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A Mathematical Model for Assessing How Obesity-Related Factors Aggravate Diabetes 评估肥胖相关因素如何加重糖尿病的数学模型
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-16 DOI: 10.1007/s10440-024-00652-3
Ani Jain, Parimita Roy
{"title":"A Mathematical Model for Assessing How Obesity-Related Factors Aggravate Diabetes","authors":"Ani Jain,&nbsp;Parimita Roy","doi":"10.1007/s10440-024-00652-3","DOIUrl":"10.1007/s10440-024-00652-3","url":null,"abstract":"<div><p>Obesity-related factors have been associated with beta cell dysfunction, potentially leading to Type 2 diabetes. To address this issue, we developed a comprehensive obesity-based diabetes model incorporating fat cells, glucose, insulin, and beta cells. We established the model’s global existence, non-negativity, and boundedness. Additionally, we introduced a delay to examine the effects of impaired insulin production resulting from beta-cell dysfunction. Bifurcation analyses were conducted for delay and non-delay models, exploring the model’s dynamic transitions through backward and forward Hopf bifurcations. Utilizing the maximal Pontryagin principle, we formulated and evaluated an optimal control problem to mitigate diabetic complications by reducing the prevalence of overweight individuals and halting disease progression. Comparative graphical outputs were generated to demonstrate the beneficial effects of glucose-regulating medication and regular exercise in managing diabetes.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140969497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boundedness and Finite-Time Blow-up in a Chemotaxis System with Flux Limitation and Logistic Source 具有流量限制和逻辑源的趋化系统中的有界性和有限时间爆炸
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-16 DOI: 10.1007/s10440-024-00653-2
Shohei Kohatsu
{"title":"Boundedness and Finite-Time Blow-up in a Chemotaxis System with Flux Limitation and Logistic Source","authors":"Shohei Kohatsu","doi":"10.1007/s10440-024-00653-2","DOIUrl":"10.1007/s10440-024-00653-2","url":null,"abstract":"<div><p>The chemotaxis system </p><div><div><span> $$begin{aligned} textstylebegin{cases} u_{t}=Delta u - chi nabla cdot (u|nabla v|^{p-2}nabla v) + lambda u - mu u^{kappa }, 0=Delta v + u - h(u,v) end{cases}displaystyle end{aligned}$$ </span></div><div>\u0000 (∗)\u0000 </div></div><p> is considered in a smoothly bounded domain <span>(Omega subset mathbb{R}^{n})</span> (<span>(n in mathbb{N})</span>), where <span>(chi &gt; 0)</span>, <span>(p &gt; 1)</span>, <span>(lambda ge 0)</span>, <span>(mu &gt; 0)</span>, <span>(kappa &gt; 1)</span>, and <span>(h = v)</span> or <span>(h = frac{1}{|Omega |} int _{Omega } u)</span>. It is firstly proved that if <span>(n = 1)</span> and <span>(p &gt; 1)</span> is arbitrary, or <span>(n ge 2)</span> and <span>(p in (1, frac{n}{n-1}))</span>, then for all continuous initial data a corresponding no-flux type initial-boundary value problem for <span>((ast ))</span> admits a globally defined and bounded weak solution. Secondly, it is shown that if <span>(n ge 2)</span>, <span>(Omega = B_{R}(0) subset mathbb{R}^{n})</span> is a ball with some <span>(R &gt; 0)</span>, <span>(p &gt; frac{n}{n-1})</span> and <span>(kappa &gt; 1)</span> is small enough, then one can find a nonnegative radially symmetric function <span>(u_{0})</span> and a weak solution of <span>((ast ))</span> with initial datum <span>(u_{0})</span> which blows up in finite time.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comprehensive Analysis of Deterministic and Stochastic Eco-Epidemic Models Incorporating Fear, Refuge, Supplementary Resources, and Selective Predation Effects 包含恐惧、避难所、补充资源和选择性捕食效应的确定性和随机性生态流行病模型的综合分析
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-14 DOI: 10.1007/s10440-024-00654-1
Sasanka Shekhar Maity, Pankaj Kumar Tiwari, Samares Pal
{"title":"Comprehensive Analysis of Deterministic and Stochastic Eco-Epidemic Models Incorporating Fear, Refuge, Supplementary Resources, and Selective Predation Effects","authors":"Sasanka Shekhar Maity,&nbsp;Pankaj Kumar Tiwari,&nbsp;Samares Pal","doi":"10.1007/s10440-024-00654-1","DOIUrl":"10.1007/s10440-024-00654-1","url":null,"abstract":"<div><p>In this investigation, we delve into the dynamics of an ecoepidemic model, considering the intertwined influences of fear, refuge-seeking behavior, and alternative food sources for predators with selective predation. We extend our model to incorporate the impact of fluctuating environmental noise on system dynamics. The deterministic model undergoes thorough scrutiny to ensure the positivity and boundedness of solutions, with equilibria derived and their stability properties meticulously examined. Furthermore, we explore the potential for Hopf bifurcation within the system dynamics. In the stochastic counterpart, we prioritize discussions on the existence of a globally positive solution. Through simulations, we unveil the stabilizing effect of the fear factor on susceptible prey reproduction, juxtaposed against the destabilizing roles of prey refuge behavior and disease prevalence intensity. Notably, when disease prevalence intensity is too low, the infection can be eradicated from the ecosystem. Our deterministic analysis reveals a complex interplay of factors: the system destabilizes initially but then stabilizes as the fear factor suppressing disease prevalence intensifies, or as predators exhibit a stronger preference for infected prey over susceptible ones, or as predators are provided with more alternative food sources. Moreover, for the stochastic system, the oscillations tend to cluster around the coexistence equilibrium of the corresponding deterministic model when white noise intensity is low. However, with increasing white noise intensity, oscillation amplitudes escalate. Critically, very high levels of white noise can lead to the eradication of infection from the ecosystem.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140979756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trend to Equilibrium for Run and Tumble Equations with Non-uniform Tumbling Kernels 具有非均匀翻滚内核的运行和翻滚方程的平衡趋势
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-14 DOI: 10.1007/s10440-024-00657-y
Josephine Evans, Havva Yoldaş
{"title":"Trend to Equilibrium for Run and Tumble Equations with Non-uniform Tumbling Kernels","authors":"Josephine Evans,&nbsp;Havva Yoldaş","doi":"10.1007/s10440-024-00657-y","DOIUrl":"10.1007/s10440-024-00657-y","url":null,"abstract":"<div><p>We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00657-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reduced Variance Random Batch Methods for Nonlocal PDEs 非局部 PDE 的减方差随机批处理方法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-09 DOI: 10.1007/s10440-024-00656-z
Lorenzo Pareschi, Mattia Zanella
{"title":"Reduced Variance Random Batch Methods for Nonlocal PDEs","authors":"Lorenzo Pareschi,&nbsp;Mattia Zanella","doi":"10.1007/s10440-024-00656-z","DOIUrl":"10.1007/s10440-024-00656-z","url":null,"abstract":"<div><p>Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random partitioning of the particle ensemble into smaller batches at each time step. The interaction of each particle within these batches is then evolved until the subsequent time step. This approach effectively decreases the computational cost by an order of magnitude while increasing the amount of fluctuations due to the random partitioning. In this work, we propose a variance reduction technique for RBM applied to nonlocal PDEs of Fokker-Planck type based on a control variate strategy. The core idea is to construct a surrogate model that can be computed on the full set of particles at a linear cost while maintaining enough correlations with the original particle dynamics. Examples from models of collective behavior in opinion spreading and swarming dynamics demonstrate the great potential of the present approach.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00656-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Alignment via Friction for Nonisothermal Multicomponent Fluid Systems 非等温多组分流体系统的摩擦对准
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-08 DOI: 10.1007/s10440-024-00655-0
Stefanos Georgiadis, Athanasios E. Tzavaras
{"title":"Alignment via Friction for Nonisothermal Multicomponent Fluid Systems","authors":"Stefanos Georgiadis,&nbsp;Athanasios E. Tzavaras","doi":"10.1007/s10440-024-00655-0","DOIUrl":"10.1007/s10440-024-00655-0","url":null,"abstract":"<div><p>The derivation of an approximate Class–I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class–II model is justified, by validating the Chapman–Enskog expansion performed from the Class–II model towards the Class–I model. The analysis proceeds by comparing two thermomechanical theories via relative entropy.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum Hamiltonian Learning for the Fermi-Hubbard Model 费米-哈伯德模型的量子哈密顿学习
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-30 DOI: 10.1007/s10440-024-00651-4
Hongkang Ni, Haoya Li, Lexing Ying
{"title":"Quantum Hamiltonian Learning for the Fermi-Hubbard Model","authors":"Hongkang Ni,&nbsp;Haoya Li,&nbsp;Lexing Ying","doi":"10.1007/s10440-024-00651-4","DOIUrl":"10.1007/s10440-024-00651-4","url":null,"abstract":"<div><p>This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve <span>(epsilon )</span>-accurate estimation for all parameters, only <span>(tilde{mathcal{O}}(epsilon ^{-1}))</span> total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition 带动力学边界条件的波方程的多项式能量衰减率
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-22 DOI: 10.1007/s10440-024-00650-5
K. Laoubi, D. Seba
{"title":"Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition","authors":"K. Laoubi,&nbsp;D. Seba","doi":"10.1007/s10440-024-00650-5","DOIUrl":"10.1007/s10440-024-00650-5","url":null,"abstract":"<div><p>This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family of eigenvalues of the corresponding operator, we prove that the rate of energy decay decreases in a polynomial way.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140677175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Indirect Boundary Controllability of Coupled Degenerate Wave Equations 耦合退化波方程的间接边界可控性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-12 DOI: 10.1007/s10440-024-00649-y
Alhabib Moumni, Jawad Salhi, Mouhcine Tilioua
{"title":"Indirect Boundary Controllability of Coupled Degenerate Wave Equations","authors":"Alhabib Moumni,&nbsp;Jawad Salhi,&nbsp;Mouhcine Tilioua","doi":"10.1007/s10440-024-00649-y","DOIUrl":"10.1007/s10440-024-00649-y","url":null,"abstract":"<div><p>In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00649-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Steady States of a Diffusive Population-Toxicant Model with Negative Toxicant-Taxis 具有负毒性-税收的扩散种群-毒素模型的稳定状态
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-12 DOI: 10.1007/s10440-024-00646-1
Jiawei Chu
{"title":"Steady States of a Diffusive Population-Toxicant Model with Negative Toxicant-Taxis","authors":"Jiawei Chu","doi":"10.1007/s10440-024-00646-1","DOIUrl":"10.1007/s10440-024-00646-1","url":null,"abstract":"<div><p>This paper is dedicated to studying the steady state problem of a population-toxicant model with negative toxicant-taxis, subject to homogeneous Neumann boundary conditions. The model captures the phenomenon in which the population migrates away from regions with high toxicant density towards areas with lower toxicant concentration. This paper establishes sufficient conditions for the non-existence and existence of non-constant positive steady state solutions. The results indicate that in the case of a small toxicant input rate, a strong toxicant-taxis mechanism promotes population persistence and engenders spatially heterogeneous coexistence (see, Theorem 2.3). Moreover, when the toxicant input rate is relatively high, the results unequivocally demonstrate that the combination of a strong toxicant-taxis mechanism and a high natural growth rate of the population fosters population persistence, which is also characterized by spatial heterogeneity (see, Theorem 2.4).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00646-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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