We propose a discrete, stage-dependent model for metabolic scaling grounded in approximately geometric growth across successive developmental steps, using Fibonacci recursion as an archetype. In contrast to continuous fractal models such as the West-Brown-Enquist (WBE) theory, our framework treats metabolism as the cumulative activity of structures formed in prior stages. The scaling exponent b(n) emerges from a logarithmic relation between consecutive stages and varies with the growth stage n. A refined logarithmic expression improves descriptive agreement with empirical mammalian data relative to the WBE baseline. Across nine species, model-based b(n) values are on average closer (mean deviation [Formula: see text], with improvements up to [Formula: see text]) to intraspecific estimates. The stage index n is inferred deterministically as [Formula: see text], where [Formula: see text] is the golden ratio, from reported birth mass [Formula: see text] and mass at stage n, M(n). The model is intended for moderate developmental stages under basal conditions and complements classical 2/3 and 3/4 baselines by capturing systematic, stage-specific departures from a single constant exponent. This discrete perspective clarifies when and why deviations from classical allometries arise and offers a compact mechanism linking recursive growth to metabolic scaling.
The metaphor of "scaffolding" originates from developmental psychology, and has become a central theoretical concept that plays explanatory roles in psychology, developmental biology, and evolutionary biology. In developmental psychology, the scaffolding process is typically characterized as a child's temporary reliance on external structure in training activities, which leads to long-term transformation of the child's capacities. In recent attempts to clarify this concept for wider usage (e.g., Caporael, Griesemer, and Wimsatt 2014a, b; Neto et al. 2023), the temporariness of dependence on scaffolds is still seen as a typical, if not defining, feature of scaffolding explanations. In this paper, we follow Bill Wimsatt's footsteps (Wimsatt 2014a, 2019; Wimsatt and Griesemer 2007) in examining the development of skills that require complex developmental trajectories. Our cases are jazz improvisation and scientific expertise, both of which are distinctively social and improvisational. We argue that the social scaffolds required to reach the maturity of such expertise are continually required thereafter for maintenance and further development. This is because improvisational training is somewhat indistinguishable from improvisational performance, and performance in social expertise aims at interactions, communications, and rapport between interlocutors.
The compartmental epidemiological model is commonly used to study dengue dynamics; some of these models precisely consider the mosquito population, and others indirectly capture its role in disease transmission term. In this article, we have performed a comparative analysis between a simple SIR model and a vector-host interaction model (VH model) by fitting the dengue fever data of the ongoing outbreak in America. Parameter estimations for both models have been performed using the Nelder-Mead simplex algorithm, considering the normalized root mean square error (NRMSE) as an optimization function. The significance and reliability of the estimated parameters towards the models' predictions have been analysed through uncertainty and sensitivity analyses. Uncertainty analysis utilizing the Latin hypercube sampling (LHS) method has been performed to evaluate how various parameters within the models influence the basic reproduction number ([Formula: see text]). Sensitivity analysis for the basic reproduction number ([Formula: see text]), has been carried out by the partial rank correlation coefficients (PRCC) method. Additionally, we have computed the parameter regions ensuring the persistence of equilibrium points of both models. This study offers profound insights into model selection, parameter estimation, and forecasting future data trends for the ongoing dengue outbreak in America. However, this article focuses on exploring two key scientific questions: (1) Which type of compartmental model (SIR or VH) is more suitable to capture the trend of data on dengue fever for the ongoing outbreak in America? (2) Is America likely to face a prolonged dengue outbreak in the near future?
We present a neutral delay differential equation (NDDE) modification of the FitzHugh–Nagumo (FHN) model. One linear and three nonlinear variants are proposed to capture the interaction between delayed effects in the membrane potential and the stimulating current, including a delayed rate (neutral) term. We derive fixed points, compute eigenvalues, and obtain Hopf conditions to map regions of stability, instability, and oscillation. Parameter studies show how the neutral delay reorganizes dynamics and modulates the robustness of nerve firing. Numerical simulations quantify frequency, ISI, amplitude, and spike counts and reproduce canonical phenotypes: regular spiking adapts to large stimulus delays, intrinsic bursting yields rapid spikes, chattering shows high-frequency bursts with moderate delays, fast-spiking exhibits high rates, and low-threshold neurons adapt to high frequencies with small delays. Overall, the NDDE representation provides a compact, physically motivated framework in which time delay governs stability and synchronization, offering insight for diagnostic modeling and potential therapies for disorders with irregular firing.
Epidemiological surveillance systems often provide data on specific characteristics of an infected population. For instance, sex, geographical location, socioeconomic level and age of the registered individuals. This allows us to study the population divided into groups. However, information on the dynamics of infected people classified by group is not usually exploited when analyzing the evolution of an epidemic. In this work, we propose a tool to analyze how the spread of an epidemic is heterogeneous among different population groups. Based on records of infected individuals we identify synchronicity and causality interactions among population groups. Describing this dynamics and which population groups are the first focus of infection is essential for decision makers. We represent time series by population group and their degree of similarity using a weighted graph, and we apply a community detection algorithm to partition this graph. Each community is composed of synchronized age groups. The direction of interaction among different communities is identified using sample cross-correlation in a domain that can indicate causality. This is illustrated by considering age groups and using datasets of COVID-19 in Jalisco, Mexico and influenza A(H1N1) in the USA. In both cases, the proposed methodology detected which age groups show synchronized behavior across time, and which age groups influence the subsequent appearance of epidemic outbreaks in other groups.
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Instabilities and Turing patterns in stochastic spatiotemporal systems in which a fraction of an evolving population, after undergoing a series of dynamic transitions, returns to its original state, remain largely unexplored. Adopting an epidemic model incorporating reinfections as an exemplar of such a system, we present stability and pattern-formation analyses of the stochastic reaction-diffusion equations that represent the model. Saturation effects in epidemic spread lead to nonlinear considerations, while random environmental effects motivate a stochastic term. Turing bifurcation and the emergence of equilibrium patterns are analysed with respect to three fundamental parameters - reinfection, saturation, and noise intensity. Using higher-order stability analysis and stochastic averaging, we find the Turing instability and also uncover self–organized, distinct equilibrium patterns of infection spread. Additionally, results elucidating the effects of stochastic excitation and its intensity, as well as the competing influence of saturation and reinfection on stability and pattern formation, are presented. The results are also expected to be broadly significant beyond epidemic modelling, for studies of noise-induced instabilities and morphogenesis in spatiotemporal nonlinear dynamical systems.
This study presents a computational model that integrates bone remodeling dynamics with damage accumulation, focusing on both physiological and pathological conditions. Building upon Komarova’s classical model of osteoclast and osteoblast interactions, this work introduces fatigue-induced damage using a stress-life (S-N) approach. By simulating bone responses under sinusoidal and random mechanical loads, the model captures the cyclical nature of bone turnover. The results show that under normal physiological conditions, bone is able to repair microdamage and maintain structural integrity. However, in pathological scenarios such as osteoporosis and tumors, the remodeling cycle is disrupted, leading to an increase in damage accumulation and eventual structural failure. Through numerical simulations, the study also demonstrates the significant impact of fatigue on bone health, showing that repetitive mechanical loads, even below critical stress levels, can result in bone degradation over time. By capturing the accumulation of microdamage and its repair, the model offers potential applications in personalized medicine to assess fracture risks in varying stress and health scenarios. This approach provides a framework for understanding how different stress patterns contribute to bone damage and offers insights into the progression of bone diseases. The model could be extended using metabolic and age-related characteristics and serves as a potential tool for personalized medicine, helping to predict bone failure risks in individuals when they are submitted to repetitive mechanical loads.
Classical statistical analysis is a frequently employed methodology in numerous domains of genetic research. In recent times, however, there has been a notable increase in the interest accorded to the deployment of Bayesian statistics in the field of genetics, as it incorporates a priori hypotheses about genetic knowledge into the problem. The potential risk of developing a genetic disease is influenced by the patient's genetics, ethnicity, gender, age, and family history. The objective of this study is there[Formula: see text]fore to provide molecular pathologists working with genetic testing with a comprehensive overview of the basic principles of Bayesian analysis and genetic risk assessment. Furthermore, the study aims to develop a computer code that estimates the probability of transmission of genetic traits between generations and performs risk analysis within the framework of Bayesian logical inference. This framework facilitates the calculation of the probability of a specific hypothesis, whether it pertains to disease state or a determination of carrier status, by integrating familial data and/or the results obtained from genetic testing. The present algorithm was utilized for the purpose of evaluating the genetic risk of everyone within a given pedigree, in addition to predicting the likelihood of cystic fibrosis (CF) manifesting in human genetics. This objective was accomplished by employing transition matrices in Markov chains and subsequently calculating the final probability vector of the transmission of genetic traits. The primary function of this tool is to evaluate the genetic susceptibility of individuals within a family history to cystic fibrosis and to predict the probability of developing the condition. The results demonstrate the effectiveness of the proposed algorithm in performing reliable genetic risk assessments for patients and family members with cystic fibrosis disease or other autosomal recessive disorders.
To understand the dynamics of Alzheimer's disease, we formulate a generalized mathematical model based on three events: aggregation of disease-related proteins, activation of immune cells and initiation of inflammation. We incorporate functional forms in the model to represent the complex biological interactions between components related to Alzheimer's disease. We take explicit forms depending on the properties of functions in the model. We describe the system dynamics by locating biologically feasible steady states, determining stability properties and identifying the effective parameters. Parameters are estimated using two methods: biological literature and data fitting. We perform sensitivity and uncertainty analyses to identify the most influential parameters. Partial Rank Correlation Coefficient and scatter plots are used to visualize global sensitivity. Our results reveal that lower activation rate and higher proliferation rate of microglia may contribute to a reduction in toxic protein aggregate levels, thus slowing the disease's early progression.
The discipline of immunology has historically been foundationally framed by metaphors of war, portraying the body as a sovereign state defending its territory against foreign invaders. This paradigm, however, is not strictly a biological necessity but also a historical artifact of colonial logic that arguably limits our understanding of symbiosis, tolerance, and the nature of relational pathologies. This paper argues for a decolonial paradigm shift, proposing a comprehensive reframing of the immune system not as a military force but as a sophisticated system of communication, governance, and diplomacy within a multi-species community, the holobiont. We trace the colonial genealogy of war metaphors and expose its conceptual inadequacies in the face of modern biology, distinguishing between historical rhetorical resonances and causal scientific developments. Drawing inspiration from relational and ecological philosophies, we then propose a new conceptual lexicon, using the metaphor of the body as a quilombo, a diverse and resilient community. By separating canonical biological mechanisms from metaphorical interpretation, this framework reframes core immunological processes: inflammation becomes an urgent community assembly, the adaptive response a journey of information, and pathologies like autoimmunity, cancer, and immunodeficiency become crises of communication and social cohesion. Offered as a conceptual heuristic rather than a wholesale structural equivalent, this relational approach offers not only new avenues for research and therapy but also serves as a powerful pedagogical tool to foster a more holistic, integrated, and ecologically conscious view of life itself.
Bill Wimsatt and Mark Wilson are each the author of a body of work whose fruitfulness is rivaled only by its forbiddingness. Despite deep sympathies between their approaches and conclusions, their work has not yet been read together. This paper makes the case for doing so. We identify a shared question at the heart of their work: how is it that limited beings such as ourselves come to possess genuine knowledge of a complex world? We then show that Wimsatt and Wilson arrive at similar answers to this question. Over a range of topics (investigative strategies, the uses of models, and theoretical and conceptual structure), both scholars emphasize the functional messiness of science. This is complemented by a pragmatist-leaning philosophical methodology that recognizes that one of the core uses of knowledge is to scaffold the acquisition of more knowledge. The core of the paper traces the mutually supportive interplay between their philosophical doctrines and methods. We end with two brief discussions: one a defense of their winding, playful writing styles, the other a brief consideration of the relationship between their work and Arthur Fine’s natural ontological attitude.
In an in vivo situation, the tissue near a blood vessel is rich in oxygen supply compared to the one far from a blood vessel. In this article, our objective is to explore the effect of non-uniform oxygen supply on the development of the necrotic core of a tumor. We adopt a multiphase continuum-based approach to model the growth of a tumor. To simulate the model, a finite-difference-based numerical approach in line with the “Semi-Implicit Method for Pressure-Linked Equations" (SIMPLE) algorithm is adopted. Investigations reveal that the necrotic core develops near the boundary with lower oxygen concentration. The position of the necrotic core strongly depends on the oxygen supply through the tumor boundary. The results predict asymmetrical tumor growth under unequal oxygen supply at tumor boundaries. Also, it is hinted that a tumor with a larger necrotic core grows more slowly than a tumor containing a smaller necrotic core. The present model has the potential to anticipate in vivo and in vitro situations. The findings will be beneficial for clinicians and medical practitioners in predicting the stage of a tumor.
Biological systems depend on communication over distances, ranging from molecular gradients to systemic neuroendocrine and neuroimmune circuits. While many distance effects in biology are explained by well-established mechanisms such as diffusion, paracrine signaling, neural conduction, and extracellular vesicle trafficking, there are also claims of long-distance influences that may be mediated by consciousness, electromagnetic fields, or hypothesized morphic fields. This review synthesizes controlled laboratory evidence, evaluates speculative mechanisms, including quantum field effects and morphic resonance, and compares them with well-replicated findings in immunology and bioelectromagnetics. The Constrained Disorder Principle (CDP) is a novel theoretical framework that posits variability within constraints as essential for biological function and may underlie some of these effects. The paper discusses the debate over methodological rigor and replicability in research on nonlocal biological effects. While evidence supports the importance of distance in biological communication through known carriers, claims regarding consciousness and morphic resonance remain unverified, despite challenges to their validity. Future research must strike a balance between openness and rigorous experimental standards.
In this paper we study genetic variation at a highly polymorphic locus of a monoecious or dioecious population whose census and effective sizes differ and possibly vary independently over time. More specifically, we develop a general framework for the allele frequency spectrum (AFS) at this locus, and functions of the AFS. Examples of such functions are number of alleles, number of common and rare alleles, allelic diversity, gene diversity, higher order gene diversity and Hill numbers. We develop exact recursions for the expected AFS, and its functionals, with particular interest in populations that experience a rapid (a few generations) bottleneck followed by approaching a new equilibrium between mutation and drift. A grid-based numerical algorithm is developed, which is exact for small populations and approximate for large populations. This algorithm is exemplified with exact calculations for small populations that undergo a bottleneck, and approximate calculations for a moderately large population that rapidly decreases in size.
This paper considers the behavior of Wolbachia infection in a dioecious population as a discrete dynamical system. A recurrence relation is obtained as a function of the initial infected male/female frequencies and the cytoplasmic incompatibility of the population. Experimental data from Wolbachia-infected terrestrial isopod populations and a model proposed in Wolbachia-infected mosquitoes from the literature are compared with the proposed system.
The COVID-19 pandemic has presented an unprecedented global challenge, significantly impacting public health, economies, and daily life worldwide. In response to this crisis, scientists and researchers around the world have worked tirelessly to understand the virus, its transmission dynamics, and most importantly, to develop effective vaccines. However, questions remain about the comparative effectiveness of these vaccines, particularly in real-world scenarios. This paper aimed to address this critical issue by employing advanced statistical techniques, including time-varying copulas. In this study, we employed four types of copula, namely Gaussian, Student-t, Clayton, and Gumbel, to model the temporal association between vaccination and the emergence of COVID-19 cases. The results of this study suggested that the number of subsequent vaccinations, especially the first to fourth vaccines, has a significant impact on the occurrence and spread of COVID-19 under particular conditions. Furthermore, we proposed several modeling scenarios for COVID-19 cases based on their temporal interactions with the number of subsequent vaccinations. The findings of this research provided a comprehensive understanding of the temporal relationship between vaccination and its impact on reducing COVID-19 cases.
This paper deals with the computational modelling of the bioluminescence pattern formation in suspensions of luminous Escherichia coli bacteria. The aim of this work is to improve the reaction-diffusion-chemotaxis model by introducing modulation functions applied to the rates of the bacterial growth, the chemoattractant production and the oxygen consumption as well as to investigate the influence of the function form on the spatiotemporal pattern formation in an E. coli colony. The nonlinear two-dimensional-in-space model was used to simulate the pattern formation in aqueous cultures of bacteria along the inner lateral surface and along the three-phase contact line of a cylindrical micro-container. The simulated patterns are analysed in order to determine the form of the modulation functions and values of the model parameters closely matching patterns experimentally observed in a luminous E. coli colony. A linear stability analysis of the corresponding one-dimensional-in-space model is applied to determine values of the parameters triggering the self-organisation of the bacterial colony. The numerical simulation at the transient conditions was carried out using the finite difference technique.
The construction of a circular code through a biological process, particularly a primitive one in the absence of the protein world, has remained an open problem since the discovery of a maximal [Formula: see text] self-complementary trinucleotide circular code in genes in 1996 (Arquès and Michel, 1996). Circular codes are defined by their ability to recover the correct reading frame of genes at any position. While a class of 216 such trinucleotide codes has been identified, the KL method (Koch and Lehman, 1997), based on nucleotide probability products, generates only a restricted subclass of 88 [Formula: see text]-codes (Lacan and Michel, 2001). Revisiting this probabilistic framework 25 years later, we demonstrate that various classes of dinucleotide circular codes can be generated using a nucleotide probability product model (called Construction 2). We introduce the concept of transitive dinucleotide codes and prove new theorems characterizing their circularity and comma-free properties. Using codon usage from bacteria, archaea, and eukaryotes, 2 "universal" maximal dinucleotide circular codes are observed: [Formula: see text] in the codon site [Formula: see text] and [Formula: see text] in the codon site [Formula: see text] which can be deduced from [Formula: see text] by 1-letter cyclical permutation [Formula: see text] or identically by reversing permutation [Formula: see text]. Unexpectedly, we then show that, under the independence assumption, the dinucleotide code [Formula: see text] through Construction 2 from nucleotide frequencies in the codon sites 1 and 2, is a maximal dinucleotide circular code and is equal to the observed dinucleotide code: [Formula: see text]. These findings support a theoretical model in which dinucleotide circular codes may have originated from statistical properties of primitive nucleotide distributions, providing insights into the possible emergence of the genetic code.
Reaction-diffusion epidemic models play a central role in understanding how infectious diseases propagate through space and time, offering valuable insight for public health analysis. A key element of such models is the incidence function, which governs the nonlinear interaction between susceptible and infected populations. Despite extensive studies on various incidence formulations, the systematic identification of a suitable one for a given setting remains an open question. This work introduces a theoretical framework that interprets the selection of an incidence function as quantifying the contribution of several plausible formulations to the overall transmission dynamics, inferred from observational data. The resulting problem takes the form of a PDE-constrained optimization, where the objective is to determine the optimal weights in a convex combination of incidence functions that best fit the observed epidemic patterns. The analysis establishes the Fréchet differentiability of the parameter-to-state operator and derives first-order optimality conditions via an adjoint system. A numerical illustration, based on the Landweber iteration method, highlights the framework's potential as a mathematical tool to enhance modeling accuracy and support strategies aimed at disease prevention.