European Journal of Applied Mathematics最新文献_第4页

Recurrent and chaotic outbreaks in SIR model SIR 模型中的反复和混乱爆发

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-01-18 DOI: 10.1017/s0956792523000360

Chunyi Gai, Theodore Kolokolnikov, Jan Schrader, Vedant Sharma

We examine several extensions to the basic Susceptible-Infected-Recovered model, which are able to induce recurrent outbreaks (the basic Susceptible-Infected-Recovered model by itself does not exhibit recurrent outbreaks). We first analyse how slow seasonal variations can destabilise the endemic equilibrium, leading to recurrent outbreaks. In the limit of slow immunity loss, we derive asymptotic thresholds that characterise this transition. In the outbreak regime, we use asymptotic matching to obtain a two-dimensional discrete map which describes outbreak times and strength. We then analyse the resulting map using linear stability and numerics. As the frequency of forcing is increased, the map exhibits a period-doubling route to chaos which alternates with periodic outbreaks of increasing frequency. Other extensions that can lead to recurrent outbreaks include the addition of noise, state-dependent variation and fine-graining of model classes.

我们研究了基本的易感-感染-恢复模型的几个扩展模型，这些模型能够诱发反复爆发（基本的易感-感染-恢复模型本身并不表现出反复爆发）。我们首先分析了缓慢的季节性变化如何破坏地方性平衡，从而导致疾病的反复爆发。在缓慢丧失免疫力的情况下，我们推导出描述这种转变的渐近阈值。在疫情爆发机制中，我们利用渐近匹配法获得了描述疫情爆发时间和强度的二维离散图。然后，我们利用线性稳定性和数值分析法对得到的图谱进行分析。随着强迫频率的增加，该图呈现出周期加倍的混乱路线，与频率增加的周期性爆发交替出现。可导致周期性爆发的其他扩展包括添加噪声、状态依赖性变化和模型类别的精细划分。

引用次数: 0

Absolute concentration robustness and multistationarity in reaction networks: Conditions for coexistence 反应网络中的绝对浓度稳健性和多稳定性：共存的条件

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2024-01-02 DOI: 10.1017/s0956792523000335

Nidhi Kaihnsa, Tung Nguyen, Anne Shiu

Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state, while some networks exhibit absolute concentration robustness (ACR), which means that some species concentration is the same at all steady states. Both multistationarity and ACR are significant in biological settings, but only recently has attention focused on the possibility for these properties to coexist. Our main result states that such coexistence in at-most-bimolecular networks (which encompass most networks arising in biology) requires at least three species, five complexes and three reactions. We prove additional bounds on the number of reactions for general networks based on the number of linear conservation laws. Finally, we prove that, outside of a few exceptional cases, ACR is equivalent to non-multistationarity for bimolecular networks that are small (more precisely, one-dimensional or up to two species). Our proofs involve analyses of systems of sparse polynomials, and we also use classical results from chemical reaction network theory.

应用中出现的许多反应网络都是多稳态的，也就是说，它们有能力出现不止一种稳态，而有些网络则表现出绝对浓度稳健性（ACR），这意味着某些物种的浓度在所有稳态下都是相同的。多稳态和绝对浓度鲁棒性在生物环境中都很重要，但直到最近，人们才开始关注这两种特性共存的可能性。我们的主要结果表明，在最多双分子网络（包括生物学中出现的大多数网络）中，这种共存需要至少三个物种、五个复合物和三个反应。我们还根据线性守恒定律的数量证明了一般网络中反应数量的额外界限。最后，我们证明，除少数例外情况外，对于小型（更准确地说，一维或最多两个物种）双分子网络来说，ACR 等同于非多重性。我们的证明涉及稀疏多项式系统的分析，我们还使用了化学反应网络理论的经典结果。

引用次数: 0

Variational inequalities arising from credit rating migration with buffer zone 有缓冲区的信用评级迁移所产生的变量不等式

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-12-14 DOI: 10.1017/s095679252300030x

Xinfu Chen, Jin Liang

In Chen and Liang previous work, a model, together with its well-posedness, was established for credit rating migrations with different upgrade and downgrade thresholds (i.e. a buffer zone, also called dead band in engineering). When positive dividends are introduced, the model in Chen and Liang (SIAM Financ. Math. 12, 941–966, 2021) may not be well-posed. Here, in this paper, a new model is proposed to include the realistic nonzero dividend scenarios. The key feature of the new model is that partial differential equations in Chen and Liang (SIAM Financ. Math. 12, 941–966, 2021) are replaced by variational inequalities, thereby creating a new free boundary, besides the original upgrading and downgrading free boundaries. Well-posedness of the new model, together with a few financially meaningful properties, is established. In particular, it is shown that when time to debt paying deadline is long enough, the underlying dividend paying company is always in high grade rating, that is, only when time to debt paying deadline is within a certain range, there can be seen the phenomenon of credit rating migration.

在Chen和Liang之前的工作中，建立了一个具有不同升降阈值(即缓冲区，在工程上也称为死区)的信用评级迁移模型，并给出了模型的适定性。当引入正股利时，SIAM finance的Chen和Liang的模型。数学。12,941-966,2021)可能不是适定的。在此，本文提出了一个新的模型，以包括现实的非零股息情景。新模型的主要特点是在陈亮(SIAM finance)的偏微分方程中。数学。12,941-966,2021)被变分不等式取代，从而创建了一个新的自由边界，除了原来的升级和降级的自由边界。建立了新模型的完备性，以及一些有经济意义的性质。特别表明，当到偿债期限的时间足够长时，基础派息公司始终处于高评级状态，即只有到偿债期限的时间在一定范围内，才会出现信用评级迁移的现象。

引用次数: 0

Analysis and numerical simulations of travelling waves due to plant–soil negative feedback 植物-土壤负反馈引起的行波分析与数值模拟

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-12-07 DOI: 10.1017/s0956792523000323

Annalisa Iuorio, Nicole Salvatori, Gerardo Toraldo, Francesco Giannino

In this work, we carry out an analytical and numerical investigation of travelling waves representing arced vegetation patterns on sloped terrains. These patterns are reported to appear also in ecosystems which are not water deprived; therefore, we study the hypothesis that their appearance is due to plant–soil negative feedback, namely due to biomass-(auto)toxicity interactions. To this aim, we introduce a reaction-diffusion-advection model describing the dynamics of vegetation biomass and toxicity which includes the effect of sloped terrains on the spatial distribution of these variables. Our analytical investigation shows the absence of Turing patterns, whereas travelling waves (moving uphill in the slope direction) emerge. Investigating the corresponding dispersion relation, we provide an analytic expression for the asymptotic speed of the wave. Numerical simulations not only just confirm this analytical quantity but also reveal the impact of toxicity on the structure of the emerging travelling pattern. Our analysis represents a further step in understanding the mechanisms behind relevant plants‘ spatial distributions observed in real life. In particular, since vegetation patterns (both stationary and transient) are known to play a crucial role in determining the underlying ecosystems’ resilience, the framework presented here allows us to better understand the emergence of such structures to a larger variety of ecological scenarios and hence improve the relative strategies to ensure the ecosystems’ resilience.

在这项工作中，我们对代表坡地上弧形植被模式的行波进行了分析和数值研究。据报道，这些图案也出现在不缺水的生态系统中；因此，我们研究了它们的出现是由于植物-土壤负反馈，即生物量-（自）毒性相互作用造成的这一假设。为此，我们引入了一个描述植被生物量和毒性动态的反应-扩散-对流模型，其中包括倾斜地形对这些变量空间分布的影响。我们的分析研究表明，没有图灵模式，但出现了行波（沿斜坡方向上坡）。通过研究相应的频散关系，我们给出了波的渐近速度的解析表达式。数值模拟不仅证实了这一分析量，还揭示了毒性对新出现的游波模式结构的影响。我们的分析进一步加深了对现实生活中观察到的相关植物空间分布背后机制的理解。特别是，由于植被模式（包括静态和瞬态模式）在决定生态系统的恢复能力方面起着至关重要的作用，因此本文提出的框架使我们能够更好地理解这种结构在更多生态情景中的出现，从而改进相关策略，确保生态系统的恢复能力。

{"title":"Analysis and numerical simulations of travelling waves due to plant–soil negative feedback","authors":"Annalisa Iuorio, Nicole Salvatori, Gerardo Toraldo, Francesco Giannino","doi":"10.1017/s0956792523000323","DOIUrl":"https://doi.org/10.1017/s0956792523000323","url":null,"abstract":"In this work, we carry out an analytical and numerical investigation of travelling waves representing arced vegetation patterns on sloped terrains. These patterns are reported to appear also in ecosystems which are not water deprived; therefore, we study the hypothesis that their appearance is due to plant–soil negative feedback, namely due to biomass-(auto)toxicity interactions. To this aim, we introduce a reaction-diffusion-advection model describing the dynamics of vegetation biomass and toxicity which includes the effect of sloped terrains on the spatial distribution of these variables. Our analytical investigation shows the absence of Turing patterns, whereas travelling waves (moving uphill in the slope direction) emerge. Investigating the corresponding dispersion relation, we provide an analytic expression for the asymptotic speed of the wave. Numerical simulations not only just confirm this analytical quantity but also reveal the impact of toxicity on the structure of the emerging travelling pattern. Our analysis represents a further step in understanding the mechanisms behind relevant plants‘ spatial distributions observed in real life. In particular, since vegetation patterns (both stationary and transient) are known to play a crucial role in determining the underlying ecosystems’ resilience, the framework presented here allows us to better understand the emergence of such structures to a larger variety of ecological scenarios and hence improve the relative strategies to ensure the ecosystems’ resilience.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579176","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

Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal 具有非局部扩散的槲寄生与鸟类共生模式的繁殖动力学

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-12-04 DOI: 10.1017/s0956792523000311

Juan He, Guo-Bao Zhang, Ting Liu

This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed

$c^*$

, the existence of travelling wavefronts with the wave speed

$cge c^*$

and the nonexistence of travelling wavefronts with

$clt c^*$

. It turns out that the spreading speed coincides with the minimal wave speed of travelling wavefronts. Moreover, some lower and upper bound estimates of the spreading speed

$c^*$

are provided.

本文研究了具有非局部扩散的槲寄生与鸟类共生模式的繁殖动力学。利用单调半流的传播波和行波的渐近速度理论，证明了其渐近传播速度$c^*$的存在性，波速$c c^*$的行波前的存在性和行波前$clt c^*$的不存在性。结果表明，传播速度与行波前的最小波速一致。此外，给出了扩展速度$c^*$的下界和上界估计。

{"title":"Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal","authors":"Juan He, Guo-Bao Zhang, Ting Liu","doi":"10.1017/s0956792523000311","DOIUrl":"https://doi.org/10.1017/s0956792523000311","url":null,"abstract":"This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed $c^*$ , the existence of travelling wavefronts with the wave speed $cge c^*$ and the nonexistence of travelling wavefronts with $clt c^*$ . It turns out that the spreading speed coincides with the minimal wave speed of travelling wavefronts. Moreover, some lower and upper bound estimates of the spreading speed $c^*$ are provided.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"35 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539695","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

Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal 具有非局部扩散的槲寄生与鸟类共生模式的繁殖动力学

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-12-04 DOI: 10.1017/s0956792523000311

Juan He, Guo-Bao Zhang, Ting Liu

This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed

$c^*$

, the existence of travelling wavefronts with the wave speed

$cge c^*$

and the nonexistence of travelling wavefronts with

$clt c^*$

. It turns out that the spreading speed coincides with the minimal wave speed of travelling wavefronts. Moreover, some lower and upper bound estimates of the spreading speed

$c^*$

are provided.

本文研究了具有非局部扩散的槲寄生与鸟类共生模式的繁殖动力学。利用单调半流的传播波和行波的渐近速度理论，证明了其渐近传播速度$c^*$的存在性，波速$c c^*$的行波前的存在性和行波前$clt c^*$的不存在性。结果表明，传播速度与行波前的最小波速一致。此外，给出了扩展速度$c^*$的下界和上界估计。

{"title":"Propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal","authors":"Juan He, Guo-Bao Zhang, Ting Liu","doi":"10.1017/s0956792523000311","DOIUrl":"https://doi.org/10.1017/s0956792523000311","url":null,"abstract":"This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed $c^*$ , the existence of travelling wavefronts with the wave speed $cge c^*$ and the nonexistence of travelling wavefronts with $clt c^*$ . It turns out that the spreading speed coincides with the minimal wave speed of travelling wavefronts. Moreover, some lower and upper bound estimates of the spreading speed $c^*$ are provided.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"35 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539699","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

Leveraging memory effects and gradient information in consensus-based optimisation: On global convergence in mean-field law 在基于共识的优化中利用记忆效应和梯度信息:关于平均场律的全局收敛

4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-10-20 DOI: 10.1017/s0956792523000293

Konstantin Riedl

Abstract In this paper, we study consensus-based optimisation (CBO), a versatile, flexible and customisable optimisation method suitable for performing nonconvex and nonsmooth global optimisations in high dimensions. CBO is a multi-particle metaheuristic, which is effective in various applications and at the same time amenable to theoretical analysis thanks to its minimalistic design. The underlying dynamics, however, is flexible enough to incorporate different mechanisms widely used in evolutionary computation and machine learning, as we show by analysing a variant of CBO which makes use of memory effects and gradient information. We rigorously prove that this dynamics converges to a global minimiser of the objective function in mean-field law for a vast class of functions under minimal assumptions on the initialisation of the method. The proof in particular reveals how to leverage further, in some applications advantageous, forces in the dynamics without loosing provable global convergence. To demonstrate the benefit of the herein investigated memory effects and gradient information in certain applications, we present numerical evidence for the superiority of this CBO variant in applications such as machine learning and compressed sensing, which en passant widen the scope of applications of CBO.

摘要本文研究了基于共识的优化方法(consensus-based optimization, CBO)，这是一种通用的、灵活的、可定制的优化方法，适用于高维的非凸和非光滑全局优化。CBO是一种多粒子元启发式算法，由于其简约的设计，它在各种应用中都是有效的，同时也适合于理论分析。然而，潜在的动力学足够灵活，可以纳入进化计算和机器学习中广泛使用的不同机制，正如我们通过分析利用记忆效应和梯度信息的CBO变体所展示的那样。在方法初始化的最小假设条件下，我们严格地证明了该动力学收敛于目标函数在平均场律下的全局极小值。该证明特别揭示了如何在不失去可证明的全局收敛性的情况下，在某些应用程序中进一步利用有利的动态力量。为了证明本文研究的记忆效应和梯度信息在某些应用中的优势，我们提供了数值证据，证明该CBO变体在机器学习和压缩感知等应用中的优越性，从而扩大了CBO的应用范围。

{"title":"Leveraging memory effects and gradient information in consensus-based optimisation: On global convergence in mean-field law","authors":"Konstantin Riedl","doi":"10.1017/s0956792523000293","DOIUrl":"https://doi.org/10.1017/s0956792523000293","url":null,"abstract":"Abstract In this paper, we study consensus-based optimisation (CBO), a versatile, flexible and customisable optimisation method suitable for performing nonconvex and nonsmooth global optimisations in high dimensions. CBO is a multi-particle metaheuristic, which is effective in various applications and at the same time amenable to theoretical analysis thanks to its minimalistic design. The underlying dynamics, however, is flexible enough to incorporate different mechanisms widely used in evolutionary computation and machine learning, as we show by analysing a variant of CBO which makes use of memory effects and gradient information. We rigorously prove that this dynamics converges to a global minimiser of the objective function in mean-field law for a vast class of functions under minimal assumptions on the initialisation of the method. The proof in particular reveals how to leverage further, in some applications advantageous, forces in the dynamics without loosing provable global convergence. To demonstrate the benefit of the herein investigated memory effects and gradient information in certain applications, we present numerical evidence for the superiority of this CBO variant in applications such as machine learning and compressed sensing, which en passant widen the scope of applications of CBO.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617449","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

Effects of concurrency on epidemic spreading in Markovian temporal networks 马尔可夫时间网络中并发性对流行病传播的影响

4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-10-18 DOI: 10.1017/s095679252300027x

Ruodan Liu, Masaki Ogura, Elohim Fonseca Dos Reis, Naoki Masuda

Abstract The concurrency of edges, quantified by the number of edges that share a common node at a given time point, may be an important determinant of epidemic processes in temporal networks. We propose theoretically tractable Markovian temporal network models in which each edge flips between the active and inactive states in continuous time. The different models have different amounts of concurrency while we can tune the models to share the same statistics of edge activation and deactivation (and hence the fraction of time for which each edge is active) and the structure of the aggregate (i.e., static) network. We analytically calculate the amount of concurrency of edges sharing a node for each model. We then numerically study effects of concurrency on epidemic spreading in the stochastic susceptible-infectious-susceptible and susceptible-infectious-recovered dynamics on the proposed temporal network models. We find that the concurrency enhances epidemic spreading near the epidemic threshold, while this effect is small in many cases. Furthermore, when the infection rate is substantially larger than the epidemic threshold, the concurrency suppresses epidemic spreading in a majority of cases. In sum, our numerical simulations suggest that the impact of concurrency on enhancing epidemic spreading within our model is consistently present near the epidemic threshold but modest. The proposed temporal network models are expected to be useful for investigating effects of concurrency on various collective dynamics on networks including both infectious and other dynamics.

在给定时间点上共享一个公共节点的边的数量可以量化边的并发性，这可能是时间网络中流行过程的重要决定因素。我们提出了理论上可处理的马尔可夫时间网络模型，其中每条边在连续时间内在活动状态和非活动状态之间翻转。不同的模型具有不同的并发量，而我们可以调整模型以共享相同的边缘激活和停用统计数据(因此每个边缘处于活动状态的时间比例)和聚合(即静态)网络的结构。我们分析地计算每个模型共享一个节点的边的并发量。然后，我们在提出的时间网络模型上数值研究了在随机易感-感染-易感和易感-感染-恢复动力学中并发性对流行病传播的影响。我们发现并发性增强了流行病在流行阈值附近的传播，但在许多情况下这种影响很小。此外，当感染率大大大于流行阈值时，并发性在大多数情况下抑制了流行病的传播。总之，我们的数值模拟表明，在我们的模型中，并发性对增强流行病传播的影响一直存在于流行病阈值附近，但幅度不大。所提出的时间网络模型有望用于研究并发性对网络中各种集体动态的影响，包括感染动态和其他动态。

{"title":"Effects of concurrency on epidemic spreading in Markovian temporal networks","authors":"Ruodan Liu, Masaki Ogura, Elohim Fonseca Dos Reis, Naoki Masuda","doi":"10.1017/s095679252300027x","DOIUrl":"https://doi.org/10.1017/s095679252300027x","url":null,"abstract":"Abstract The concurrency of edges, quantified by the number of edges that share a common node at a given time point, may be an important determinant of epidemic processes in temporal networks. We propose theoretically tractable Markovian temporal network models in which each edge flips between the active and inactive states in continuous time. The different models have different amounts of concurrency while we can tune the models to share the same statistics of edge activation and deactivation (and hence the fraction of time for which each edge is active) and the structure of the aggregate (i.e., static) network. We analytically calculate the amount of concurrency of edges sharing a node for each model. We then numerically study effects of concurrency on epidemic spreading in the stochastic susceptible-infectious-susceptible and susceptible-infectious-recovered dynamics on the proposed temporal network models. We find that the concurrency enhances epidemic spreading near the epidemic threshold, while this effect is small in many cases. Furthermore, when the infection rate is substantially larger than the epidemic threshold, the concurrency suppresses epidemic spreading in a majority of cases. In sum, our numerical simulations suggest that the impact of concurrency on enhancing epidemic spreading within our model is consistently present near the epidemic threshold but modest. The proposed temporal network models are expected to be useful for investigating effects of concurrency on various collective dynamics on networks including both infectious and other dynamics.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135885139","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

Sharp asymptotic profile of the solution to a West Nile virus model with free boundary 具有自由边界的西尼罗病毒模型解的尖锐渐近轮廓

4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-10-13 DOI: 10.1017/s0956792523000281

Zhiguo Wang, Hua Nie, Yihong Du

Abstract We consider the long-time behaviour of a West Nile virus (WNv) model consisting of a reaction–diffusion system with free boundaries. Such a model describes the spreading of WNv with the free boundary representing the expanding front of the infected region, which is a time-dependent interval $[g(t), h(t)]$ in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. J. Math. Biol. 75, 1381–1409, 2017). The asymptotic spreading speed of the front has been determined in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019) by making use of the associated semi-wave solution, namely $lim _{tto infty } h(t)/t=lim _{tto infty }[!-g(t)/t]=c_nu$ , with $c_nu$ the speed of the semi-wave solution. In this paper, by employing new techniques, we significantly improve the estimate in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019): we show that $h(t)-c_nu t$ and $g(t)+c_nu t$ converge to some constants as $tto infty$ , and the solution of the model converges to the semi-wave solution. The results also apply to a wide class of analogous Ross–MacDonold epidemic models.

我们考虑了西尼罗病毒(WNv)模型的长时间行为，该模型由具有自由边界的反应-扩散系统组成。该模型描述了西尼罗河病毒的传播，其自由边界代表了感染区域的扩展前沿，在Lin和Zhu模型(西尼罗河病毒在鸟类和蚊子中自由边界的空间传播模型和动力学)中，这是一个时间依赖区间$[g(t), h(t)]$。J.数学。生物学报，75,1381-1409,2017)。在Wang等人的研究中，已经确定了锋面的渐近传播速度(具有自由边界的西尼罗河病毒模型的传播速度)。J.数学。生物学报。79,433-466,2019)，利用相关的半波溶液，即$lim _{tto infty } h(t)/t=lim _{tto infty }[!-g(t)/t]=c_nu$，以$c_nu$半波溶液的速度。本文采用新技术，显著提高了Wang等人对具有自由边界的西尼罗病毒模型的传播速度估计。J.数学。生物学报，79,433-466,2019):我们证明$h(t)-c_nu t$和$g(t)+c_nu t$收敛于一些常数$tto infty$，并且模型的解收敛于半波解。结果也适用于广泛的一类类似的罗斯-麦克唐纳流行病模型。

{"title":"Sharp asymptotic profile of the solution to a West Nile virus model with free boundary","authors":"Zhiguo Wang, Hua Nie, Yihong Du","doi":"10.1017/s0956792523000281","DOIUrl":"https://doi.org/10.1017/s0956792523000281","url":null,"abstract":"Abstract We consider the long-time behaviour of a West Nile virus (WNv) model consisting of a reaction–diffusion system with free boundaries. Such a model describes the spreading of WNv with the free boundary representing the expanding front of the infected region, which is a time-dependent interval $[g(t), h(t)]$ in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. J. Math. Biol. 75, 1381–1409, 2017). The asymptotic spreading speed of the front has been determined in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019) by making use of the associated semi-wave solution, namely $lim _{tto infty } h(t)/t=lim _{tto infty }[!-g(t)/t]=c_nu$ , with $c_nu$ the speed of the semi-wave solution. In this paper, by employing new techniques, we significantly improve the estimate in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019): we show that $h(t)-c_nu t$ and $g(t)+c_nu t$ converge to some constants as $tto infty$ , and the solution of the model converges to the semi-wave solution. The results also apply to a wide class of analogous Ross–MacDonold epidemic models.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853170","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

Generalised solution to a 2D parabolic-parabolic chemotaxis system for urban crime: Global existence and large-time behaviour 城市犯罪的二维抛物-抛物趋化系统的一般解:全局存在性和大时间行为

4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics

Pub Date : 2023-09-25 DOI: 10.1017/s0956792523000268

Bin Li, Li Xie

Abstract We consider a parabolic-parabolic chemotaxis system with singular chemotactic sensitivity and source functions, which is originally introduced by Short et al to model the spatio-temporal behaviour of urban criminal activities with the particular value of the chemotactic sensitivity parameter $chi =2$ . The available analytical findings for this urban crime model including $chi =2$ are restricted either to one-dimensional setting, or to initial data and source functions with appropriate smallness, or to initial data and source functions with some radial symmetry. In the present work, our first result asserts that for any $chi gt 0$ the initial-boundary value problem of this urban crime model possesses a global generalised solution in the two-dimensional setting, without imposing any small or radial conditions on initial data and source functions. Our second result presents the asymptotic behaviour of such solution, under some additional assumptions on source functions.

本文考虑一个具有奇异趋化敏感性和源函数的抛物-抛物趋化系统，该系统最初由Short等人引入，以趋化敏感性参数$chi =2$的特定值来模拟城市犯罪活动的时空行为。对于包含$chi =2$的城市犯罪模型，现有的分析结果要么局限于一维设置，要么局限于初始数据和具有适当小的源函数，要么局限于具有一定径向对称性的初始数据和源函数。在目前的工作中，我们的第一个结果断言，对于任何$chi gt0 $，该城市犯罪模型的初始边值问题在二维设置中具有全局广义解，而无需对初始数据和源函数施加任何小或径向条件。我们的第二个结果在一些附加的源函数假设下给出了这种解的渐近行为。

引用次数: 0