Journal of Theoretical Biology最新文献_第2页

From Bayes to Darwin: Evolutionary search as an exaptation from sampling-based Bayesian inference 从贝叶斯到达尔文：从基于抽样的贝叶斯推理的进化搜索。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-19 DOI: 10.1016/j.jtbi.2024.112032

Márton Csillag , Hamza Giaffar , Eörs Szathmáry , Mauro Santos , Dániel Czégel

Building on the algorithmic equivalence between finite population replicator dynamics and particle filtering based approximation of Bayesian inference, we design a computational model to demonstrate the emergence of Darwinian evolution over representational units when collectives of units are selected to infer statistics of high-dimensional combinatorial environments. The non-Darwinian starting point is two units undergoing a few cycles of noisy, selection-dependent information transmission, corresponding to a serial (one comparison per cycle), non-cumulative process without heredity. Selection for accurate Bayesian inference at the collective level induces an adaptive path to the emergence of Darwinian evolution within the collectives, capable of maintaining and iteratively improving upon complex combinatorial information. When collectives are themselves Darwinian, this mechanism amounts to a top-down (filial) transition in individuality. We suggest that such a selection mechanism can explain the hypothesized emergence of fast timescale Darwinian dynamics over a population of neural representations within animal and human brains, endowing them with combinatorial planning capabilities. Further possible physical implementations include prebiotic collectives of non-replicating molecules and reinforcement learning agents with parallel policy search.

基于有限种群复制因子动力学和基于贝叶斯推理的粒子滤波近似之间的算法等价，我们设计了一个计算模型，以证明当选择单位集体来推断高维组合环境的统计数据时，达尔文进化在代表性单位上的出现。非达尔文主义的起点是两个单位经历了几个有噪声的、依赖于选择的信息传递周期，对应于一个序列（每个周期一个比较），没有遗传的非累积过程。在集体水平上对精确贝叶斯推理的选择诱导了一条适应路径，从而在集体中出现达尔文进化，能够维持和迭代地改进复杂的组合信息。当集体主义本身是达尔文主义时，这种机制相当于个体自上而下（孝顺）的过渡。我们认为，这种选择机制可以解释动物和人类大脑中神经表征群体中快速时间尺度达尔文动力学的假设出现，赋予它们组合规划能力。进一步可能的物理实现包括非复制分子的益生元集体和具有并行策略搜索的强化学习代理。

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引用次数: 0

Bridging Wright–Fisher and Moran models 连接Wright-Fisher和Moran模型。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-19 DOI: 10.1016/j.jtbi.2024.112030

Arthur Alexandre , Alia Abbara , Cecilia Fruet , Claude Loverdo , Anne-Florence Bitbol

The Wright–Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model which bridges the Wright–Fisher and the Moran descriptions. We assume that a fixed fraction of the population is updated at each discrete time step. In this model, we determine the fixation probability of a mutant and its average fixation and extinction times, under the diffusion approximation. We further study the associated coalescent process, which converges to Kingman’s coalescent, and we calculate effective population sizes. We generalize our model, first by taking into account fluctuating updated fractions or individual lifetimes, and then by incorporating selection on the lifetime as well as on the reproductive fitness.

Wright-Fisher模型和Moran模型在群体遗传学中都有广泛的应用。他们描述了一个固定大小的混合良好的群体中等位基因频率的时间进化。我们提出了一个简单易行的模型，将Wright-Fisher和Moran的描述联系起来。我们假设在每个离散的时间步长，总体中有固定的一部分被更新。在该模型中，我们确定了在扩散近似下突变体的固定概率及其平均固定和消光时间。我们进一步研究了相关聚结过程，该过程收敛于Kingman聚结，并计算了有效种群大小。我们对模型进行了推广，首先考虑了波动的更新分数或个体寿命，然后结合了对寿命和生殖适合度的选择。

引用次数: 0

Beyond predation: Fish–coral interactions can tip the scales of coral disease 除了捕食：鱼与珊瑚的相互作用可以改变珊瑚疾病的规模。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-19 DOI: 10.1016/j.jtbi.2024.112031

Buddhadev Ranjit , Arnab Chattopadhyay , Arindam Mandal , Santosh Biswas , Joydev Chattopadhyay

Coral reefs are critical ecosystems, fostering biodiversity and sustaining the livelihoods of millions globally. Nonetheless, they confront escalating threats, with infectious diseases emerging as primary catalysts for extensive damage, surpassing the impacts of other human-induced stressors. Disease transmission via biotic factors, particularly during fish predation, is a crucial yet often overlooked pathway. While their feeding can spread infectious diseases through spores, it also controls the growth of macroalgae, a major competitor for space on the reef. Given this dual effect, the precise impact of fish on coral disease remains ambiguous and requires additional investigation. In this study, we addressed this gap for the first time by employing a mathematical model. Our analyses unveil intricate interactions between fish predation and coral health, revealing potential benefits and drawbacks for coral reef ecosystems. Coral survival hinges on a delicate balance of fish predation, with extremes (both low and high) offering some protection against disease outbreaks compared to moderate predation, which can cause sudden die-offs. More specifically, as fish predation intensifies, the ecosystem undergoes a tipping point, transitioning from a disease-dominated state to a healthier one. Moreover, the interplay between transmission rate and virulence in coral populations is significantly shaped by fish predation rates. Specifically, the threshold ratio of transmission to virulence, signalling a regime shift from a healthy to a disease-dominated state, exhibits a linear increase with fish predation rate. Overall, our findings emphasize the importance of considering biotic interactions in coral disease ecology and offer insights essential for effective reef conservation strategies.

珊瑚礁是至关重要的生态系统，促进生物多样性，维持全球数百万人的生计。然而，它们面临着不断升级的威胁，传染病成为造成广泛损害的主要催化剂，其影响超过了其他人为造成的压力源。通过生物因素传播疾病，特别是在鱼类捕食期间，是一个至关重要但往往被忽视的途径。虽然它们的进食可以通过孢子传播传染病，但它也控制了大型藻类的生长，而大型藻类是珊瑚礁空间的主要竞争对手。鉴于这种双重影响，鱼类对珊瑚疾病的确切影响仍然不明确，需要进一步的研究。在这项研究中，我们首次通过采用数学模型来解决这一差距。我们的分析揭示了鱼类捕食和珊瑚健康之间复杂的相互作用，揭示了珊瑚礁生态系统的潜在好处和缺点。珊瑚的生存取决于鱼类捕食的微妙平衡，与适度捕食相比，极端捕食（低和高）提供了一些防止疾病爆发的保护，而适度捕食会导致突然死亡。更具体地说，随着鱼类捕食的加剧，生态系统经历了一个临界点，从疾病主导的状态过渡到更健康的状态。此外，珊瑚种群中传播率和毒性之间的相互作用在很大程度上受鱼类捕食率的影响。具体来说，传播与毒力的阈值比率，标志着从健康状态到疾病主导状态的转变，与鱼类捕食率呈线性增长。总的来说，我们的研究结果强调了考虑珊瑚疾病生态学中生物相互作用的重要性，并为有效的珊瑚礁保护策略提供了必要的见解。

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引用次数: 0

Analysis of electrical activities in a functional neuron with dual memristors 双忆阻器功能神经元的电活动分析。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-18 DOI: 10.1016/j.jtbi.2024.112034

Xinlin Song , Feifei Yang

Neuron as a charged body, it is easily disturbed by the external electromagnetic field, which changes the electrical activities of the neurons. In fact, the interference of external electric or magnetic field is the process of energy injection of neurons, the injection of energy will redistribute the field energy inside the neurons, and the redistribution of energy will change the electrical activities of the neurons. Therefore, we design a neuron model with double memristors to explore the external electromagnetic field on the regulation of neural electrical activity. The dimensionless equations of the model with double memristors and its energy function are obtained based on the Kirchhoff’s and the Helmholtz’s theorems. The electrical activities of the neuron model under the external electromagnetic field distribution are researched by applying the nonlinear analysis methods, and the coherence resonance of the neuron is explored under the external noise electromagnetic field. The results indicate that the electrical activities of the model are controlled by the external electromagnetic field. This neuron model can be used to study the synchronization between magnetic field coupled or electric field coupled neurons.

神经元作为带电体，容易受到外界电磁场的干扰，从而改变神经元的电活动。实际上，外界电场或磁场的干扰是神经元能量注入的过程，能量的注入会将神经元内部的场能量重新分配，能量的重新分配会改变神经元的电活动。为此，我们设计了一种双忆阻器神经元模型，探索外加电磁场对神经电活动的调节作用。基于基尔霍夫定理和亥姆霍兹定理，得到了双忆阻器模型的无因次方程及其能量函数。应用非线性分析方法研究了外加电磁场分布下神经元模型的电活动，探讨了外加噪声电磁场下神经元的相干共振。结果表明，模型的电活动受外加电磁场的控制。该神经元模型可用于研究磁场耦合或电场耦合神经元之间的同步。

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引用次数: 0

Channel noise induced stochastic effect of Hodgkin–Huxley neurons in a real classification task 信道噪声诱导分类任务中霍奇金-赫胥黎神经元的随机效应。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-16 DOI: 10.1016/j.jtbi.2024.112028

Yasemin Erkan , Erdem Erkan

Noise is generally considered to have negative effects on information processing performance. However, it has also been proven that adding random noise or a certain level of stochastic (random) variability to a nonlinear system can increase its performance or sensitivity to weak signals. Despite the studies on this concept, called stochastic resonance in computational neuroscience, this phenomenon is still among the topics that need detailed research, especially in machine learning. In this study, the effect of noise arising from the intrinsic dynamics of the neurons forming the network in a spiking neural network consisting of Hodgkin–Huxley neurons on the image classification success of the network is investigated. In the first part of this two-part study, a practical neural network model consisting of Hodgkin–Huxley neurons is proposed and the network is tested in a 4-class real classification task. It is observed that the network consisting of Hodgkin–Huxley neurons has a classification performance at least as successful as the artificial neural network. In the second part of the study, the neurons in the network are replaced with stochastic Hodgkin–Huxley neurons, which more realistically represent the biological neuron, and the classification performance of the network at different cell membrane sizes is examined. Findings reveal that a spiking network consisting of stochastic Hodgkin–Huxley neurons, in which intrinsic noise dynamics are incorporated into the system, shows maximum classification performance at an optimal intrinsic noise level. It is called this reflection observed in the classification performance of a spiking network, which is referred to as stochastic resonance in computational neuroscience, as stochastic classification resonance in this study. This study also highlights the importance of bridging the gap between biological neuroscience and artificial neural networks for a better understanding of neurological structure.

噪声通常被认为对信息处理性能有负面影响。然而，也已经证明，在非线性系统中加入随机噪声或一定程度的随机（随机）可变性可以提高其性能或对弱信号的灵敏度。尽管对这一概念的研究在计算神经科学中被称为随机共振，但这一现象仍然是需要详细研究的主题之一，特别是在机器学习中。在本研究中，研究了霍奇金-赫胥黎神经元构成的尖峰神经网络中神经元的内在动力学对网络图像分类成功的影响。在本研究的第一部分中，提出了一个由Hodgkin-Huxley神经元组成的实用神经网络模型，并在一个4类真实分类任务中对该网络进行了测试。观察到，由霍奇金-赫胥黎神经元组成的网络具有至少与人工神经网络一样成功的分类性能。在研究的第二部分，将网络中的神经元替换为更真实地代表生物神经元的随机霍奇金-赫胥黎神经元，并检验了网络在不同细胞膜尺寸下的分类性能。研究结果表明，随机霍奇金-赫胥黎神经元组成的尖峰网络在最优的内禀噪声水平下表现出最大的分类性能。在计算神经科学中称为随机共振的尖峰网络的分类性能中观察到的这种反射，本研究称之为随机分类共振。这项研究还强调了弥合生物神经科学和人工神经网络之间的差距对于更好地理解神经结构的重要性。

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引用次数: 0

Deciphering circulating tumor cells binding in a microfluidic system thanks to a parameterized mathematical model 基于参数化数学模型的微流控系统循环肿瘤细胞结合解译。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-16 DOI: 10.1016/j.jtbi.2024.112029

Giorgia Ciavolella , Julien Granet , Jacky G. Goetz , Naël Osmani , Christèle Etchegaray , Annabelle Collin

The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their trajectories under the influence of hemodynamic and adhesion forces. We focus on already available in vitro measurements performed with a microfluidic device corresponding to the trajectories of CTCs – without or with different protein depletions – interacting with an endothelial layer. A key difficulty is the weak knowledge of the fluid velocity that has to be reconstructed. Our strategy combines a differential equation model – a Poiseuille model for the fluid velocity and an ODE system for the cell adhesion model – and a robust and well-designed calibration procedure. The parameterized model quantifies the strong influence of fluid velocity on adhesion and confirms the expected role of several proteins in the deceleration of CTCs. Finally, it enables the generation of synthetic cells, even for unobserved experimental conditions, opening the way to a digital twin for flowing cells with adhesion.

转移的扩散是一个关键的过程，其中一些问题仍未得到解答。在这项工作中，我们专注于在血液中循环的肿瘤细胞，即所谓的循环肿瘤细胞（CTCs）。我们的目的是表征它们在血流动力学和粘附力影响下的轨迹。我们专注于已经可用的体外测量，使用微流控装置进行相应的ctc轨迹-没有或具有不同的蛋白质消耗-与内皮层相互作用。一个关键的困难是对必须重建的流体速度知之甚少。我们的策略结合了微分方程模型-流体速度的泊泽维尔模型和细胞粘附模型的ODE系统-以及稳健且精心设计的校准程序。参数化模型量化了流体速度对黏附的强烈影响，并证实了几种蛋白质在ctc减速中的预期作用。最后，即使在未观察到的实验条件下，它也能生成合成细胞，为具有粘附性的流动细胞的数字双胞胎开辟了道路。

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引用次数: 0

Perceived risk induced multiscale model: Coupled within-host and between-host dynamics and behavioral dynamics 感知风险诱导的多尺度模型：宿主内和宿主间动力学与行为动力学的耦合。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-10 DOI: 10.1016/j.jtbi.2024.111998

Xiaodan Sun , Weike Zhou , Yuhua Ruan , Guanghua Lan , Qiuying Zhu , Yanni Xiao

A novel multiscale model is formulated to examine the co-evolution among behavioral dynamics, disease transmission dynamics and viral dynamics, in which perceived risk act as a bridge for realizing the bidirectional coupling of between-host dynamics and within-host dynamics. The model is validated by real data and exhibits rich dynamic behaviors including the periodic oscillations of the solutions, the discordance of transmission dynamics and viral dynamics. It is observed that new infections may increase with improving treatment efficacy, which may reveal the hidden mechanisms why it is hard to eliminate HIV/AIDS infection only with the strategy of treatment. If increasing treatment efficacy but without improving diagnosis rate, “nearly elimination” phenomenon may happen when the risk threshold for behavior changes is low, in which the number of new infections may drop to a relatively low level but increase again to a relatively high level after a period of time as people may hardly keep their awareness and increase their high risk behaviors. The findings indicate that the intervention measures should be implemented both at individual level and population level to realize “ending the AIDS”.

建立了一种新的多尺度模型来研究行为动力学、疾病传播动力学和病毒动力学之间的共同进化，其中感知风险是实现宿主间动力学和宿主内动力学双向耦合的桥梁。实际数据验证了该模型的有效性，该模型具有解的周期振荡、传播动力学的不一致性和病毒动力学等丰富的动力学特性。观察到随着治疗效果的提高，新发感染可能会增加，这可能揭示了仅靠治疗策略难以消除HIV/AIDS感染的隐藏机制。如果提高了治疗效果，但没有提高诊断率，在行为改变的风险阈值较低的情况下，可能会出现“近乎消除”现象，即新发感染人数可能会下降到较低水平，但一段时间后，由于人们很难保持认识，高危行为增加，新发感染人数可能会再次上升到较高水平。研究结果表明，要实现“终结艾滋病”，干预措施应在个体层面和群体层面同时实施。

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引用次数: 0

Learning to hunt: A data-driven stochastic feedback control model of predator–prey interactions 学习狩猎：数据驱动的捕食者-猎物相互作用的随机反馈控制模型。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-09 DOI: 10.1016/j.jtbi.2024.112021

Deze Liu, Mohammad Tuqan, Daniel Burbano

The dynamics unfolding during predator–prey interactions encapsulate a critical aspect of the natural world, dictating the survival and evolutionary trajectories of animal species. Underlying these complex dynamics, sensory-motor control strategies orchestrate the locomotory gates essential to guarantee survival or predation. While analytical models have been instrumental in understanding predator–prey interactions, dissecting sensory-motor control strategies remains a great challenge due to the adaptive and stochastic nature of animal behavior and the strong coupling of predator–prey interactions. Here, we propose a data-driven mathematical model describing the adaptive learning response of a dolphin while hunting a fish. Grounded in feedback control systems and stochastic differential equations theory, our model embraces the inherent unpredictability of animal behavior and sheds light on the adaptive learning strategies required to outmaneuver agile prey. The efficacy of our model was validated through numerical experiments mirroring crucial statistical properties of locomotor activity observed in empirical data. Finally, we explored the role of stochasticity in predator–prey dynamics. Interestingly, our findings indicate that varying noise levels can selectively favor either fish survival or dolphin hunting success.

在捕食者-猎物相互作用过程中展开的动态囊括了自然世界的一个关键方面，决定了动物物种的生存和进化轨迹。在这些复杂的动态背后，感觉-运动控制策略协调了保证生存或捕食所必需的运动门。虽然分析模型有助于理解捕食者-猎物相互作用，但由于动物行为的适应性和随机性以及捕食者-猎物相互作用的强耦合性，解剖感觉-运动控制策略仍然是一个巨大的挑战。在这里，我们提出了一个数据驱动的数学模型来描述海豚在捕鱼时的适应性学习反应。基于反馈控制系统和随机微分方程理论，我们的模型包含了动物行为固有的不可预测性，并阐明了战胜敏捷猎物所需的适应性学习策略。通过数值实验验证了我们模型的有效性，该实验反映了在经验数据中观察到的运动活动的关键统计特性。最后，我们探讨了随机性在捕食者-猎物动力学中的作用。有趣的是，我们的研究结果表明，不同的噪音水平可以选择性地有利于鱼类的生存或海豚的狩猎成功。

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引用次数: 0

Super-resolution ultrasound imaging of ischaemia flow: An in silico study 缺血血流的超分辨率超声成像：模拟研究

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-06 DOI: 10.1016/j.jtbi.2024.112018

Lachlan Arthur , Vasiliki Voulgaridou , Georgios Papageorgiou , Weiping Lu , Steven R. McDougall , Vassilis Sboros

Super-resolution ultrasound (SRU) is a new ultrasound imaging mode that promises to facilitate the detection of microvascular disease by providing new vascular bio-markers that are directly linked to microvascular pathophysiology, thereby augmenting current knowledge and potentially enabling new treatment. Such a capability can be developed through thorough understanding as articulated by means of mathematical models. In this study, a 2D numerical flow model is adopted for generating flow adaptation in response to ischaemia, in order to determine the ability of SRU to register the resulting flow perturbations. The flow model results demonstrate that variations in flow behaviour in response to locally induced ischaemia can be significant throughout the entire vascular bed. Measured velocities have variations that are dependent on the location of ischaemia, with median values ranging between

2 – 7

mms⁻¹. Moreover, the distinction between healthy and ischaemic networks are recorded accurately in the SRU results showing excellent agreement between SRU maps and the model. Up to 7-fold spatial resolution improvement to conventional contrast ultrasound was achieved in microbubble localisation while the detection precision and recall was consistently above 98

%

. The microbubble tracking precision was of a similar accuracy, whereas the recall was reduced (77

%

) under varying ischaemic impacted flow. Further, regions with velocities up to 30 mms⁻¹ are in excellent agreement with SRU maps, while at regions that include a proportion of higher velocities, the median velocity values are within 1.28

%

–3.32

%

of the ground-truth. In conclusion, SRU is a highly promising methodology for the direct measurement of microvascular flow dynamics and may provide a valuable tool for the understanding and subsequent modelling of behaviour in the vascular bed.

超分辨率超声（SRU）是一种新的超声成像模式，有望通过提供与微血管病理生理学直接相关的新的血管生物标志物来促进微血管疾病的检测，从而增加现有知识并可能实现新的治疗方法。这样的能力可以通过对数学模型的透彻理解来开发。在本研究中，采用二维数值流动模型来产生响应缺血的流动适应，以确定SRU记录由此产生的流动扰动的能力。流动模型结果表明，响应局部诱导缺血的流动行为变化在整个血管床中都是显著的。测量到的流速随缺血位置的不同而变化，中位数在2-7 mm -1之间。此外，SRU结果准确地记录了健康和缺血网络之间的区别，表明SRU地图与模型之间具有良好的一致性。微泡定位的空间分辨率比常规对比超声提高了7倍，检测精度和召回率均在98%以上。微泡跟踪精度具有相似的精度，而在不同的缺血冲击流量下召回率降低（77%）。此外，速度高达30 mm -1的区域与SRU地图非常吻合，而在包含一定比例更高速度的区域，中位速度值在地面真值的1.28%-3.32%之间。总之，SRU是一种非常有前途的方法，用于直接测量微血管流动动力学，并可能为理解和随后的血管床行为建模提供有价值的工具。

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引用次数: 0

The impact of contact-network structure on important epidemiological quantities of infectious disease transmission and the identification of the extremes 接触网络结构对传染病传播的重要流行病学数量和极端情况识别的影响。

IF 1.9 4区数学 Q2 BIOLOGY

Journal of Theoretical Biology

Pub Date : 2024-12-05 DOI: 10.1016/j.jtbi.2024.112010

Demetris Avraam , Christoforos Hadjichrysanthou

An individual-based stochastic model was developed to simulate the spread of an infectious disease in an SEIR-type system on all possible contact-networks of size between six and nine nodes. We assessed systematically the impact of the change in the population contact structure on four important epidemiological quantities: i) the epidemic duration, ii) the maximum number of infected individuals at a time point during the epidemic, iii) the time at which the maximum number of infected individuals is reached, and iv) the total number of individuals that have been infected during the epidemic. We considered the potential relationship of these quantities as the network changes and identified the networks that maximise and minimise each of these in the case of an epidemic outbreak. Chain-like networks minimise the peak and final epidemic size, but the disease spread is slow on such contact structures which leads to the maximisation of the epidemic duration. Star-like networks maximise the time to the peak whereas highly connected networks lead to faster disease transmission, and higher peak and final epidemic size. While the pairwise relationship of most of the quantities becomes almost linear, or inverse linear, as the network connectivity increases and approaches the complete network, the relationships are non-linear towards networks of low connectivity. In particular, the pairwise relationship between the final epidemic size and other quantities is changed in a ‘bow-shaped’ manner. There is a strong inverse linear relationship between epidemic duration and peak epidemic size with increasing network connectivity. The (inverse) linear relationships between quantities are more pronounced in cases of high disease transmissibility. All the values of the quantities change in a non-linear way with the increase of network connectivity and are characterised by high variability between networks of the same degree. The variability decreases as network connectivity increases.

我们开发了一个基于个体的随机模型来模拟传染病在6到9个节点之间的所有可能的接触网络中的传播。我们系统地评估了人群接触结构变化对4个重要流行病学量的影响：1)流行持续时间，2)流行期间某个时间点的最大感染人数，3)达到最大感染人数的时间，4)流行期间的感染总人数。我们确定了在流行病爆发的情况下最大化和最小化这些数量的网络。链状网络最大限度地减少了流行病的高峰和最终规模，但疾病在这种接触结构上传播缓慢，导致流行病持续时间最大化。星形网络最大限度地延长了到达峰值的时间，而高度连接的网络导致更快的疾病传播，以及更高的峰值和最终流行规模。当网络连通性增加并接近完整网络（其中每个个体都相互连接）时，大多数数量的成对关系几乎变为线性或逆线性，而对于低连通性的网络，这种关系是非线性的。特别是，最终流行规模与其他数量之间的成对关系以“弓形”方式变化。随着网络连通性的增加，疫情持续时间与疫情峰值规模之间存在较强的逆线性关系。在疾病高传播率的情况下，数量之间的（逆）线性关系更为明显。随着网络连通性的增加，所有量的值都以非线性方式变化，并且在相同程度的网络之间具有高变异性。可变性随着网络连接的增加而降低。

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引用次数: 0