Mathematics and Computers in Simulation最新文献

{"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":"tost.II: A temporal operator-splitting template library in deal.II","authors":"Mohammad Mahdi Moayeri,&nbsp;Raymond J. Spiteri","doi":"10.1016/j.matcom.2025.09.005","DOIUrl":"10.1016/j.matcom.2025.09.005","url":null,"abstract":"<div><div>Operator splitting (OS) is a widely used numerical method for solving differential equations by decomposing a problem into simpler sub-problems. OS methods enable consideration of different processes in a problem as separate temporal operators. These temporal operators can be integrated by specialized sub-integrators, often leading to improved computational feasibility or efficiency compared to classical monolithic approaches that treat all the processes as a single operator. This paper describes <span>tost.II</span>, a temporal operator-splitting template library built upon the <span>deal.II</span> finite element library. The <span>tost.II</span> library provides a flexible framework for implementing OS methods in <span>deal.II</span>, including those with real and complex coefficients. We demonstrate the functionality and ease of use of <span>tost.II</span> through three comprehensive examples that illustrate high-order convergence, the tradeoff in efficiency between order and desired accuracy, and the tradeoff in efficiency between the use of real versus complex arithmetic. Furthermore, because <span>tost.II</span> allows users to define any number of operators in any order and with any sub-integrator at any stage of the integration, we perform some less typical experiments with more than two operators and the use of inexpensive explicit sub-integrators for unstable sub-integrations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 790-804"},"PeriodicalIF":4.4,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266121","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":"Dynamics analysis of a delayed HIV-1 model with general incidence rate and immune impairment","authors":"Zihao Hu,&nbsp;Junxian Yang,&nbsp;Lili Lv,&nbsp;Qiang Li,&nbsp;Dongmei Fan","doi":"10.1016/j.matcom.2025.09.021","DOIUrl":"10.1016/j.matcom.2025.09.021","url":null,"abstract":"<div><div>This paper explores the dynamics analysis of an HIV-1 model with a general incidence rate, saturated Cytotoxic T Lymphocyte (CTL) immune response and immune impairment. In the model, there are two time delays: intracellular delay <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, which represents the time required for cell infection, and immune response delay <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, which represents the time required for immune response to be activated. Firstly, based on the given initial condition, we obtain two key thresholds and three possible equilibria. Secondly, the conditions for the stability of equilibria are provided through constructing Lyapunov functions. When immune delay <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> is present, the steady state of immune-activated equilibrium is disrupted and leads to a Hopf bifurcation. Furthermore, the direction and stability of the Hopf bifurcation are determined. Finally, we choose the Beddington–DeAngelis infection rate as an example to establish a mathematical model and conduct numerical simulations, investigating the impact of saturated CTL immune response delay on viral infection and revealing the general patterns of dynamic behavior of the model. Furthermore, the impact of certain parameters on the thresholds of model is discussed.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 137-164"},"PeriodicalIF":4.4,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266134","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}

{"title":"Optimization-driven group decision making with XOR comparison matrices","authors":"Ya-Ru Chen ,&nbsp;Fang Liu ,&nbsp;Humberto Bustince ,&nbsp;Hao Huang ,&nbsp;Xian-Ci Zhong","doi":"10.1016/j.matcom.2025.09.027","DOIUrl":"10.1016/j.matcom.2025.09.027","url":null,"abstract":"<div><div>The “exclusive-or”(XOR) logic describes a situation where only one of multiple options can be chosen, which is used to give the XOR number for quantifying some uncertainty in pairwise comparisons. It is interesting to develop group decision making (GDM) model with XOR comparison matrices by investigating consistency of judgements and consensus of experts. First, the consistency/acceptable consistency of XOR comparison matrices is defined by considering the basic principle of XOR logic. A mathematical programming model is constructed to check the consistency/acceptable consistency of XOR comparison matrices. Second, for improving consistency of XOR comparison matrices, an optimization model is built to obtain a multiplicative preference relation with acceptable consistency from XOR comparison matrices. The model is further developed according to the idea of minimizing the number of adjusted variables. Third, a consensus index is established for reaching consensus in GDM, which is utilized to propose an iterative algorithm for improving the consensus level. An algorithm for GDM with XOR comparison matrices is developed, which yields an optimal solution under acceptable consistency and acceptable consensus. Finally, a case study with discussion comparison is reported to illustrate the applicability of the proposed model. The results help to construct an optimization-driven mechanism of reaching consensus in GDM under XOR environments.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 763-786"},"PeriodicalIF":4.4,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220259","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":"High-order numerical method for Caputo–Hadamard fractional reaction-diffusion equations using nonuniform temporal mesh","authors":"Siyuan Chen ,&nbsp;Hengfei Ding","doi":"10.1016/j.matcom.2025.09.022","DOIUrl":"10.1016/j.matcom.2025.09.022","url":null,"abstract":"<div><div>This paper presents a high-order numerical scheme for solving the Caputo–Hadamard time-fractional reaction–diffusion equation. To address the inherent initial singularity of the solution, the method employs the L1 approximation formula on a specially designed nonuniform temporal mesh. This mesh is defined by the points <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>=</mo><mi>a</mi><mo>+</mo><mfrac><mrow><mi>k</mi><mrow><mo>(</mo><mn>4</mn><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>3</mn></mrow></mfrac><mi>β</mi></mrow></math></span>, where <span><math><mrow><mi>β</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mrow><mo>(</mo><mi>T</mi><mo>−</mo><mi>a</mi><mo>)</mo></mrow></mrow><mrow><mi>N</mi><mrow><mo>(</mo><mn>2</mn><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mi>N</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></mfrac></mrow></math></span>, whose graded structure effectively captures the singular behavior near the initial time <span><math><mrow><mi>t</mi><mo>=</mo><mi>a</mi></mrow></math></span>. For spatial discretization, a fourth-order compact difference formula is applied on a uniform grid to ensure high accuracy. Rigorous theoretical analysis demonstrates that the proposed scheme is unconditionally stable and achieves the optimal convergence rate of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>α</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>N</mi></math></span> and <span><math><mi>h</mi></math></span> represent the temporal and spatial discretization parameters, respectively. Systematic numerical experiments comprehensively validate the theoretical findings, clearly confirming the predicted convergence rates. Furthermore, experiments conducted across various fractional derivative orders and parameter configurations consistently demonstrate the effectiveness and robustness of the proposed method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 634-658"},"PeriodicalIF":4.4,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220255","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":"Novel pattern dynamics in a vegetation-water reaction–diffusion model","authors":"Hao Lu Zhang ,&nbsp;Yu Lan Wang ,&nbsp;Jun Xi Bi ,&nbsp;Shu Hong Bao","doi":"10.1016/j.matcom.2025.09.020","DOIUrl":"10.1016/j.matcom.2025.09.020","url":null,"abstract":"<div><div>This paper investigates the pattern dynamics of a four-variable vegetation-water reaction–diffusion model. By incorporating inhibitory factors and promoting factors, the model provides a more comprehensive framework for describing the interaction mechanisms between vegetation growth and environmental factors. Through linear stability analysis and Turing bifurcation theory, the amplitude equation near the Turing bifurcation point is derived. Furthermore, multi-scale analysis and weakly nonlinear analysis are employed to elucidate the pattern selection mechanism, revealing that diverse vegetation patterns emerge under different parameter conditions. For numerical simulations, a new high-precision Fourier spectral method is constructed to simulate the model with varying parameter conditions. The results validate the theoretical analysis and demonstrate the emergence of multiple novel pattern morphologies. Additionally, the study extends the classical model by introducing a fractional-order Laplacian operator, constructing a spatiotemporal fractional-order diffusion model to explore the effects of sub-diffusion and super-diffusion on vegetation pattern formation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 97-116"},"PeriodicalIF":4.4,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266066","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":"Fractional modeling of human liver dynamics using Hilfer fractional derivatives: A numerical and clinical validation study","authors":"Neetu Sharma,&nbsp;Ekta Mittal,&nbsp;Surendra Kumar Agarwal","doi":"10.1016/j.matcom.2025.09.017","DOIUrl":"10.1016/j.matcom.2025.09.017","url":null,"abstract":"<div><div>In this study, the Hilfer fractional derivative is incorporated into a fractional model describing the dynamics of the human liver. Using the Laplace homotopy analysis transform method, the suggested model is solved, and its convergence is carefully investigated. To give a more lucid depiction of the results, numerical simulations are also carried out. A comparison with actual clinical BSP test data shows that the proposed fractional model works better than the traditional integer-order model that is based on standard temporal derivatives.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"241 ","pages":"Pages 754-762"},"PeriodicalIF":4.4,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220258","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}