Mathematical Biosciences最新文献_第4页

Effects of nonlinear impulsive controls and seasonality on hantavirus infection 非线性脉冲控制和季节性对汉坦病毒感染的影响。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-02-01 DOI: 10.1016/j.mbs.2025.109378

Yuhang Li, Yanni Xiao

Hemorrhagic fever with renal syndrome (HFRS) caused by hantavirus is prevalent across China and causes a significant number of deaths every year. This study aims to examine the transmission dynamics of hantavirus and to suggest effective control measures. We extend a periodic model of HFRS infection including house/field mice, contaminated environments, and the human population by introducing nonlinear pulses used to describe impulsive interventions. In our model, the systemic period determined by natural factors may be inconsistent with the periods of control strategies for the two kinds of mice. We prove that the model is uniformly and ultimately bounded and discuss the existence and uniqueness of the disease-free periodic solution. We calculate the basic reproduction number for the house/field mouse subsystem denoted by

R_{01}

/

R_{02}

. We then examine the threshold dynamics and analyze the conditions for global asymptotic stability of the disease-free periodic solution. Additionally, we determine that the HFRS infection uniformly persists in the human population when

max {R_{01}, R_{02}} > 1

. Further, the existence of nontrivial periodic solutions for subsystems is examined via bifurcation theory. In particular, we observe complicated dynamics in the proposed model with multiple periods and nonlinear pulses. By fitting data on HFRS cases, we estimate the unknown parameters and predict the trend of HFRS infection in the human population. Numerical simulations show that enhancing the intensity and frequency of culling mice could curb the spread of hantavirus. Our findings suggest that improving the vaccination rate and decreasing the number of rodents, especially wild mice, are crucial in reducing HFRS infection.

由汉坦病毒引起的肾综合征出血热（HFRS）在中国流行，每年造成大量死亡。本研究旨在探讨汉坦病毒的传播动态，并提出有效的控制措施。通过引入用于描述脉冲干预的非线性脉冲，我们扩展了HFRS感染的周期模型，包括家鼠/田鼠、受污染的环境和人群。在我们的模型中，由自然因素决定的系统周期可能与两种小鼠的控制策略周期不一致。证明了模型是一致最终有界的，并讨论了无病周期解的存在唯一性。我们计算了家鼠/田鼠子系统的基本繁殖数，用R01/R02表示。然后，我们检查了阈值动力学，并分析了无病周期解的全局渐近稳定的条件。此外，我们确定HFRS感染在最大{R01，R02} bb01时在人群中均匀持续存在。进一步，利用分岔理论验证了子系统非平凡周期解的存在性。特别是在多周期非线性脉冲模型中，我们观察到复杂的动力学。通过对HFRS病例数据的拟合，估计未知参数，预测人群中HFRS感染趋势。数值模拟表明，提高扑杀小鼠的强度和频率可以抑制汉坦病毒的传播。我们的研究结果表明，提高疫苗接种率和减少啮齿动物，特别是野生小鼠的数量是减少HFRS感染的关键。

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引用次数: 0

Investigating seasonal disease emergence and extinction in stochastic epidemic models

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-02-01 DOI: 10.1016/j.mbs.2025.109383

Mahmudul Bari Hridoy, Linda J.S. Allen

Seasonal disease outbreaks are common in many infectious diseases such as seasonal influenza, Zika, dengue fever, Lyme disease, malaria, and cholera. Seasonal outbreaks are often due to weather patterns affecting pathogens or disease-carrying vectors or by social behavior. We investigate disease emergence and extinction in seasonal stochastic epidemic models. Specifically, we study disease emergence through seasonally varying parameters for transmission, recovery, and vector births and deaths in time-nonhomogeneous Markov chains for SIR, SEIR, and vector-host systems. A branching process approximation of the Markov chain is used to estimate the seasonal probabilities of disease extinction. Several disease outcome measures are used to compare the dynamics in seasonal and constant environments. Numerical investigations illustrate and confirm previous results derived from stochastic epidemic models. Seasonal environments often result in lower probabilities of disease emergence and smaller values of the basic reproduction number than in constant environments, and the time of peak emergence generally precedes the peak time of the seasonal driver. We identify some new results when both transmission and recovery vary seasonally. If the relative amplitude of the recovery exceeds that of transmission or if the periodicity is not synchronized in time, lower average probabilities of disease emergence occur in a constant environment than in a seasonal environment. We also investigate the timing of vector control. This investigation provides new methods and outcome measures to study seasonal infectious disease dynamics and offers new insights into the timing of prevention and control.

季节性疾病爆发在许多传染病中都很常见，如季节性流感、寨卡病毒、登革热、莱姆病、疟疾和霍乱。季节性疾病爆发通常是由于天气模式影响了病原体或携带疾病的病媒，或者是由于社会行为造成的。我们研究了季节性随机流行病模型中疾病的出现和消亡。具体来说，我们研究的是在时间非均质马尔可夫链中，通过季节性变化的传播、恢复、病媒出生和死亡参数，在 SIR、SEIR 和病媒-宿主系统中出现疾病。马尔可夫链的分支过程近似用于估计疾病灭绝的季节概率。使用几种疾病结果测量方法来比较季节性环境和恒定环境下的动态变化。数值研究说明并证实了之前从随机流行病模型中得出的结果。与恒定环境相比，季节性环境通常导致较低的疾病出现概率和较小的基本繁殖数值，而且疾病出现的高峰时间通常早于季节性驱动因素的高峰时间。当传播和恢复都随季节变化时，我们发现了一些新的结果。如果恢复的相对幅度超过传播的相对幅度，或者周期在时间上不同步，那么在恒定环境中出现疾病的平均概率要低于季节性环境。我们还调查了病媒控制的时机。这项调查为研究季节性传染病的动态提供了新的方法和结果衡量标准，并为预防和控制的时机提供了新的见解。

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引用次数: 0

Competing mechanisms for the buckling of an epithelial monolayer identified using multicellular simulation 使用多细胞模拟鉴定上皮单层屈曲的竞争机制。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-02-01 DOI: 10.1016/j.mbs.2024.109367

Phillip J. Brown , J. Edward F. Green , Benjamin J. Binder , James M. Osborne

A model using the rigid body multi-cellular framework (RBMCF) is implemented to investigate the mechanisms of buckling of an epithelial monolayer. Specifically, the deformation of a monolayer of epithelial cells which are attached to a basement membrane and the surrounding stromal tissue. The epithelial monolayer, supporting basement membrane and stromal tissue are modelled using two separate vertex dynamics models (one for the epithelial monolayer layer and one for the basement membrane and stromal tissue combined) and interactions between the two are considered using the RBMCF to ensure biologically realistic interactions. Model simulations are used to investigate the effects of cell–stromal attachment and membrane rigidity on buckling behaviour. We demonstrate that there are two competing modes of buckling, stromal deformation and stromal separation.

采用刚体多细胞框架（RBMCF）模型来研究上皮单层屈曲的机制。具体地说，是附着在基底膜和周围基质组织上的上皮细胞单层的变形。上皮单分子层、支持基底膜和基质组织使用两个单独的顶点动力学模型（一个用于上皮单分子层，另一个用于基底膜和基质组织组合）进行建模，并使用RBMCF考虑两者之间的相互作用，以确保生物学上真实的相互作用。模型模拟用于研究细胞间质附着和膜刚度对屈曲行为的影响。我们证明存在两种相互竞争的屈曲模式，即基质变形和基质分离。

引用次数: 0

A constrained optimisation framework for parameter identification of the SIRD model 用于确定 SIRD 模型参数的约束优化框架。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-02-01 DOI: 10.1016/j.mbs.2025.109379

Andrés Miniguano–Trujillo , John W. Pearson , Benjamin D. Goddard

We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are described by a system of ordinary differential equations associated with the epidemiological SIRD model. Applying an optimise-then-discretise approach, we examine properties of the solution operator and determine existence of optimal parameters for the problem considered. Further, first-order optimality conditions are derived, the solution of which provides a certificate of goodness of fit, which is not always guaranteed with parameter tuning techniques. We then propose strategies for the numerical solution of such problems, based on projected gradient descent, Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), nonmonotone Accelerated Proximal Gradient (nmAPG), and limited memory BFGS trust-region approaches. We carry out a thorough computational study for a range of problems of interest, determining the relative performance of these numerical methods. Our results provide insights into the effectiveness of these strategies, contributing to ongoing research into optimising parameters for accurate and reliable disease spread modelling. Moreover, our approach paves the way for calibration of more intricate compartmental models.

我们考虑一个数字框架，以确定在建模疾病传播的背景下的最佳参数。我们的重点是理解这类问题的优化算法的行为，其中动力学是由与流行病学SIRD模型相关的常微分方程系统描述的。应用先优化后离散的方法，我们检验了解算子的性质，并确定了所考虑问题的最优参数的存在性。进一步，导出了一阶最优性条件，其解提供了拟合优度的证明，而参数调整技术并不总是保证这一点。然后，我们提出了基于投影梯度下降、快速迭代收缩阈值算法（FISTA）、非单调加速近端梯度（nmAPG）和有限内存BFGS信任域方法的数值解决这些问题的策略。我们对一系列感兴趣的问题进行了彻底的计算研究，确定了这些数值方法的相对性能。我们的结果为这些策略的有效性提供了见解，有助于正在进行的优化参数的研究，以实现准确可靠的疾病传播建模。此外，我们的方法为更复杂的区室模型的校准铺平了道路。

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引用次数: 0

A numerical evaluation of the economic tradeoff of vaccination against chikungunya virus in Brazil 巴西基孔肯雅病毒疫苗接种经济权衡的数值评估。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-02-01 DOI: 10.1016/j.mbs.2025.109376

Vinicius V.L. Albani , Eduardo Massad

This article uses a compartmental model describing the dynamic of the chikungunya virus in populations of humans and mosquitoes with parameters fitted to the incidence in Brazil to estimate the economic trade-off of vaccination against the virus infection. The model uses time-dependent parameters to incorporate fluctuations in the transmission and the mosquito population across the years. Using the model predictions of symptomatic infections and literature data concerning the proportions of post-acute and chronic cases, the vaccination cost is compared with the disease cost. Numerical results considering different scenarios indicate that vaccination has a limited impact on reducing the disease cost assuming that vaccination is applied uniformly countrywide. We do not consider regional targets. In some scenarios, vaccinating about 10

%

of the population as early as possible can reduce the disease cost and is more economically efficient. Larger proportions make vaccination not viable.

本文使用一个隔间模型描述基孔肯雅病毒在人类和蚊子种群中的动态，其参数拟合巴西的发病率，以估计接种疫苗预防病毒感染的经济权衡。该模型使用与时间相关的参数，将传播和蚊子数量的波动纳入多年来的波动。利用有症状感染的模型预测和关于急性和慢性病例比例的文献数据，比较了疫苗接种成本与疾病成本。考虑不同情景的数值结果表明，在全国统一实施疫苗接种的情况下，疫苗接种对降低疾病成本的影响有限。我们不考虑区域目标。在某些情况下，尽早为大约10%的人口接种疫苗可以降低疾病成本，并更具经济效益。更大的比例使疫苗接种不可行。

引用次数: 0

A nonautonomous model for the impact of toxicants on size-structured aquatic populations: Well-posedness and long-term dynamics

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-02-01 DOI: 10.1016/j.mbs.2025.109382

Xiumei Deng , Qihua Huang , Hao Wang

Mathematical models have played a crucial role in understanding and assessing the impacts of toxicants on populations. However, many existing population-toxicant interaction models are physically unstructured and represented by autonomous systems, assuming all individuals are identical and model parameters are constant over time. In this paper, we develop a nonautonomous model describing the interaction between a size-structured population and an unstructured toxicant in a polluted aquatic ecosystem. This model allows us to investigate the influence of size- and time-dependent individual vital rates (growth, reproduction, and mortality), time-varying toxicant input and degradation, and size-specific sensitivity of individuals to toxicants on population persistence. We establish the existence and uniqueness of solutions for this model using the monotone method, based on a comparison principle. We then analyze how time- and size-dependent parameters affect the long-term population dynamics. Specifically, we derive conditions on these parameters that lead to either extinction or persistence of the population. We provide a comparative analysis of numerical solutions between our size-structured model and an unstructured model with size-averaged parameters, emphasizing the significance of incorporating size structure when evaluating the effects of toxicants on populations.

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引用次数: 0

A simple model for the analysis of epidemics based on hospitalization data

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-01-26 DOI: 10.1016/j.mbs.2025.109380

Katelyn Plaisier Leisman , Shinhae Park , Sarah Simpson , Zoi Rapti

An epidemiological model with a minimal number of parameters is introduced and its structural and practical identifiabity is investigated both analytically and numerically. The model is useful when a high percentage of unreported cases is suspected, hence only hospitalization data are used to fit the model parameters and calculate the basic reproductive number

R_{0}

and the effective reproductive number

R_{e}

. As a case study, the model is used to study the initial surge and the Omicron wave of the COVID-19 epidemic in Belgium. It was found that the reported cases largely underestimate the actual cases, and the estimated values of

R_{0}

are consistent with other studies. The exact number of people initially in each epidemiological class is also considered unknown and was estimated directly and not considered as additional parameters to be fitted. Furthermore, the parameter fitting was performed with two different available data sets, in order to improve confidence. The methodology presented here can be easily modified to study outbreaks of diseases for which little information on confirmed cases is known a priori or when the available information is largely unreliable.

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引用次数: 0

Fibrotic extracellular matrix preferentially induces a partial Epithelial–Mesenchymal Transition phenotype in a 3-D agent based model of fibrosis 在基于3-D药物的纤维化模型中，纤维化细胞外基质优先诱导部分上皮-间质转化表型。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-01-18 DOI: 10.1016/j.mbs.2025.109375

Kristin P. Kim, Christopher A. Lemmon

One of the main drivers of fibrotic diseases is epithelial–mesenchymal transition (EMT): a transdifferentiation process in which cells undergo a phenotypic change from an epithelial state to a pro-migratory state. The cytokine transforming growth factor-

β

1 (TGF-

β

1) has been previously shown to regulate EMT. TGF-

β

1 binds to fibronectin (FN) fibrils, which are the primary extracellular matrix (ECM) component in renal fibrosis. We have previously demonstrated experimentally that inhibition of FN fibrillogenesis and/or TGF-

β

1 tethering to FN inhibits EMT. However, these studies have only been conducted on 2-D cell monolayers, and the role of TGF-

β

1-FN tethering in 3-D cellular environments is not clear. As such, we sought to develop a 3-D computational model of epithelial spheroids that captured both EMT signaling dynamics and TGF-

β

1-FN tethering dynamics. We have incorporated the bi-stable EMT switch model developed by Tian et al. (2013) into a 3-D multicellular model to capture both temporal and spatial TGF-

β

1 signaling dynamics. We showed that the addition of increasing concentrations of exogeneous TGF-

β

1 led to faster EMT progression, indicated by increased expression of mesenchymal markers, decreased cell proliferation and increased migration. We then incorporated TGF-

β

1-FN fibril tethering by locally reducing the TGF-

β

1 diffusion coefficient as a function of EMT to simulate the reduced movement of TGF-

β

1 when tethered to FN fibrils during fibrosis. We showed that incorporation of TGF-

β

1 tethering to FN fibrils promoted a partial EMT state, independent of exogenous TGF-

β

1 concentration, indicating a mechanism by which fibrotic ECM can promote a partial EMT state.

纤维化疾病的主要驱动因素之一是上皮-间质转化（EMT）：细胞经历从上皮状态到亲迁移状态的表型变化的转分化过程。细胞因子转化生长因子-β1 （TGF-β1）先前已被证明可调节EMT。TGF-β1结合纤维连接蛋白（FN）原纤维，是肾纤维化的主要细胞外基质（ECM）成分。我们之前已经通过实验证明，抑制FN纤维形成和/或TGF-β1粘附在FN上可抑制EMT。然而，这些研究仅在二维细胞单层上进行，TGF-β1-FN系固在三维细胞环境中的作用尚不清楚。因此，我们试图开发上皮球体的三维计算模型，以捕获EMT信号动力学和TGF-β1-FN系固动力学。我们将Tian等人（2013）开发的双稳态EMT开关模型纳入到三维多细胞模型中，以捕获TGF-β1信号的时空动态。我们发现，增加外源TGF-β1浓度的加入导致EMT进展更快，表现为间充质标志物表达增加，细胞增殖减少，迁移增加。然后，我们通过局部降低TGF-β1扩散系数作为EMT的函数，将TGF-β1拴在FN原纤维上，模拟TGF-β1在纤维化过程中拴在FN原纤维上时减少的运动。我们发现TGF-β1与FN原纤维的结合促进了部分EMT状态，不依赖于外源性TGF-β1浓度，这表明纤维化ECM可以促进部分EMT状态的机制。

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引用次数: 0

Mechanical causes and implications of repetitive DNA motifs 重复 DNA 主题的机械原因和影响。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2025-01-01 DOI: 10.1016/j.mbs.2024.109343

Paul Torrillo , David Swigon

Experimental research suggests that local patterns in DNA sequences can result in stiffer or more curved structures, potentially impacting chromatin formation, transcription regulation, and other processes. However, the effect of sequence variation on DNA geometry and mechanics remains relatively underexplored. Using rigid base pair models to aid rapid computation, we investigated the sample space of 100 bp DNA sequences to identify mechanical extrema based on metrics such as static persistence length, global bend, or angular deviation. Our results show that repetitive DNA motifs are overrepresented in these extrema. We identified specific extremal motifs and demonstrated that their geometric and mechanical properties significantly differ from standard DNA through hierarchical clustering. We provide a mathematical argument supporting the presence of DNA repeats in extremizing sequences. Finally, we find that repetitive DNA motifs with extreme mechanical properties are prevalent in genetic databases and hypothesize that their unique mechanical properties could contribute to this abundance.

实验研究表明，DNA 序列的局部模式可导致结构更坚硬或更弯曲，从而对染色质形成、转录调控和其他过程产生潜在影响。然而，序列变异对 DNA 几何学和力学的影响仍然相对缺乏探索。利用刚性碱基对模型帮助快速计算，我们研究了 100 bp DNA 序列的样本空间，根据静态持续长度、全局弯曲度或角度偏差等指标确定力学极值。我们的研究结果表明，重复的 DNA 主题在这些极值中的比例过高。我们确定了特定的极值图案，并通过分层聚类证明它们的几何和机械特性与标准 DNA 有显著不同。我们提供了支持极端化序列中存在 DNA 重复的数学论据。最后，我们发现具有极端机械特性的重复 DNA 主题在基因数据库中非常普遍，并假设它们独特的机械特性可能是造成这种现象的原因。

引用次数: 0

A new method for the estimation of stochastic epidemic descriptors reinforced by Kalman-based dynamic parameter estimation. Application to mpox data 通过基于卡尔曼的动态参数估计加强随机流行病描述符估计的新方法。应用于 mpox 数据。

IF 1.9 4区数学 Q2 BIOLOGY

Mathematical Biosciences

Pub Date : 2024-12-11 DOI: 10.1016/j.mbs.2024.109365

Vasileios E. Papageorgiou , Georgios Vasiliadis , George Tsaklidis

In the realm of epidemiology, it is essential to accurately assess epidemic phenomena through the adoption of innovative techniques that yield reliable predictions. This article introduces an advanced method that merges the Extended Kalman Filter approach with recursive algorithms to compute critical stochastic attributes important for evaluating epidemics. A new three-dimensional discrete Markov chain is presented, according to which the total number of infections, deaths, and the duration of epidemic outbreaks are estimated. This approach represents a notable improvement over the standard estimation procedure, which relies on Markov-based stochastic models with fixed parameters. Furthermore, it constitutes a real-time estimation process, as opposed to the standard method, which is more suitable for offline applications. The proposed methodology marks an original attempt to integrate computational techniques for modeling stochastic epidemic characteristics with dynamic parameter estimation procedures. An additional advantage is the reduction of noise in the system's states enhancing the overall precision. The method's performance is thoroughly assessed through 3 simulated epidemic instances. Furthermore, its application to the actual 2022 monkeypox (mpox) data from the Czech Republic demonstrates promising effectiveness. In comparison to the standard methodology, our approach yields estimates with deviations of only 4.383 weeks, 3.542 infections, and 0.266 deaths, as opposed to the standard method where we observe deviations of 15.372 weeks, 5.786 infections, and 0.501 deaths. Overall, the proposed estimation procedure proves to be a valuable tool for investigating epidemic phenomena characterized by fluctuating dynamics, potentially providing valuable insights for addressing the associated public health challenges.

MSC

62M20, 60J22, 65C40, 62G30, 62P10

在流行病学领域，必须通过采用产生可靠预测的创新技术来准确评估流行病现象。本文介绍了一种将扩展卡尔曼滤波方法与递归算法相结合的高级方法，以计算对评估流行病重要的关键随机属性。提出了一种新的三维离散马尔可夫过程，根据该过程估计了感染总数、死亡人数和流行病爆发的持续时间。这种方法比标准估计过程有了显著的改进，标准估计过程依赖于具有固定参数的基于马尔可夫的随机模型。此外，与更适合离线应用程序的标准方法相反，它构成了一个实时评估过程。提出的方法标志着将随机流行病特征建模的计算技术与动态参数估计程序相结合的原始尝试。另一个优点是减少了系统状态中的噪声，提高了整体精度。通过3个模拟疫情实例，对该方法的性能进行了全面评价。此外，将其应用于捷克共和国2022年mpox的实际数据显示出良好的有效性。与标准方法相比，我们的方法得出的估计值偏差仅为4.383周，3.542例感染和0.266例死亡，而标准方法的偏差为15.372周，5.786例感染和0.501例死亡。总的来说，拟议的估计程序证明是调查以波动动态为特征的流行病现象的宝贵工具，可能为解决相关的公共卫生挑战提供宝贵的见解。Msc: 62m20, 60j22, 65c40, 62g30, 62p10。

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引用次数: 0