Dengue is one of the most widespread vector-borne diseases, with no specific medical treatment for a cure. In some cases, dengue infection progresses to hemorrhagic shock, a life-threatening condition that requires immediate medical intervention. At this critical stage, the timely infusion of intravenous fluids is essential for patient survival. However, unsystematic fluid administration can result in fluid overload and lead to adverse outcomes. In this study, we extend a minimal within-host dengue model to incorporate both plasma dynamics and intravenous fluid infusion. Using hematocrit level data from hospitalized dengue patients, collected between days 5 and 14 after the onset of fever, we estimate parameters related to intravenous fluid leakage via the Maximum Likelihood Estimation method. To determine the optimal fluid infusion strategy, we apply optimal control theory, proving the existence of a time-dependent optimal infusion strategy. The model is solved numerically using the forward-backward sweep method to determine the optimal fluid infusion rate. Our results indicate that, in contrast to the WHO guidelines, which recommend initiating fluid therapy at the highest infusion rate followed by a gradual taper, the optimal strategy begins with a lower infusion rate, increases gradually during the first 24 hours, and subsequently tapers off. Despite this markedly different infusion profile, the proposed strategy successfully maintains the plasma deficit within a clinically feasible range throughout treatment, thereby preventing the onset of shock. Furthermore, our analysis reveals that a broad range of infusion strategies can achieve the same therapeutic objective, allowing fluid administration to be tailored to the patient's clinical condition and the physician's judgment. The results also indicate the critical need for timely fluid therapy, demonstrating that fluid requirements rise significantly with delayed treatment. Additionally, the uncertainty regarding restoration increases with prolonged delays. While delays of a few hours in initiating fluid support can be compensated for, delays exceeding one day could be life-threatening.
The COVID-19 pandemic was strongly shaped by population behavioural responses. As cases surged, populations adopted contact precautions that reduced infection levels. This, in turn encouraged relaxation of control measures and prepared the ground for the next pandemic wave. Standard mathematical models do not account for this interaction between infection dynamics and behaviour. Here, we compare a standard transmission model to a coupled behaviour-disease model. We parameterise the models for 13 European countries, using data on SARS-CoV-2 infection incidence and stringency of control measures. We show how coupling behavioural and disease dynamics improves the ability of mathematical models to explain and predict crucial features of pandemic waves. Our findings demonstrate how behavioural feedback influences not only current transmission patterns but also the timing and magnitude of future pandemic waves. Such models could help decision-makers anticipate population responses to public health interventions, thereby contributing to scenario planning and intervention design.
Mechanical adaptation underlies mechanical homeostasis by enabling living systems to maintain characteristic mechanical states under sustained perturbations. Turnover-mediated remodeling contributes to this process by renewing or reorganizing internal structures under load across biological scales. While substantial advances have been made in understanding remodeling mechanisms, reduced-order system-level interpretations that relate feedback structure to characteristic timescales remain limited. Here, we develop a systems-based reduced-order formulation that provides a feedback representation for turnover-mediated mechanical adaptation processes. We first formulate a minimal actin-based model as a concrete starting point for linking turnover-mediated remodeling with mechanical response and identifying three system-level elements: a disturbance input, a remodeling state, and a regulated mechanical quantity. In the resulting local linearized representation, turnover-mediated remodeling dynamics can be represented in an integral-equivalent closed-loop form, yielding a local characteristic timescale determined by the local turnover and mechanical gains. A literature-based descriptive comparison shows that reported adaptation times lie near or above the corresponding turnover-related timescale ranges in representative multiscale systems. The present formulation provides a reduced-order system-level representation that relates turnover-mediated mechanical adaptation to feedback structure and characteristic timescales.
Early epidemic control often relies on case-finding operations. To assess their theoretical efficacy, we develop an infection-age structured early growth transmission model that incorporates symptom-based diagnosis, mass screening, and both forward and backward contact tracing. By deriving integral equations for the forward and backward tracing rates and coupling them with a Lotka-Euler-type equation for the early growth rate, we obtain a closed deterministic system. This system enables the computation of early growth rates and reproduction numbers under different case-finding scenarios. Using parameter values calibrated from the 2021 Yangzhou outbreak, the theoretical scenario comparisons show that diagnosis alone provides limited control of early epidemic growth, whereas the integrated case-finding scenario substantially suppresses transmission. The results further show that reducing the effective reproduction number below one requires stronger mass screening and contact tracing when infected individuals generate more secondary infections on average. Together, these findings indicate that the theoretical efficacy of case-finding operations depends jointly on intervention intensity and the effective transmission structure.
Vaccination is widely used to control the spread of infectious diseases. However, there is substantial evidence suggesting that the perceived immunity from vaccine drives the decrease of risk-awareness among vaccinated individuals, which results in the paradoxical increase of transmission risk, consequently leads to the counter-intuitive outcomes in disease control in the case of low vaccine effectiveness. In this study, we propose a novel method to quantify the counter-intuitive effects of vaccination in a complex environment with integrated dynamic factors. To this end, we begin by linking shifts in risk awareness to human behavior changes, and subsequently, we couple the evolution dynamic of human behaviors with the disease transmission dynamic system by applying game theory within a multi-scale model, distinguishing between vaccinated and unvaccinated populations. We calibrate the proposed model using vaccination data and epidemic data for the Omicron variant of COVID-19, spanning from 23/12/2021 to 20/09/2022 with two epidemic waves in Tokyo Metropolis, Japan. The calibration results provide the quantitative evidence that the vaccinated group exhibits a slower rate of risk perception to adjust their behaviors and a higher mental threshold for behavioral changes needed to protect themselves against infection. The model estimates that if vaccinated individuals had maintained the same level of NPI adherence and behavioral responses to infection prevalence as unvaccinated individuals, the accumulative confirmed cases during the study period would have been reduced by approximately 40% (although the exact proportion depends on the chosen time window). This finding highlights the importance of post-vaccination behavioral responses. Additionally, our analysis suggests an optimal vaccination coverage that minimizes accumulative infections by balancing the protective effects and the counter-intuitive effects of mass vaccination. Therefore, it’s of significant meaning to collect and disclose the epidemic data with vaccination status and timely evaluate the effective transmission among the population involving human behavior dynamics for designing the proper vaccination strategy, and improve the vaccine effectiveness and maintain high risk-awareness for vaccinated individuals would still be the key to flatten the epidemics.
This work is dedicated to a computational framework for predicting FGF2-induced cell proliferation in bovine satellite cells by integrating mechanistic and statistical modeling approaches covering signaling events up to the point of nuclear translocation of key effectors. The model advances previous studies by introducing a third signaling pathway, p38, alongside the established ERK and Akt pathways, to capture a more comprehensive view of signaling dynamics. Sensitivity and stability analyses are performed to assess the system’s robustness, specifically its ability to return to equilibrium following perturbations in initial conditions and kinetic parameters, and to identify key regulatory components. At the experimental level, the effects of media additives such as BSA (Bovine Serum Albumin), fetuin, and FGF2 on cell proliferation are explored using linear models, providing statistical insights into their contributions and interactions. To connect intracellular signaling with population-level dynamics, we propose an integrative model that incorporates time-dependent signaling features into a logistic-type population growth formulation. The model predicts cell proliferation based on simulated signaling outputs (area under curves and time-to-peak of pERK, pAkt, and Pp38) alongside experimentally controlled media components. The model’s predictive accuracy is assessed using experimental data across multiple cell lines of bovine satellite cells, demonstrating its ability to capture both within cell line variability and overall proliferation trends. This combination of mechanistic and statistical techniques may provide a robust framework for predicting cellular responses while addressing the challenge of modeling biological processes.
Antibiotic resistance remains an urgent challenge in medicine, shaped not only by genetic mechanisms but also by adaptation of bacteria under drug exposure. Comprehending these constraints requires integrating how translational capacity, nutrient supply, and global feedback determine recovery and survival. In this work, we integrate a refined mechanistic model of reversible protein synthesis inhibition with experimental measurements of bacterial growth. Our framework incorporates a metabolically limited recovery phase and a proportional feedback controller that links amino acid supply to ribosome synthesis. These refinements resolve unrealistic recovery dynamics predicted by earlier formulations and capture the physiological adaptation of Escherichia coli observed under pulse-dose exposure to tetracycline in both glucose- and glycerol-based media. The resulting framework unifies steady-state and transient antibiotic responses, explaining how metabolic limitation and feedback regulation shape cellular recovery following translational stress. Clinically, the model supports high-intensity antibiotic pulses of limited duration (on the order of several hours) that maximize inhibition while minimizing the selective window for resistance, providing a quantitative rationale for pulse- and intermittent-dosing strategies.
We introduce the concept of learning duration, defined as the minimal exposure time to an environmental signal required for a cell to undergo a fate change. We provide a formal definition of learning duration for hysteretic systems, which are canonical models for cell fate decision mechanisms. We hypothesize that when multiple fate decision pathways are regulated by the same driving signal, differences in their learning durations may enable the signal to discriminate between distinct cell fates. Such bi-hysteretic systems offer simple yet insightful models of graded cellular responses. As an application, we use numerical simulations on a published model, available in the BioModels Database, of the p53-dependent response to DNA damage, which can lead to either cell cycle arrest or apoptosis. We demonstrate that the system is bi-hysteretic and confirm the existence of distinct learning durations : approximately a few hours for cell cycle arrest, and over two days for apoptosis. These findings support the experimentally observed requirement for a sustained p53 signal to trigger apoptosis.
The infection of target cells by viruses involves several positive feedback loops. Many viruses increase the likelihood of infecting a target cell by increasing the local multiplicity of infection (MOI), and viruses like HIV-1 increase the availability of target cells by activating quiescent CD4+ cells. Positive feedbacks during viral infection can lead to bistability phenomena, meaning that a stable uninfected steady state co-exists with a stable infected steady state. This could have the consequence that too small viral inocula are unable to infect a host, which is a so-called Allee effect, and that crippled viruses with a low fitness are nevertheless able to persist. By mathematically modeling the acute phase of human HIV-1 infections with a form of immune activation that increases target cell levels, and an infection rate that increases with the MOI, we find that Allee effects can occur for a wide range of parameter values. Because the MOI feedback is instantaneous and immune activation feedback takes time, this parameter range is somewhat larger for MOI feedback. Combining both feedbacks increases the parameter domain. As Allee effects allow the growth rate to increase over time, viral infections can grow faster than exponential, which sometimes occurs during the rebound of virus when treatment is interrupted. Bistability due to immune exhaustion can coexist with the bistability due to a positive feedback, and approaching the exhausted state can be subjected to similar Allee effects as approaching an immune-controlled chronic infection.
Because exact likelihood is often intractable, likelihood-free inference plays an important role in population genetics. Indeed, several methodological developments in Approximate Bayesian computation (ABC) were inspired by applications in population genetics. Here, we explore a novel combination of recently proposed ABC tools capable of handling high-dimensional summary statistics and apply them to infer selection strength and the number of selected loci from experimental evolution data. While several methods infer selection strength at the single-nucleotide polymorphism (SNP) level, our approach provides additional information about the selective architecture, including the number of selected positions in a candidate window of interest. Providing such additional information is non-trivial, as the spatial correlation induced by genomic linkage can produce selection signals at neighbouring SNPs. A further advantage of our approach is that it readily quantifies uncertainty via the ABC posterior. On both simulated and real data, we demonstrate promising performance. Our results suggest that this ABC variant may also prove useful in broader applications.
Borrelia burgdorferi (Bb) is a tick-borne zoonosis. Humans are not competent for transmission, but can become infected and develop Lyme disease (LD) via the bite of an infected blacklegged tick. Over the last decades, there has been a sustained increase in Borrelia prevalence in wildlife in North America, leading to an increase in spillover events, particularly in residential areas that border woodland. Understanding tick ecology is essential for predicting the spread of LD, informing control strategies, and assessing the impact of environmental changes. In this study, we develop a hybrid deterministic-stochastic metapopulation model for tick population dynamics in a fragmented peridomestic environment. Our principal aim is to elucidate how deer movement and the treatment of deer with acaricides affect the density of infected blacklegged nymphs (DIN) and the parasite basic reproduction number R0. Deer are primary hosts for adult ticks and can move over large distances, transporting feeding ticks in the process. Deer tend to visit peridomestic areas in small numbers. Consequently, deer location is inherently stochastic and the tick population dynamics are drawn into this stochasticity. When we implement the model for a simple landscape consisting of two patches connected by deer movement we find that the DIN quasi-steady state values are reduced if the acaricides administered to deer are more effective, last longer, or are applied more frequently. When deer movement behaviour is biased towards areas with higher feeder availability (independent of whether they include an acaricide treatment), the redistribution deer and the transportation of ticks by moving deer can drive up the local DIN even if those feeders include an acaricide treatment and mice are targetted with acaricide treatment elsewhere. Our results suggest that maintaining deer feeders for acaricide administration in land away from peridomestic areas could be a more effective strategy for reducing human infection risk than placing those feeders in peridomestic areas. Since this strategy concentrates the tick population in the area with the feeder, further depletion or eradication may be possible if acaricide is also administered to the mice there.
Bone remodeling in the mandible is governed by the interplay between local mechanical loads, cellular population dynamics, and overload-induced resorption. While mastication is the primary physiological driver of mandibular adaptation, low-magnitude vibration has emerged as a promising noninvasive adjunct to enhance peri-implant bone stability. However, the mechanistic interaction between vibration and chewing-induced stimuli remains insufficiently clarified.This study presents a hybrid mechanobiological model that integrates a reaction-diffusion formulation for osteoblast, osteoclast, and mediator fields with a density evolution law combining adaptive regulation and overload penalization. The framework incorporates accumulated stimulus dynamics, a threshold-regulated lazy zone, and frequency-dependent vibratory modulation of cellular activity. Numerical simulations were performed under controlled physiological and mechanical conditions using spatially resolved density fields and Gaussian-distributed masticatory stresses.The model reproduced the canonical biphasic response of bone adaptation, with an initial anabolic phase followed by stabilization governed by overload-driven resorption. Under chewing alone, the density evolution progressively approached a quasi-stationary regime near 1.02-1.03 g/cm3, depending on load magnitude. When vibration was superimposed, a strong frequency-dependent anabolic effect emerged: 40 Hz increased steady-state density by approximately 3.5%, whereas 120 Hz produced gains near 10% (0.08-0.10 g/cm3), consistent with 80-100 HU changes measurable by CBCT. Spatially, mastication alone generated localized densification, while vibration broadened and homogenized the anabolic region, particularly at 120 Hz. Cellular simulations revealed accelerated and synchronized reductions in osteoblast and osteoclast populations under vibration, indicating enhanced mechanotransductive efficiency rather than increased metabolic demand. The agreement between simulated density gains and spatial adaptation patterns demonstrates that the proposed hybrid model captures key mechanobiological features of mandibular adaptation. The framework offers a rigorous and computationally efficient tool for predicting peri-implant bone remodeling under combined masticatory and vibratory stimuli, supporting the development of patient-specific vibration-based therapeutic strategies in oral and maxillofacial biomechanics.
Despite extensive studies of single hair-bundle dynamics, comparatively little attention has been paid to the collective dynamics arising in coupled hair-bundle systems. In this work, we investigate the collective dynamics of coupled hair bundles using a simplified dimensionless mechanical model that captures the essential nonlinear features of hair-bundle activity. We focus on two physically motivated interaction mechanisms: elastic and viscous coupling between neighboring bundles. The stability of synchronized motion is first analyzed using the master stability function framework and complemented by extensive numerical simulations. Our results demonstrate that within the present model, viscous coupling is significantly more effective than elastic coupling in promoting stable synchronization across a wide range of system parameters. Beyond complete synchronization, the network exhibits a variety of complex collective states, including non-stationary chimera patterns and clustered dynamics with distinct dynamical behaviors. Finally, we establish the occurrence of coherence resonance in the network, showing that an intermediate level of noise can enhance temporal regularity in the absence of external periodic forcing. These findings provide new insights into the mechanisms governing collective phenomena in interacting hair-bundle systems.
Epidemic control is inherently dynamic because viral transmissibility and human behavior co-evolve and vary across spatial scales. Consequently, identical intervention strategies can yield divergent outcomes depending on regional connectivity, temporal changes in transmission, and the relative costs of control. Many existing analytical and policy frameworks, however, assume fixed transmission rates or rely on static thresholds, limiting their ability to guide effective interventions in heterogeneous and evolving epidemic landscapes. We present a mathematical framework that couples a time-varying, multi-patch SEIIR model with reinforcement learning to generate adaptive, region-specific social-distancing strategies under varying cost scenarios. Using COVID-19 incidence and mobility data from 17 administrative regions in South Korea, we estimate time-varying transmission and construct a decision environment in which an agent observes epidemiological states, selects intervention intensities for each region, and receives rewards that integrate epidemiological and economic costs. In the early period, low intervention costs lead the learned policy to impose strong early actions in highly connected metropolitan regions, suppressing incidence after a single peak. Under high costs, sustained control is limited to Gyeonggi Province, allowing persistent circulation elsewhere. In the later period, cost considerations dominate, and high intervention costs suppress actions even during substantial epidemic waves. These results demonstrate that rapid temporal shifts in transmissibility can render strict suppression suboptimal and that optimal strategies may require tolerating ongoing transmission. They highlight the importance of adaptive, spatially explicit control frameworks that integrate mechanistic epidemic models with RL approaches.
Harmful algal blooms in eutrophic waters motivate the development of effective and environmentally compatible control strategies. Algicidal bacteria can inhibit algae through direct contact (enzyme-mediated cell-wall disruption) and indirect action via secreted extracellular algicidal compounds. Guided by experimental observations, we develop a mechanistic ordinary differential equation model that integrates both pathways and explicitly represents three lysis modes: bacterial suspension, bacterial cells, and cell-free filtrate. The model reproduces observed time courses of algal density and bacterial abundance across treatments through parameter estimation, and it reveals a rich dynamical structure including forward and backward bifurcations, transcritical and saddle-node bifurcations, and Hopf bifurcations, implying threshold responses, potential bistability, and oscillatory regimes under plausible conditions. When the initial algal density is 105 cells/ml, the predicted algicidal rates by day 6 are 99.99%, 99.99%, and 84.2% for bacterial suspension, bacterial cells, and filtrate, respectively; for 106 cells/ml the corresponding rates decrease to 82.5%, 69.38%, and 45.1%. Analysis indicates that direct lysis is dominant, while indirect lysis provides auxiliary suppression and can act synergistically with direct effects to reduce algal biomass. The model further predicts delayed and weakened control when initial algal density exceeds a critical level associated with severe blooms ( ∼ 106 cells/ml), and we provide forecasts for an initial density of 107 cells/ml.
Dictyostelium discoideum (Dd) aggregation is driven by propagating waves of cyclic adenosine monophosphate (cAMP), which coordinate chemotactic motion across large cell populations. While classical models emphasize nearest-neighbor signaling via diffusive relay, growing evidence highlights the importance of long-range interactions (LRIs) in shaping wave dynamics. Here, we investigate how the interaction range influences the evolution of cAMP waves using a two-dimensional discrete FitzHugh-Nagumo-type framework. Our simulations show that LRIs act as a key control parameter governing pattern formation, yielding three distinct regimes: multi-spiral turbulence at weak coupling, coherent spiral organization at intermediate coupling, and global synchronization or homogenization at strong coupling. These transitions are quantitatively characterized using synchronization measures, spatial correlations, and spectral analysis, revealing a shift from broadband spiral activity to coherent oscillations. A weak periodic forcing term is introduced to probe the interplay between excitability and long-range coordination while preserving intrinsic dynamics. The predicted frequencies, correlation lengths, and dynamical regimes are consistent with experimental observations, demonstrating that the model captures biologically relevant scales and provides a framework linking microscopic excitability to macroscopic pattern formation.
Mathematical models are often used to predict the impact of infectious disease interventions. Most models, however, neglect how the intervention might influence patterns of contact within the population, and consequently change the dynamics of the epidemic. Here we introduce a mathematical model of disease transmission where contact rates change in response to a vaccination campaign. We explore two scenarios: homogeneous mixing, where contact rates increase uniformly across the population as vaccination coverage increases, and heterogeneous mixing, where the probability of contact depends on the vaccination statuses of the two individuals involved. We derive the effective reproduction number as a function of vaccine coverage and its transmission-blocking effectiveness, and show the conditions under which an increase in vaccination coverage leads to a growing number of infections. The model is then parameterised using United Kingdom COVID-19 data between 2020 and 2022 and vaccine-dependent contact rates are estimated using contact survey data. We observe that contact increases concordantly with vaccination coverage. Implementing this relationship in the model, we infer that the epidemiological impact of the rising contact rate was tempered by a mixing structure where contacts predominantly involve at least one vaccinated individual.
We extend the equivalence between the two-allele Moran process and the two-candidate voter model in a finite population to the multi-allele Moran process with parent-independent mutation and a multi-candidate voter model. This exact mapping yields a concise derivation of the finite-population Dirichlet-multinomial stationary distribution for the labeled allele-count vector in fully mixed populations of size n with an arbitrary number m of alleles. It also gives the critical mutation threshold uc=1/(m+2n-2), making its dependence on m explicit. We then extend the analysis to randomly connected populations modeled by Erdős-Rényi (ER) interaction networks. Under an ER mean-field reduction, the Moran stationary distribution and the corresponding diversity threshold uc remain unchanged and coincide with the fully mixed results, even though the associated voter model exhibits amplified zealot influence on sparse random networks. Finally, simulations on several sparse and structured network topologies, including Erdős-Rényi, scale-free, ring, and small-world networks, show that structural heterogeneity can substantially reshape the stationary allele distribution and, consequently, the level of genetic diversity. More broadly, the correspondence developed in this paper turns the voter-model perspective into a tractable framework for analyzing the multi-allele Moran process, yielding the stationary law, the critical mutation threshold, and new insight into how network structure shapes stationary diversity.
