterion based on the decrease of the cost function is proposed to determine the optimal variable stacking length, ensuring better performance. Extensive experimental results confirm the effectiveness of the proposed methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 676-688"},"PeriodicalIF":4.4,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(25)00402-1","DOIUrl":"10.1016/S0378-4754(25)00402-1","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Page 1118"},"PeriodicalIF":4.4,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vegetation-water system with positive feedback: Effects of local versus nonlocal grazing","authors":"Nishan Li,&nbsp;Daiyong Wu,&nbsp;Zidie Zhang,&nbsp;Luhong Ye","doi":"10.1016/j.matcom.2025.09.019","DOIUrl":"10.1016/j.matcom.2025.09.019","url":null,"abstract":"<div><div>Positive feedback plays a crucial role in maintaining ecosystem stability and preventing desertification in semi-arid regions. However, researches on the evaporation suppression as part of this positive feedback remain limited. To deeply explore the influence of positive feedback effect on the stability of positive equilibrium point in local and nonlocal grazing systems, we propose and investigate a nonlocal grazing vegetation water model system with saturated evaporation suppression effect and soil water diffusion intensity. The eigenvalue method is used to analyze the stability of the positive equilibrium point, and different parameters are controlled to analyze the influence on the stability of the positive equilibrium point in the local and nonlocal systems. Our results show that in the absence of evaporation suppression, overgrazing may lead to the disappearance of positive equilibrium points, indicating desertification in semi-arid regions. In the presence of evaporation suppression, the grazing intensity beyond a certain threshold may destabilize the system, resulting in Hopf bifurcations. Moreover, inhomogeneous Hopf bifurcations do not occur under the nonlocal grazing. Furthermore, we obtain that the positive feedback effect with soil water diffusion affects the stability of positive equilibrium points and leads to the occurrence of Turing instability. Note that the range of the intensity of soil water diffusion that causes Turing instability becomes small for the nonlocal grazing system. Numerical simulations reveal that the nonlocal grazing is more conducive to the growth and survival of vegetation compared to the local grazing.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 689-703"},"PeriodicalIF":4.4,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00401-X","DOIUrl":"10.1016/S0378-4754(25)00401-X","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Page 1117"},"PeriodicalIF":4.4,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatial heterogeneity and diffusion-driven dynamics of HCV infection: A mathematical modeling framework","authors":"Feng Rao ,&nbsp;Dandan Xue ,&nbsp;Shufen Wei ,&nbsp;Rui Liu","doi":"10.1016/j.matcom.2025.09.028","DOIUrl":"10.1016/j.matcom.2025.09.028","url":null,"abstract":"<div><div>Hepatitis C virus (HCV) infection in the body includes not only virus-to-cell infection, but also cell-to-cell infection. This infection will stimulate the body to produce cytotoxic T lymphocyte (CTL) immune response and antibody immune response. In this paper, we study the disease dynamics of two kinds of infection and two kinds of immune models, which include spatial diffusion and heterogeneity of internal environment, and further explore the influence of spatial heterogeneity on the extinction and persistence of hepatitis C virus (HCV). We defined the basic reproduction number, deduced the corresponding expression of the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, and proved that the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> can be used as the threshold of whether the virus exists or not. That is, if the basic reproduction number <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the disease-free balance is globally stable and HCV is extinct; if the basic reproduction number <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, there is at least one local equilibrium, and HCV will persist. Furthermore, we performed numerical simulations to investigate how spatial diffusion and heterogeneity affect disease dynamics. Combining theoretical analysis with numerical simulations, our findings reveal that spatial heterogeneity can increase the risk of viral infection within the host. However, the mobility of infected cells and viruses may serve to diminish these risks.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 727-753"},"PeriodicalIF":4.4,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sliding dynamics and codimension-2 bifurcations of an epidemic Filippov system with nonlinear threshold control","authors":"Qian Li ,&nbsp;Yujia Zhang ,&nbsp;Biao Tang","doi":"10.1016/j.matcom.2025.09.024","DOIUrl":"10.1016/j.matcom.2025.09.024","url":null,"abstract":"<div><div>The implementation of preventive and control measures for major infectious diseases is often influenced by a multitude of factors, including the progression of infectious diseases, the current epidemic status, and the population size of various disease states. This paper introduces a threshold control strategy based on a non-smooth Filippov system, wherein the weighted sum of the susceptible population size and its change rate determines whether to enforce vaccination and isolation measures. We investigate the impact of this strategy on the dynamics of infectious disease transmission and analyze the effects of intermittent vaccination and isolation strategies with nonlinear recovery and threshold control functions. Based on the dynamics of subsystems, we analyze the sliding mode and the properties of the sliding regions, as well as the existence of the pseudo-equilibria. Additionally, we analyze the codimension-1 boundary equilibrium bifurcations of the proposed system, including boundary node bifurcation, boundary stable/unstable focus bifurcation, and boundary unstable-stable focus bifurcation. Leveraging the rich codimension-1 boundary equilibrium bifurcations, we explore two types of codimension-2 bifurcations and numerically illustrate the homoclinic boundary focus bifurcation and boundary Hopf bifurcation. Through an in-depth examination of boundary equilibrium bifurcations, we discover that the proposed system displays complex dynamical behaviors under different parameter values, including the emergence of new limit cycles, saddle–node bifurcations and grazing bifurcations of limit cycles. The main results indicate that under a specific control strategy, there exists a threshold value for the weighted sum of the size and change rate of the susceptible population that can effectively control the spread of infectious diseases. Moreover, whether the infected population remains low is contingent on the system’s initial state. Consequently, tailored and comprehensive control strategies must be devised to address the distinct characteristics of different population groups.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 704-726"},"PeriodicalIF":4.4,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical analysis of linearly implicit Milstein method for stochastic SEIR models with nonlinear incidence rates","authors":"Huizi Yang ,&nbsp;Zhanwen Yang ,&nbsp;Aoyun Ming","doi":"10.1016/j.matcom.2025.09.015","DOIUrl":"10.1016/j.matcom.2025.09.015","url":null,"abstract":"<div><div>In this paper, we focus on the numerical analysis of stochastic SEIR models with nonlinear incidence rates. By reformulating the stochastic basic reproduction number <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>S</mi></mrow></msubsup></math></span>, it is shown that the disease extinction of deterministic models is preserved under stochastic noises. On the other hand, the total population of stochastic SEIR models is varying and even unbounded when there are some noises in the natural death rate. Therefore, as the fundamental approach, we have to present the boundedness in the 4th moment and Hölder continuity of the exact solutions for the numerical convergence analysis. Numerically, a linearly implicit Milstein method is employed to ensure the numerical positivity under the condition of <span><math><mrow><mi>h</mi><mo>&lt;</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> and hence the numerical boundedness is obtained in the 4th moment. After the strong convergence analysis under the fundamental theory, we are much more interested in the numerical dynamic behaviors. Since the previous technique, the exponent representation of the stability function, is not available for the higher dimensional models, a logarithmic martingale estimation to the numerical disease is introduced in this paper, and hence the numerical replications of the long-time dynamic behaviors are discussed thoroughly. Finally, some numerical experiments are provided to verify the theoretical analysis and illustrate the convergence analysis of the numerical steady distribution in the future.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 659-675"},"PeriodicalIF":4.4,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}