Nonlinear Dynamics

We develop a mathematical model of Rift Valley Fever integrating mosquito vectors, ruminants, and humans, based on an SEIR-type structure with vertical transmission in vectors. Local data from the Sudanian and especially the Sahelian zones are used to capture the impact of climatic variations on mosquito population dynamics. The mathematical analysis establishes the models positivity, determines the basic reproduction number R0, and demonstrates the local and global stability of the disease-free equilibrium. Sensitivity analysis (PRCC) highlights the most influential parameters, while the stochastic approach using a continuous-time Markov chain confirms the major role of seasonal rainfall. Numerical simulations reveal a peak in animal and human infections around the 9th month, correlating with periods of heavy rainfall. This model provides a relevant tool for surveillance and prevention within a "One Health" approach in Chad.

The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.

Malaria and diabetes represent two globally significant metabolic disorders whose co-occurrence leads to complex, poorly understood pathophysiological interactions. Plasmodium infection disrupts glucose homeostasis through parasite-driven glucose consumption, inflammatory cytokine production, and pancreatic /{beta}-cell dysfunction, while diabetes impairs host immunity and increases malaria susceptibility. To date, no mathematical framework has captured the bidirectional coupling between these systems. Here we extend the insulin-glucose-glucagon (IGG) model of Dalton et al.\ (2026) by introducing a fourth state variable representing parasite load, incorporating malaria-induced insulin suppression, parasite-driven glucose consumption, inflammatory gluconeogenesis, bidirectional glucagon dysregulation, and insulin-dependent immune enhancement of parasite clearance. We establish positivity, boundedness, existence and uniqueness of steady states, local stability via Routh-Hurwitz criteria, global stability via Lyapunov functions, and sensitivity analysis of parameters driving hypoglycemia risk. Numerical simulations characterise the model across healthy, diabetic, and co-infected states. They show that parasite-driven glucose consumption and inflammatory gluconeogenesis act antagonistically on circulating glucose, that insulin-enhanced immunity lowers peak parasitemia through a saturating clearance term, and that increasing the half-life of exogenous insulin raises hypoglycemia risk in all host states. These mechanisms provide testable hypotheses for the clinical management of malaria-diabetes patients and identify potential therapeutic targets (TNF- blockade, glucagon analogues) for mitigating co-infection morbidity.

In this paper, we propose a new model to estimate the impact of an intervention on human hosts of a vector-borne infection, such as dengue, which occurs in yearly outbreaks of different magnitudes. The model applies to these outbreaks and, in fact, is independent of their intensity, that is, it does not require the steady-state assumption. The model takes as input the officially reported age-dependent number of cases of a vector-borne infection. It is deterministic and does not account for stochasticity. Our objective is to estimate the impact of the intervention (the efficacy), and we rely on the observed fact that the age distribution of the proportion of cases of the infections transmitted by the same vector is independent of both the intensity of transmission and the geographic area studied, at least for Brazilian regions. This finding is highlighted in the main text and forms the basis of our calculations. A hypothetical intervention is simulated using a dengue vaccine, which allows the determination of the optimal strategy for a vaccination campaign.

The basic reproduction number R0 confounds pathogen biology with adaptive human contact behavior. Earlier epidemiological--economic theory predicted a forward-looking behavioral contact response but could not test it in the absence of appropriate behavioral data. Using directly measured mobility as an observable proxy for contact, we (i) estimate the behavioral response function directly from data; (ii) show that the biology/behavior decomposition and hence the behavioral correction to R0 is not identified from an epidemic trajectory, the apparent constant-contact R0 being one endpoint of an observational-equivalence class that fits the factual curve identically yet diverges under counterfactual; and (iii) characterize that divergence ("what R0 deletes") as state-dependent, unimodal in counterfactual severity and vanishing when behavior saturates. We then show that, across US jurisdictions, the correction is empirically bounded because risk-responsiveness and behavioral non-saturation are confounded (r=-0.57, n=51): where behavior could compensate, it was already maximal, and where it was not maximal it did not respond. What R0 deletes is thus real and structurally characterizable yet empirically modest here, for reasons the framework itself supplies.

An epidemic's expected course is determined by the magnitude and timing of a typical person's infectiousness --- captured, in turn, by the basic reproduction number and the generation-time distribution. These fundamental, population-average quantities can mask individual-level variation that shapes how an epidemic actually unfolds: for example, individual variation in the magnitude of infectiousness (overdispersion) creates superspreading, a key feature of the SARS-CoV-1 and SARS-CoV-2 epidemics. However, the impact of individual variation in infectiousness timing is less well understood. Here, we demonstrate that individual infectiousness timing varies substantially and to different degrees across pathogens. For some common pathogens, including influenza, measles, and SARS-CoV-2, infectiousness is "bursty", or highly concentrated and variably-timed across individuals: for example, the window of appreciable infectiousness for SARS-CoV-2 may last for roughly a day, vs. the 9--12 days usually quoted. We show that bursty infectiousness creates superspreading without inherent superspreaders, makes epidemic timing more variable, amplifies the time-sensitivity of common interventions, and complicates inference of key epidemiological parameters. Together with the reproduction number, the generation-time distribution, and overdispersion, burstiness completes a family of basic parameters that govern how epidemics unfold.

Viral infection can coactivate interferon (IFN)--JAK/STAT1 signalling and the p53--Mdm2 stress-response pathway, two modules that jointly shape antiviral defence and cell-fate decisions. Here, we focus on viral infection contexts capable of inducing genotoxic stress associated with DNA double-strand breaks, thereby triggering oscillatory or sustained p53--Mdm2 dynamics. Whether p53 acts merely as a parallel stress pathway, or actively reshapes how an activated JAK/STAT1 response is temporally decoded and functionally routed, remains unclear. We develop a coupled ordinary [ndash]differential-equation model linking an IFN{gamma}centred JAK/STAT1 core, a p53--Mdm2 module, downstream antiviral and apoptotic effectors, and a coarse-grained viral-burden layer, with p53 regulation placed downstream of STAT1 activation. We find that p53 does not simply increase nuclear STAT1 availability; it redistributes the response towards DNA-bound STAT1 persistence, transcriptional memory and STAT1-driven feedback, producing a persistence--recovery trade-off in which prior p53 stress prolongs the transcriptionally active STAT1 state but delays re-inducibility after repeated IFN stimulation. When IFN and p53-associated stress are both driven by viral burden, p53 is not a uniform amplifier of host defence: p53 preactivation strengthens the upstream memory layer, but downstream effectors buffer rather than mirror this priming. The model further separates antiviral-state engagement from realised viral control: strong effector activation does not guarantee suppression of poorly sensitive viral classes, whereas sensitive viral classes can be cleared before apoptosis. The origin of the stimulus also matters: exogenous IFN or p53 stimulation allows us to assess the host's intrinsic response capacity, whereas virus-induced IFN and p53 stress remain coupled to viral persistence. Persistent viral burden thus emerges as the dynamical link between IFN induction, p53 stress-memory, antiviral maintenance, viral control and the choice between JAK/STAT--IRF1-associated, p53-autonomous or dual apoptotic routing.

Abstract Purpose This study introduces a novel approach to address unmeasured confounding in terminal event studies using the prior event rate ratio (PERR) method. The proposed approach PERR_{proxy} used a proxy event to replace the original terminal event in the pre-exposure period, enabling the application of PERR in terminal event settings. Additionally, we also applied difference in difference (DID) regression, which is conceptually analogous to PERR to estimate the standard errors and confidence intervals of PERR_{proxy}. Methods We conducted numeric simulations to evaluate the validity of PERR_{proxy} approach and assessed its performance under varying levels of unmeasured confounding effects, baseline hazard ratios, and the correlation between the proxy and terminal events. To demonstrate its practical applicability, we also performed an empirical analysis to investigate the impact of severe hospitalized COVID-19 on circulatory system disease mortality using the PERR_{proxy}. Results In simulation studies, PERR_{proxy} effectively reduced the unmeasured confounding effects compared to the conventional methods. The performance of PERR_{proxy} was influenced by the strength of unmeasured confounding, baseline hazard ratios, and the correlation between the proxy and terminal outcomes. In addition, difference in difference (DID) regression had much faster computational speed for estimating standard errors and confidence intervals compared to bootstrap. In the empirical analysis, PERR_{proxy} identified that severe hospitalized COVID-19 as a significant risk factor for the circulatory system disease mortality and reduced the unmeasured confounding effects. Conclusions The PERR_{proxy} approach extends the applicability of the original PERR method to terminal event studies, offering a promising solution for addressing unmeasured confounding. Additionally, the DID regression framework provides a computationally efficient alternative for parameter estimation in PERR-based studies. However, careful consideration is still required in PERR_{proxy} for proxy events selection and other underlying assumptions of the PERR method to ensure valid results. Keywords: prior event rate ratio, unmeasured confounding, proxy event, terminal event study, observational study, electronic health records

Compartmental models of infectious disease transmission make assumptions about human behaviors. Specifically, they parameterize interactions across population groups, assumed to have distinct epidemiologically-relevant behavioral patterns, primarily through contact matrices stratified by demographic variables such as age, gender, or socioeconomic status. Although such demographic characteristics are readily measurable, they may inadequately capture the social and psychological forces that govern protective behaviors. Drawing on 20 waves of a national survey conducted throughout the COVID-19 pandemic in the United States, we show that institutional trust - particularly trust in public health agencies, physicians, and hospitals - is a dominant predictor of protective behavior adoption. For mask wearing during periods of strongest pandemic activity, for example, institutional trust explains more behavioral variance across population groups than age, income, education, and partisan affiliation combined. In unadjusted analyses, the difference in protective behavior adoption between individuals with the highest and lowest trust in the CDC was four- to six-fold larger than the corresponding differences by age, income, or educational attainment, and exceeded the difference between Democratic and Republican respondents. This association was institutionally specific (e.g., the relationship attenuates for trust in banks), and behaviorally specific (e.g., trust in the CDC is associated with protective behaviors but not visiting a doctor). The latter suggests that trust modifies voluntary compliance with public health recommendations rather than access to or use of healthcare. We conclude that compartmental models of disease transmission would be substantially improved by incorporating institutional trust as a stratifying variable. We additionally offer a trust-integrated mathematical modeling framework and recommendations for the data infrastructure needed for its implementation.

Despite extensive study of cellular mechanisms underlying long-term potentiation, no single specific protein or gene has been identified which encodes an individual unit of information, or memory bit. Indeed, the brain engram remains a knowledge gap. The theory of exclusion led us to cancel one-by-one several unrealistic biological options, suggesting that the explanation resides somewhere else. Superposition of up to concentric 300 myelin layers, spiraled, and highly compacted wrapping a single axon and each wrap could host hundreds to thousands of niches, as memory cells, collectively consisting of a massive array of cells. The disjointed 3D spatial superposition allows storage of charges, nodes not facing from a layer to next. The thickness of a single myelin layer ranges from 7.0 to 20 nm. The dimension scale is approximately the exact dimensions of the charge trap, the tunnel and dielectric also equipping current AI microchips. Stored charges are positive ions, with similar effect whether charges are negative or positive charges creating an electromagnetic field. To write data, following an action potential, this voltage applies to the control gates of the myelin layers producing an ionic charge injection. This causes charges to gain energy and tunnel through the myelin layer across Ranvier nodes, via quantum tunneling, and deep into the concentric myelin multilayers. This is creating an insulated trapping of K+ ions isolated from the system. In a long white matter tract bundle, the near-perfect isolation of millions of axons within compressed myelin wrap-ion channel K+/Na+ systems provides quantum coherence and precision of asynchronous firing property. The injected ionic charges (K+) become physically stuck in traps within the myelin layers. The K+ ions may not move freely, completely trapped after AP ceases. Mirroring a single-bit, single-level-cell, a trapped ionic charge (ions K+) may represent a 1, while an empty cell (absence of K+) represents a 0. The trial-and-error process, with a Bayesian inference which may have also been the core evolution of the learning human brain. Based on selected mathematical equations, we analyzed the general scheme on how deep learning may be embedded in the brain

We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

In recent years, the use of multi-model ensemble projections in infectious disease modeling has become an established methodological approach to account for and integrate across uncertainties and structural differences present in individual models. However, the creation of long-term ensemble projections through these coordinated efforts is resource-intensive, demanding the input of multiple research teams and substantial computational power. This typically limits the ability to refine projections, update the selection of plausible epidemic trajectories, or expand the number of scenarios that can be assessed, even as new empirical data become available. To address this challenge, we define an adaptive ensemble approach that, analogously to a multi-model particle filtering method, dynamically selects individual model trajectories based on observed data throughout the epidemic projection period. We demonstrate the effectiveness of this methodology using the U.S. Flu Scenario Modeling Hub (SMH) projections for influenza hospitalizations in the United States during the 2023-2024 and 2024-2025 winter seasons. Our findings show that the adaptive ensemble yields improved predictive accuracy with respect to the original SMH ensemble projections across several scoring rules and geographical resolutions. Furthermore, the adaptive ensemble approach offers two additional applications: i) the dynamic assignment of posterior probabilities to epidemic scenarios, identifying the most plausible scenario, and representing how reality is captured by a combination of scenarios, and ii) the potential use for short-term forecasting. The adaptive ensemble approach is able to identify the most likely scenarios for the 2023-2024 and 2024-2025 U.S. influenza seasons, even in the early stages of the epidemic. It outperforms, retrospectively, a baseline model in short-term forecasting of influenza hospitalizations in the United States during the two seasons across various horizons and scoring rules, showing potential to contribute to real-time collaborative forecasting challenges such as CDC's FluSight. The proposed approach offers an efficient or low-resource strategy to increase the impact of multi-model epidemic projections by providing real-time support to modeling teams, public health authorities, and decision-makers.

Understanding how network connectivity shapes neural representations is central to systems neuroscience. While dimensionality reduction methods uncover low-dimensional manifold structure in population recordings, a rigorous framework connecting manifold geometry to network mechanisms and information encoding remains lacking. We develop a differential geometric approach for analyzing neural manifolds in rate-based recurrent networks receiving tuned feedforward inputs. We derive expressions for the pullback metric of neural manifolds, showing how input tuning curves, feedforward and recurrent synaptic connectivity shape manifold geometry. Critically, we establish that the Fisher information matrix at steady states also has the structure of a pullback metric, directly linking intrinsic manifold geometry to stimulus discriminability and information encoding. For noise with slow temporal correlations propagated through the network, we show that recurrent effects on information geometry cancel: Fisher information depends only on the feedforward connectivity. Thus, feedforward connectivity critically determines representational geometry. As an example, we demonstrate that the representation of space by a module of hexagonal grid cells is approximately isometric for random distribution of grid phases. Moreover, a linear feedforward transformation can map spatially random input tuning curves into a population of hexagonal grid cells, forming a toroidal manifold. Thus, feedforward connectivity alone can generate structured spatial representations without requiring carefully tuned recurrent connectivity or continuous attractor dynamics. Recurrent connectivity, however, is shown to improve stimulus encoding under fast noise, thereby implementing a selective noise reduction.

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

Learning new information in the presence of distracters and changing conditions requires the ability to adapt. In the brain, this adaptive capability has been linked to dynamic interactions between attention and working memory, which enable the selective filtering of irrelevant input while preserving behaviorally relevant information. Specific neural oscillations have been implicated in this process. Here, we introduce a phenomenological data-driven framework for oscillatory network modeling that learns condition-dependent coupling laws directly from neural recordings and enables inference of condition-dependent directed pathways. We apply our approach to magnetoen-cephalography (MEG) data collected while participants performed a working-memory task with and without distracters. Recall dynamics in the non-distracter condition are first modeled using a linear oscillatory network in which each region of interest is represented by two alpha-band harmonic oscillators. We use universal differential equations (UDE), an extension of neural differential equations, to capture distracter-induced changes in coupling laws. Symbolic regression is then used to interpret the modifications identified by UDE as nonlinear functions, and an additional method is proposed to identify the directed pathway from the newly emerging nonlinear terms in the dynamics of brain regions of interest. Despite inter-subject variability, working memory recall data from all four participants examined under distraction showed the emergence of a pathway from the dorsolateral prefrontal cortex (dlPFC) to the primary visual cortex (V1). This finding is consistent with the established role of the dlPFC in cognitive control and suggests that distracter processing recruits a directed interaction from prefrontal to visual regions. More broadly, our results illustrate that combining linear models whose parameters are learned from the data with universal differential equations augmented by interpretability methods enables the identification of condition-dependent coupling laws, their representation as interpretable mathematical functions, and the discovery of candidate directed pathways underlying adaptive changes in oscillatory networks without requiring strong prior assumptions about the underlying mechanisms.

Large-scale brain imaging has relied heavily on fluorescent reporters; however, photobleaching and signal variability limit quantitative analysis in intact tissues. Here, we intro-duce MelaCAST (melanin-based scattering CAST imaging), a genetically encoded scattering strategy for whole-brain imaging. AAV-mediated delivery of tyrosinase enables cell-type-specific melanin production, generating stable intracellular scattering contrast throughout the mouse brain. By integrating tissue clearing with scattering tomography, MelaCAST enables non-photobleaching, high-throughput volumetric imaging of genetically defined cell populations in in-tact brains. This approach establishes melanin as a genetically encoded scattering reporter and expands whole-organ imaging beyond fluorescence-based modalities.

Skilled control of visually-guided reaching is fundamental for many daily activities. Visual information about hand and target position are used for movement planning and online corrections through rapid visuomotor feedback responses. Such feedback control is generally believed to implicate a single error signal, representing a difference vector between hand and target position. Here, we directly assess whether shared or independent systems serve visually-guided feedback control. We tested whether feedback gains can be independently modulated by hand/cursor and target motion through manipulating the task-relevance of each signal during goal-directed reaching. Our results demonstrate that the gains of visuomotor feedback responses to perturbed hand and target motion can be set independently of one another, at the same time, as a function of task-relevance. By dissociating feedback control of cursor and target signals, our findings support the existence of two independent visuomotor feedback pathways, revealing a more flexible neural architecture for goal-directed action.

Intelligent behavior depends on the brain's ability to represent multiple features of the environment simultaneously while keeping those representations independent [1,2]. Patients with Alzheimer's disease often mix up objects, people, and events [3-7], raising the possibility that disease mixes up the way that information is represented in the brain. Here we show that the independence of visual representations progressively breaks down during early stages of disease progression in a rhesus macaque model of Alzheimer's disease and related dementias [8-10]. In visual area V4, representations of different visual features become progressively less independent, such that the representation of one feature is increasingly influenced by the value of another. We term this loss of independence neuronal feature confusion. This neuronal change predicts a specific behavioral consequence: because feature representations become less independent, preferences associated with one visual feature increasingly influence visually guided choices associated with other, independent features. Using an analogous image-selection task, we found the same behavioral signature in people with mild cognitive impairment, distinguishing them from age-matched controls. These results identify a specific and measurable alteration in neuronal population representations that predicts a behavioral change observed across species. More broadly, these findings demonstrate that neuronal population representations can guide the development of sensitive, non-invasive behavioral methods for early detection of functional changes associated with Alzheimer's disease.

Ethological tasks promise to engage the integrated perception, memory, and decision-making that define natural behavior, yet laboratory implementations are often so sparsified that they may fail to recruit the very cognitive processes of interest. We tested whether increasing environmental complexity in a standard task could expose this hidden cognition. Mice that were already expert hunters in a bare arena were challenged to capture live insect prey in arenas filled with objects that obstruct movement, occlude vision, and offer the prey places to hide. Despite their prior mastery, the added complexity revealed an entire layer of learning that the simple task failed to engage: rather than refining the sensorimotor details of pursuit, mice reorganized how they searched the environment. Across trajectory, kinematic, and object-referenced analyses, learning was expressed predominantly within the search state. To analyze behavior in explicit relation to environmental structure, we developed an open-source framework-a compact ethogram with hierarchical, pose- and object-based classification-that links each action to its environmental context. Unsupervised analyses revealed structured search dynamics across multiple timescales, and a minimal, interpretable agent-based model showed that short-term spatial memory and object-specific value are together sufficient to reproduce the non-random structure of search, including a learned, non-backtracking bias that emerged within the first days of object exposure. Classifiers further showed that mice selectively acquired the object interactions most likely to expose hidden prey. Reproducible with inexpensive materials, the paradigm and its analysis tools offer a sensitive behavioral readout of search, memory, and strategy for studies that conventional low-dimensional assays leave unresolved.

Oxytocin and vasopressin are endogenous bioactive peptides with conserved roles in reproduction and, more recently recognized, in peripheral lipid metabolism. Whether this signaling system also shapes how reproduction declines with age has not been tested in any animal. Here we show that in C. elegans, the oxytocin/vasopressin-like neuropeptide nematocin restrains reproductive output as animals reach mid-life. Nematocin and its two receptors are produced throughout adult life and peak as reproduction begins to wane. Animals lacking receptor signaling produce more offspring in mid-life, an improvement that reflects better egg quality and fertilization rather than improved embryo survival. This benefit is accompanied by changes in intestinal fat metabolism, the worm's equivalent of liver and adipose tissue: nematocin normally limits the activity of a fatty-acid desaturase that is otherwise induced by mating, and it shapes how much yolk reaches developing eggs. The two receptors act through separate routes, one tuning intestinal fat metabolism and the other controlling yolk delivery to the egg. Together, these findings reveal nematocin as a regulator of the intestinal metabolic environment across reproductive age, mirroring the recently described oxytocin-hepatocyte-adipocyte lipid axis in mammals and implicate this conserved signaling system in the coordination of maternal investment during reproductive aging.