Mathematical Biosciences and Engineering最新文献_第2页

Hopf bifurcation and stability in a tumor-immune model with discrete and distributed delays. 具有离散和分布延迟的肿瘤免疫模型的Hopf分岔与稳定性。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-21 DOI: 10.3934/mbe.2026082

Rukiye Kara

引用次数: 0

Analysis of a mathematical model for fluid transport in poroelastic materials in 2D space. 二维孔隙弹性材料中流体运移的数学模型分析。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-21 DOI: 10.3934/mbe.2026083

Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka, Jacek Waniewski

{"title":"Analysis of a mathematical model for fluid transport in poroelastic materials in 2D space.","authors":"Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka, Jacek Waniewski","doi":"10.3934/mbe.2026083","DOIUrl":"https://doi.org/10.3934/mbe.2026083","url":null,"abstract":"Mathematical models that are based on the poroelastic theory are applied in biology, medicine, and biomedical engineering to describe a wide range of processes. In this work, a mathematical model for poroelastic materials (PEM) with variable volumes is developed in a multidimensional case. Governing equations of the model are constructed using continuity equations, which reflect the well-known physical laws. The deformation vector is specified using the Terzaghi effective stress tensor. In the two-dimensional space case, the model is studied by analytical methods. Using the classical Lie method, it is proven that the relevant nonlinear system of the $ (1+2) $-dimensional governing equations admits highly nontrivial Lie symmetries which lead to an infinite-dimensional Lie algebra. The radially-symmetric case is studied in details. It is shown how correct boundary conditions in the case of PEM in the form of a ring and an annulus are constructed. As a result, boundary-value problems with a moving boundary describing the ring (annulus) deformation are constructed. The relevant nonlinear boundary-value problems are analytically solved in the stationary case. In particular, the analytical formulae for unknown deformations and an unknown radius of the annulus are derived. Moreover, illustrative plots for parameters, which are typical for the tumor tissue deformation, are presented.","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 8","pages":"2287-2306"},"PeriodicalIF":2.6,"publicationDate":"2026-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148908031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A spatial SIS point pattern model with movement. 具有运动的空间SIS点模式模型。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-17 DOI: 10.3934/mbe.2026080

Eka Suci Pramana Sari, Nanang Susyanto, Fajar Adi-Kusumo, Atina Husnaqilati, Fugo Takasu

引用次数: 0

Using active subspaces to explore discrepancies between global and local parameter sensitivities in a Lotka-Volterra system. 利用有源子空间探讨Lotka-Volterra系统中全局和局部参数灵敏度之间的差异。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-16 DOI: 10.3934/mbe.2026079

Huiyan Zou, Allison L Lewis

{"title":"Using active subspaces to explore discrepancies between global and local parameter sensitivities in a Lotka-Volterra system.","authors":"Huiyan Zou, Allison L Lewis","doi":"10.3934/mbe.2026079","DOIUrl":"https://doi.org/10.3934/mbe.2026079","url":null,"abstract":"Global sensitivity metrics are essential tools for assessing parameter importance in complex models, particularly when precise information about parameter values is unavailable. In many cases, such metrics are used to provide parameter rankings that allow for necessary dimension reduction in moderate-to-high dimensional systems. However, globally derived sensitivity results may obscure localized variability in parameter sensitivities, resulting in misleading conclusions about parameter importance and ensuing consequences for subsequent tasks such as model calibration and surrogate model construction. In this study, we illustrated how discrepancies between globally and locally based sensitivity information may arise for an emerging sensitivity metric based on active subspace methodology, as well as for other commonly used sensitivity techniques. In response, we outlined a framework that exploits the active subspace to evaluate the stability of parameter sensitivities over the admissible parameter space. This analysis allows one to determine the subregions of the parameter space in which a globally derived sensitivity metric may be considered representative of local behavior. The proposed framework was illustrated on a collection of simple examples for ease of visualization, as well as a variation of the Lotka-Volterra model used to study interactions between competing tumor cell lines, for which we demonstrated how these issues may be exacerbated in higher dimensions. Our findings suggest that globally derived sensitivity information should be treated with caution, and that incorporating analysis on local subregions may improve robustness and accuracy in downstream modeling tasks.","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 7","pages":"2178-2207"},"PeriodicalIF":2.6,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mathematical analysis of a vector model using larvicides and Wolbachia-infected male mosquitoes: an optimal and impulsive control approach. 使用杀幼虫剂和感染沃尔巴克氏体的雄蚊的媒介模型的数学分析：一种最佳和脉冲控制方法。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-15 DOI: 10.3934/mbe.2026078

Wendpanga Birba, Boureima Sangaré, Abdoulaye Kaboré

{"title":"Mathematical analysis of a vector model using larvicides and Wolbachia-infected male mosquitoes: an optimal and impulsive control approach.","authors":"Wendpanga Birba, Boureima Sangaré, Abdoulaye Kaboré","doi":"10.3934/mbe.2026078","DOIUrl":"https://doi.org/10.3934/mbe.2026078","url":null,"abstract":"In this paper, we develop and analyze a mathematical model for mosquito population control, incorporating the release of Wolbachia-infected male mosquitoes and the application of larvicides. Two complementary approaches are considered: An optimal control model with continuous-time control functions, and an impulsive control model accounting for periodic releases of Wolbachia-infected male mosquitoes and larvicide. The main objective is to minimize the population of fertilized females, which are responsible for the transmission of vector-borne diseases, while reducing the associated biological, social, and economic costs. Using the Pontryagin maximum principle, we characterize the optimal controls and demonstrate the existence of admissible solutions. Within the framework of the impulsive model, the existence and stability conditions for periodic solutions are rigorously derived, allowing the identification of critical thresholds for the larvicide concentration and the minimum density of Wolbachia-infected mosquitoes required to achieve a significant reduction in the target population. Numerical simulations illustrate the enhanced effectiveness of the combined intervention strategy, demonstrating both faster response times and a greater impact on population suppression. These findings emphasize the necessity of a scientifically grounded, optimized, and integrated approach in the design and implementation of vector control programs.","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 7","pages":"2132-2177"},"PeriodicalIF":2.6,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An adaptive div-curl-grad least-squares finite element method for the Cahn-Hilliard equation. Cahn-Hilliard方程的自适应梯度最小二乘有限元法。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-13 DOI: 10.3934/mbe.2026077

Chad R Westphal

引用次数: 0

Learning contact policies for SEIR epidemics on networks: A mean-field game approach. 学习网络上SEIR流行病的接触策略：一种平均场博弈方法。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-13 DOI: 10.3934/mbe.2026076

Weinan Wang

{"title":"Learning contact policies for SEIR epidemics on networks: A mean-field game approach.","authors":"Weinan Wang","doi":"10.3934/mbe.2026076","DOIUrl":"https://doi.org/10.3934/mbe.2026076","url":null,"abstract":"In this paper, we develop a mean-field game model for SEIR epidemics on heterogeneous contact networks, where individuals choose state-dependent contact effort to balance infection losses against the social and economic costs of isolation. The Nash equilibrium is characterized by a coupled Hamilton-Jacobi-Bellman/Kolmogorov system across degree classes. An important feature of the SEIR setting is the exposed compartment: the incubation period separates infection from infectiousness and changes incentives after infection occurs. In the baseline formulation, exposed agents optimally maintain full contact, while susceptible agents reduce contact according to an explicit best-response rule driven by infection pressure and the value gap. We also discuss extensions that yield nontrivial exposed precaution by introducing responsibility or compliance incentives. We establish existence of equilibrium via a fixed-point argument and prove the uniqueness under a suitable monotonicity condition. The analysis identifies a delay in the onset of precaution under longer incubation, which can lead to weaker behavioral responses and larger outbreaks. Numerical experiments illustrate how network degree and the cost exponent shape equilibrium policies and epidemic outcomes.","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 7","pages":"2083-2109"},"PeriodicalIF":2.6,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling the relation between intraocular pressure and human trabecular meshwork fluid-mechanical properties. 眼内压与人体小梁网流体力学特性关系的建模。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-10 DOI: 10.3934/mbe.2026075

Riccardo Sacco, Greta Chiaravalli, Giovanna Guidoboni, Anita Layton, Gal Antman, Alice Verticchio, Brent Siesky, Thomas A Ciulla, Alon Harris

{"title":"Modeling the relation between intraocular pressure and human trabecular meshwork fluid-mechanical properties.","authors":"Riccardo Sacco, Greta Chiaravalli, Giovanna Guidoboni, Anita Layton, Gal Antman, Alice Verticchio, Brent Siesky, Thomas A Ciulla, Alon Harris","doi":"10.3934/mbe.2026075","DOIUrl":"https://doi.org/10.3934/mbe.2026075","url":null,"abstract":"Elevated introcular pressure (IOP) is a major risk factor for primary open angle glaucoma (POAG), the second leading cause of blindness worldwide. In this article, we investigate the relation between IOP increase and fluid-mechanical properties of the trabecular meshwork (TM), which is the main pathway of aqueous humor (AH) outflow in the human eye. TM is represented as an axisymmetric deformable biphasic porous medium (solid and fluid) with hydraulic permeability nonlinearly depending on the local AH pressure. Solving Darcy's law provides a TM hydraulic resistance (TMR) depending on the radial pressure drop, while TM stiffness is included multiplying the TMR by a shape function of TM Young's modulus constructed using postmortem measurements of human eye outflow facility. Simulations of AH flow based on an electric equivalent scheme of the eye indicate that TMR increases with TM stiffness, leading to a progressive increase of IOP until over the upper limit of the normal IOP range. The obtained results shed light on the impact of microscopic properties of the eye on its macroscopic function, and support the integration of experimental studies, mathematical modeling, and data analysis to develop an optimized patient-specific therapy to cure POAG.","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 7","pages":"2055-2082"},"PeriodicalIF":2.6,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Novel optimization techniques for inferring heterogeneous population dynamics. 推断异质种群动态的新型优化技术。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-09 DOI: 10.3934/mbe.2026074

Chenyu Wu, Nuozhou Wang, Casey Garner, Kevin Leder, Shuzhong Zhang

{"title":"Novel optimization techniques for inferring heterogeneous population dynamics.","authors":"Chenyu Wu, Nuozhou Wang, Casey Garner, Kevin Leder, Shuzhong Zhang","doi":"10.3934/mbe.2026074","DOIUrl":"https://doi.org/10.3934/mbe.2026074","url":null,"abstract":"In this paper, we introduce a new optimization algorithm that is well suited to solve parameter estimation problems that arise when inferring heterogeneous population dynamics. In these estimation problems, parameter estimation is complicated by the presence of two types of constraints: inequality constraints (e.g., non-negativity and boundedness of rates (so-called box-constraints)) and equality constraints that arise due to the need of the population fractions to sum to one. We call our new method cubic regularized Newton with affine scaling (CRNAS). In contrast to so-called first-order methods, which solely rely on the gradient of the objective function, our method utilizes the Hessian of the objective. As a result, it is able to focus on points that satisfy the second-order optimality conditions, as opposed to first-order methods that simply converge to critical points. This is an important feature in parameter estimation problems, where the objective function is often non-convex; as a result, there can be many critical points, which makes it nearly impossible to identify the global minimum. We use an affine scaling approach to handle a wide class of constraints, including equality constraints. We establish that CRNAS identifies a point that satisfies $ epsilon $-approximate second-order optimality conditions within $ O(epsilon^{-3/2}) $ iterations. Finally, we compare CRNAS with MATLAB's optimization solver fmincon on three different test problems. These test problems all feature mixtures of heterogeneous populations, a problem setting that CRNAS is particularly well-suited for. Our numerical simulations show that CRNAS has a favorable performance, thereby performing comparable, if not better than, fmincon in accuracy and computational cost for most of our examples.","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 7","pages":"2018-2054"},"PeriodicalIF":2.6,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling transmission intensity in SI epidemics via CIR and Jacobi processes: Asymptotic results and preliminary intervention strategies. 通过CIR和Jacobi过程模拟SI流行病的传播强度：渐近结果和初步干预策略。

IF 2.6 4区工程技术

Mathematical Biosciences and Engineering Pub Date : 2026-07-08 DOI: 10.3934/mbe.2026073

León A Valencia, Raúl Alejandro Morán-Vásquez, Duván H Cataño Salazar

{"title":"Modeling transmission intensity in SI epidemics via CIR and Jacobi processes: Asymptotic results and preliminary intervention strategies.","authors":"León A Valencia, Raúl Alejandro Morán-Vásquez, Duván H Cataño Salazar","doi":"10.3934/mbe.2026073","DOIUrl":"https://doi.org/10.3934/mbe.2026073","url":null,"abstract":"This paper studies an SI epidemic model with stochastic transmission rates of the form $ (beta_t = varphi(t)P_t:tgeq0) $, where $ varphi(t) $ is a deterministic modulation function and $ P_t $ is a positive stochastic process. We show that the asymptotic behavior of the epidemic is determined by the integrated intensity process $ (H_t = int_0^t beta_s, ds:tgeq0) $. We consider two stochastic models for $ (P_t:tgeq0) $: the bounded Jacobi process and the Cox-Ingersoll-Ross (CIR) process. Both preserve positivity, but differ in the support of their sample paths. In the non-modulated regime $ (varphiequiv1) $, the CIR framework allows explicit expressions for Laplace transforms and probabilistic bounds associated with the integrated intensity process. Additionally, we present numerical simulations in two regimes: the non-modulated case $ (varphi(t) = 1) $ and the exponentially damped case $ (varphi(t) = e^{-alpha t}) $. The simulations show that the bounded and unbounded structures of the stochastic transmission processes produce different tail behaviors, particularly in high-volatility regimes.","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 7","pages":"1995-2017"},"PeriodicalIF":2.6,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0