Transients and attractors in epidemics.
Ontology highlight
ABSTRACT:
SUBMITTER: Bauch CT
PROVIDER: S-EPMC1691412 | biostudies-literature | 2003 Aug
REPOSITORIES: biostudies-literature
Publications
Transients and attractors in epidemics.
Bauch Chris T CT Earn David J D DJ
Proceedings. Biological sciences 20030801 1524
Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with ...[more]
Similar Datasets
Project description:Episodic memory has a dynamic nature: when we recall past episodes, we retrieve not only their content, but also their temporal structure. The phenomenon of replay, in the hippocampus of mammals, offers a remarkable example of this temporal dynamics. However, most quantitative models of memory treat memories as static configurations, neglecting the temporal unfolding of the retrieval process. Here, we introduce a continuous attractor network model with a memory-dependent asymmetric component in the synaptic connectivity, which spontaneously breaks the equilibrium of the memory configurations and produces dynamic retrieval. The detailed analysis of the model with analytical calculations and numerical simulations shows that it can robustly retrieve multiple dynamical memories, and that this feature is largely independent of the details of its implementation. By calculating the storage capacity, we show that the dynamic component does not impair memory capacity, and can even enhance it in certain regimes.
| S-EPMC8439658 | biostudies-literature
Project description:BackgroundMany chronic human diseases are of unclear origin, and persist long beyond any known insult or instigating factor. These diseases may represent a structurally normal biologic network that has become trapped within the basin of an abnormal attractor.Methodology/principal findingsWe used the Hopfield net as the archetypical example of a dynamic biological network. By progressively removing the links of fully connected Hopfield nets, we found that a designated attractor of the nets could still be supported until only slightly more than 1 link per node remained. As the number of links approached this minimum value, the rate of convergence to this attractor from an arbitrary starting state increased dramatically. Furthermore, with more than about twice the minimum of links, the net became increasingly able to support a second attractor.Conclusions/significanceWe speculate that homeostatic biological networks may have evolved to assume a degree of connectivity that balances robustness and agility against the dangers of becoming trapped in an abnormal attractor.
| S-EPMC3008716 | biostudies-literature
Project description:Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic-they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.
| S-EPMC4930057 | biostudies-literature
Project description:Dynamical systems theory suggests that ecosystems may exhibit alternative dynamical attractors. Such alternative attractors, as for example equilibria and cycles, have been found in the dynamics of experimental systems. Yet, for natural systems, where multiple biotic and abiotic factors simultaneously affect population dynamics, it is more challenging to distinguish alternative dynamical behaviors. Although recent research exemplifies that some natural systems can exhibit alternative states, a robust methodology for testing whether these constitute distinct dynamical attractors is currently lacking. Here, using attractor reconstruction techniques we develop such a test. Applications of the methodology to simulated, experimental and natural time series data, reveal that alternative dynamical behaviors are hard to distinguish if population dynamics are governed by purely stochastic processes. However, if population dynamics are brought about also by mechanisms internal to the system, alternative attractors can readily be detected. Since many natural populations display evidence of such internally driven dynamics, our approach offers a method for empirically testing whether ecosystems exhibit alternative dynamical attractors.
| S-EPMC8370982 | biostudies-literature
Project description:The important question that arises during determining the evolution of organisms is whether evolution should be treated as a continuous process or whether groups of organisms fall into 'local' attractors during evolution. A similar question arises during considering the development of cells after cancer transformation. Answers to these questions can provide a better understanding of how normal and transformed organisms evolve. So far, no satisfactory answers have been found to these questions. To find the answers and demonstrate that organisms during evolution get trapped in 'local' attractors, an artificial neural network supported by a semihomologous approach and unified cell bioenergetics concept have been used in this work. A new universal model of cancer transformation and cancer development has been established and presented to highlight the differences between the development of transformed cells and normal organisms. An unequivocal explanation of cancer initialization and development has not been discovered so far, thus the proposed model should shed new light on the evolution of transformed cells.
| S-EPMC8100110 | biostudies-literature
Project description:For microbiome biology to become a more predictive science, we must identify which descriptive features of microbial communities are reproducible and predictable, which are not, and why. We address this question by experimentally studying parallelism and convergence in microbial community assembly in replicate glucose-limited habitats. Here, we show that the previously observed family-level convergence in these habitats reflects a reproducible metabolic organization, where the ratio of the dominant metabolic groups can be explained from a simple resource-partitioning model. In turn, taxonomic divergence among replicate communities arises from multistability in population dynamics. Multistability can also lead to alternative functional states in closed ecosystems but not in metacommunities. Our findings empirically illustrate how the evolutionary conservation of quantitative metabolic traits, multistability, and the inherent stochasticity of population dynamics, may all conspire to generate the patterns of reproducibility and variability at different levels of organization that are commonplace in microbial community assembly.
| S-EPMC8800145 | biostudies-literature
Project description:Considering the crosstalk between brain networks that contain linguistic and emotional information and that no studies have examined the impact of semantic information of affective nature on subject-verb number agreement, the present Event Related Potential (ERP) study investigated the extent to which emotional local nouns whose number mismatched that of subject head nouns might be considered by the parser during comprehension of grammatically correct sentences. To this end, twenty-eight Spanish native speakers were tested on a self-paced reading task while their brain activity was recorded. The experimental materials consisted of 120 sentences where the valence (negative vs. neutral) and number (singular vs. plural) of the local noun of the singular subject noun-phrase (NP) were manipulated; El gorro de aquel/aquellos cazador(es)/mecánico(s) era… [The hat of that/those hunter(s)/mechanic(s) was…]. ERP results measured in the local noun position showed that valence and number interacted in the 300-500 ms (negative component) and 780-880 ms (late positivity) time windows. In the (target) verb position, the two factors only interacted in the late 780-880 ms time window, revealing an "ungrammatical illusion" for plural marked neutral words. Our findings suggest that number agreement is sensitive to affective meaning but that the emotional information of an attractor is considered in different operations and at different stages during grammatical sentence processing; it can affect lexical and syntactic representation retrieval of a subject-NP and impact agreement encoding only at late stages of processing, during verb agreement and feature integration.
| S-EPMC9330507 | biostudies-literature
Project description:Significance Ecological theory predicts that under the same environmental conditions, an ecosystem could have more than one community state that is maintained by reinforcing feedbacks. If so, a sufficiently large disturbance can flip the system to a less desired community that is difficult to reverse. Here, we demonstrate that a coral reef can become trapped in a seaweed-dominated state in the same conditions under which corals thrive. The implications are profound, particularly in light of the increasing occurrence of shifts to seaweed on coral reefs worldwide. Our results indicate that anticipatory management strategies that lessen the chance of a switch to seaweeds will be more effective than those aimed at restoring the coral community after a shift. Ecological theory predicts that ecosystems with multiple basins of attraction can get locked in an undesired state, which has profound ecological and management implications. Despite their significance, alternative attractors have proven to be challenging to detect and characterize in natural communities. On coral reefs, it has been hypothesized that persistent coral-to-macroalgae “phase shifts” that can result from overfishing of herbivores and/or nutrient enrichment may reflect a regime shift to an alternate attractor, but, to date, the evidence has been equivocal. Our field experiments in Moorea, French Polynesia, revealed the following: (i) hysteresis existed in the herbivory–macroalgae relationship, creating the potential for coral–macroalgae bistability at some levels of herbivory, and (ii) macroalgae were an alternative attractor under prevailing conditions in the lagoon but not on the fore reef, where ambient herbivory fell outside the experimentally delineated region of hysteresis. These findings help explain the different community responses to disturbances between lagoon and fore reef habitats of Moorea over the past several decades and reinforce the idea that reversing an undesired shift on coral reefs can be difficult. Our experimental framework represents a powerful diagnostic tool to probe for multiple attractors in ecological systems and, as such, can inform management strategies needed to maintain critical ecosystem functions in the face of escalating stresses.
| S-EPMC6410839 | biostudies-literature
Project description:Delusions are, by popular definition, false beliefs that are held with certainty and resistant to contradictory evidence. They seem at odds with the notion that the brain at least approximates Bayesian inference. This is especially the case in schizophrenia, a disorder thought to relate to decreased - rather than increased - certainty in the brain's model of the world. We use an active inference Markov decision process model (a Bayes-optimal decision-making agent) to perform a simple task involving social and non-social inferences. We show that even moderate changes in some model parameters - decreasing confidence in sensory input and increasing confidence in states implied by its own (especially habitual) actions - can lead to delusions as defined above. Incorporating affect in the model increases delusions, specifically in the social domain. The model also reproduces some classic psychological effects, including choice-induced preference change, and an optimism bias in inferences about oneself. A key observation is that no change in a single parameter is both necessary and sufficient for delusions; rather, delusions arise due to conditional dependencies that create 'basins of attraction' which trap Bayesian beliefs. Simulating the effects of antidopaminergic antipsychotics - by reducing the model's confidence in its actions - demonstrates that the model can escape from these attractors, through this synthetic pharmacotherapy.
| S-EPMC9241990 | biostudies-literature
Project description:Stochastic processes such as genetic drift may hinder adaptation, but the effect of such stochasticity on evolution via its effect on ecological dynamics is poorly understood. Here we evaluate patterns of adaptation in a population subject to variation in demographic stochasticity. We show that stochasticity can alter population dynamics and lead to evolutionary outcomes that are not predicted by classic eco-evolutionary modeling approaches. We also show, however, that these outcomes are governed by nonequilibrium evolutionary attractors-these are maxima in lifetime reproductive success when stochasticity keeps the ecological system away from the deterministic equilibrium. These NEEAs alter the path of evolution but are not visible through the equilibrium lens that underlies much evolutionary theory. Our results reveal that considering population processes during transient periods can greatly improve our understanding of the path and pace of evolution.
| S-EPMC10078373 | biostudies-literature