Nonlinear Dynamics

Voltage perturbations to a repetitively firing Hodgkin-Huxley (HH) model of neuronal spiking in the bistable regime with coexisting limit cycle and stable steady node can either lead to the spikes phase resetting or collapse to the stable steady state. The latter describes a non-firing hyperpolarized quiescent state of the neuron despite the presence of constant external current. Using asymptotic phase response curve (PRC), the impact of voltage perturbations on a repetitively firing HH model is studied here while it is diffusively coupled to another HH model under identical external stimulation. It is observed that the pre-perturbation state of synchronization and the coupling strength critically determine the PRC response of the perturbed HH dynamics. Higher coupling strengths of perfectly in-phase (anti-phase) synchronized HH models shrink (expand) the combinatorial space of perturbation strengths and the oscillation phases causing collapse to the quiescent state. This indicates reduced (enlarged) basin of attraction, viz. the null space, associated with the steady state in the HH phase space. The findings bear important implications to the spiking dynamics of diverse interneurons, as well as special cases of pyramidal neurons, coupled through electrical synapses via. gap junctions, and suggest the role of gap junction plasticity in tuning vulnerability to quiescent state in the presence of biological noise and spikelets.

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

BackgroundTo control leishmaniasis, chemotherapy drugs are currently under development. However, these drugs often exhibit poor efficacy and are associated with toxicity, adverse effects, and drug resistance. At present, no specific drug is available for the treatment of leishmaniasis. Meanwhile, vaccine research is ongoing. Recent studies have analysed some experimental vaccines using mathematical models. AimIn previous work, drug targeting was focused on the entire human body rather than specifically addressing infected macrophages and parasites. In our current approach, we aim to eliminate infected macrophages and parasites through nano-drug design. Specifically, we utilise two types of nanoparticles: iron oxide and citric acid-coated iron oxide. Moving forward, we plan to advance this strategy using mathematical modelling of macrophage-parasite interactions. MethodsWe design PDE-based models of macrophages and parasites, incorporating cytokine dynamics, to support nano-drug development. Drug efficacy is estimated using posterior distributions to analyse phenotypic fluctuations of macrophages and parasites during the design phase. We investigate implicit and semi-implicit treatment schemes, focusing on energy decay properties. To model drug flow during treatment, we introduce a three-phase moving boundary problem. Comparative analyses are conducted to evaluate macrophage and parasite behaviour with and without treatment. Finally, the entire framework is implemented within a virtual lab environment. ResultsThe results show that the nano-drug exhibits better efficacy compared to combined drug doses. We analysed and compared two types of nano-drug particles: iron oxide and citric acid-coated iron oxide. We discuss how the drug effectively targets and eliminates infected macrophages and parasites. ConclusionOur models results and simulations will support researchers conducting further studies in nano-drug design for leishmaniasis. These simulations are performed within a virtual lab environment.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity.

A key component of intraneuronal communication is the modulation of postsynaptic firing frequencies by stochastic transmitter release from presynaptic neurons. The time interval between successive postsynaptic firings is called the inter-spike interval (ISI), and understanding its statistics is integral to neural information processing. We start with a model of an excitatory chemical synapse with postsynaptic neuron firing governed as per a classical integrate-and-fire model. Using a first-passage time framework, we derive exact analytical results for the ISI statistical moments, revealing parameter regimes driving precision in postsynaptic action potential timing. Next, we extended this analysis to include both an excitatory and an inhibitory presynaptic connection onto the same postsynaptic neuron. We consider both a fixed postsynaptic-firing threshold and a threshold that adapts based on the postsynaptic membrane potential history. Our analysis shows that the latter adaptive threshold can result in scenarios where increasing the inhibitory input frequency increases the postsynaptic firing frequency. Moreover, we characterize parameter regimes where ISI noise is hypo-exponential or hyperexponential based on its coefficient of variation being less than or higher than one, respectively.

As social beings, humans make decisions partly based on social interaction. Observing the behavior of others can lead to learning from and about them, potentially increasing trust and prompting trust-based behavioral changes. Observation-based decision making involves different neural structures. The orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC) are known as neural structures mainly involved in processing emotional and cognitive decision values, respectively, while the anterior cingulate cortex (ACC) plays a pivotal role as a social hub, integrating the afferent expectancy signals from OFC and LPFC. This paper presents a neurocomputational model of the interplay between observational learning and trust, as well as their role in individual decision-making. Our model elucidates and predicts the emotional and rational behavioral changes of an individual influenced by observing the action-outcome association of an alleged expert. We have modeled the neurodynamics of three cortical structures (OFC, LPFC, and ACC) and their interactions, where the neural oscillatory properties, modeled with Dynamic Bayesian Probability, represent the observers attitude towards the expert and the decision options. As an example of an everyday behavioral situation related to climate change, we use the choice of transportation between home and work. The EEG-like simulation outputs from our model represent the presumed brain activity of an individual making such a choice, assuming the decision-maker is exposed to social information.

Based on the 2023 Global Burden of Disease (GBD) database, this study analyzed the global burden of preterm birth from 1990 to 2023 and predicted its development trend by 2050, while exploring the disparities in disease burden across regions with different Socio-demographic Index (SDI) levels, income groups and countries. A retrospective trend analysis was conducted to collect data on preterm birth incidence, prevalence, death and disability-adjusted life years (DALYs) in 204 countries and regions worldwide from 1990 to 2023 from the GBD 2023 database. ARIMA model (p=2,d=1,q=1) and grey prediction model (GM(1,1)) were combined to predict the preterm birth burden from 2023 to 2050. In 2023, preterm birth was the primary cause of the global neonatal disease burden, with its four core indicators significantly higher than other neonatal diseases. From 1990 to 2023, the global incidence, death and DALYs of preterm birth decreased to 0.91, 0.44 and 0.52 times of the 1990 levels respectively, while the prevalence increased to 1.54 times of the baseline. Projection results showed that by 2050, the incidence, death and DALYs of preterm birth would drop to 0.79, 0.08 and 0.32 times of the 2023 levels, and the prevalence would rise to 1.23 times of 2023. Low SDI regions, lower-middle income countries, as well as India and Nigeria, bore the heaviest disease burden. Over the past three decades, the global acute health burden of preterm birth such as death has decreased notably, but the continuous rise in prevalence and severe regional and age disparities remain prominent public health challenges. The 0-6 days and 6-11 months age groups are the key time windows for preterm birth intervention. It is urgent to implement targeted prevention and control measures for low SDI regions and lower-middle income countries to reduce the global burden of preterm birth.

Sylvatic Yellow Fever (YF) is an infectious mosquito-borne disease with significant epidemiological relevance due to its widespread distribution and high lethality for human and non-human primates, particularly in tropical regions of the planet such as in Brazil. Identifying regions and periods of high environmental suitability for the occurrence of YF is essential for preventing or mitigating its burden, as it enables the efficient allocation of surveillance efforts, prevention, and implementation of control measures. Environmental modeling of YF occurrence has proven to be an effective approach toward this goal; however, its effectiveness strongly depends on the modeling framework's capabilities as well as the spatial and temporal precision of all associated data. We propose a fine-scale geospatial modeling of YF environmental suitability that is based on a generative machine-learning ensemble method built on a large set of high-resolution environmental covariates. First, we take the spatiotemporal statistical description of the environment of each of the 545 YF cases from 2019--2024 up to 30 m/monthly resolution at three buffer scales: 100 m, 500 m, and 1000 m ratios. Then, we perform a feature selection and train hundreds of One-Class Support Vector Machine submodels to form a robust ensemble model, whose predictions are projected to a 1x1 km resolution grid of Brazil under several metrics, exceeding seven million ensemble evaluations. The predictions ranked the Southern Brazil region with the highest mean suitability for YF, with a level of 0.64; Southeast comes next with 0.46, followed closely by Central-West region (0.44), North (0.39), and finally Northeast (0.28). The model exhibited high uncertainty for the North region, indicating that data collection efforts are much needed in this region. As for the environmental covariates, a feature analysis pointed out that Land use and cover accounts for the largest influence in the model output.

Evolutionary therapies regulate heterogeneous populations by altering selective pressures through treatment sequences in cancer and infections. This letter develops an invariant-set framework for treatment-induced containment based on positive triangular invariant sets. For periodically switched systems, sufficient conditions are derived for the existence of such invariant regions. Robustness with respect to mutation is established by showing that the invariant simplex persists under small perturbations of the subsystem matrices. In the two-phenotype case, the analysis yields an explicit mutation threshold that separates regimes in which therapy cycling maintains containment from regimes in which mutation can enable evolutionary escape. Simulations illustrate the geometry of the invariant sets and the role of mutation and dwell time in containment robustness.

Bangladesh is experiencing emerging burden of Non-Communicable Diseases (NCDs). Non-communicable diseases (NCDs) are the emerging as major cause of morbidity and mortality, accounting for 61% of deaths in Bangladesh. The study aims to describe the prevalence of NCDs among pregnant women in teagardens in Moulvibazar district. Three teagardens of Sreemongol upazila in Moulvibazar district was selected randomly. The pregnant women were considered for collecting the NCD related information. A sample size of 86 was purposively selected based on relevant literature review. Data was collected by conducting face to face interview with the respondents through pre-tested semi-structured questionnaire. Data was analyzed with the help of SPSS Version 24 Software. For effective use of limited resources, an increased understanding of the shifting burden and better characterization of risk factors of NCDs including Hypertension is needed. Average age of the women attended for screening test was 23 (15-45) years. More than 47% women were found with Gravida 1. The mean duration of pregnancy was found 18.8 weeks. Above 24% percent of GDM women were found at low blood pressure but 2% were identified at high blood pressure. 28% were found underweight with BMI calculation but 11% were identified with overweight. The challenges tests for blood sugar findings of women were found 12.7% GDM positive (7.8-<11 mmol/L). About 16.5% had complications during pregnancy including anaemia, eclampsia, edema, diarrhoea etc. A community based NCDs surveillance model could be developed through participation Government health managers, experts and stakeholders, which were taken by local health system for implementation.

A mean field model (MFM) is a mesoscopic description of neuronal population dynamics that can reduce the complexity of neural microcircuits into equations preserving key functional properties. The generation of a MFM is a complex mathematical process that starts with the incorporation of single neuron input/output relationships and local connectivity. Once neuron electroresponsiveness and synaptic properties are defined, in principle, the process can be automatized. Here we develop a tool for automatic MFM derivation from biophysically grounded spiking networks (Auto-MFM) by performing micro-to-mesoscale parameter remapping, estimating input/output relationships specific for different neuronal populations (i.e., transfer functions), and optimizing transfer function parameters. Auto-MFM was tested using a spiking cerebellar circuit as a generative model. The cerebellar MFM derived with Auto-MFM accurately reproduced cerebellar population dynamics of the corresponding spiking network, matching mean and time-varying firing rates across a wide range of stimulation patterns. Auto-MFM allowed us to model and explore physiological and pathological circuit variants; indeed, it was used to map ataxia-related structural connectivity alterations of the cerebellar network, in which Purkinje cells with simplified dendritic structure altered the cerebellar connectivity. Furthermore, Auto-MFM was used to create a library of cerebellar MFMs by sweeping the level of the excitatory conductance at mossy fiber - granule cell synapse, which is altered in several neuropathologies. Auto-MFM is thus proving a flexible and powerful tool to generate region-specific MFMs of healthy and pathological brain networks to be embedded in brain digital models.

This study aimed to examine whether Humanin-G (HNG), a mitochondrial derived peptide with cytoprotective properties, could improve the retinal function and gene expression profiles after intraperitoneal injections to Royal College of Surgeons (RCS) rats with Retinal Pigment Epithelium (RPE) dysfunction and retinal degeneration. Starting at postnatal day 21 (p21), RCS rats received twice a week intraperitoneal injections of either Low Dose HNG (0.4 mg/kg), High Dose HNG (4mg/kg), or sham-saline for 1 or 4 weeks. Visual function was tested with full field scotopic & photopic electroretinography (ERG) and optokinetic testing (OKT) 1 and 4 weeks after first injection (WAFI). The rats were euthanized after the ERG and OKT (1 or 4 WAFI) and the dissected retinas and RPE were collected for RNA, cDNA and Quantitative Real-time PCR (qRT-PCR) analysis. The results of our study showed that high dose (4mg/kg) HNG at 4 WAFI was associated with the largest change in gene expression in the RPE and retina of treated animals, altering expression of genes involved in apoptosis, oxidative stress, inflammation and retinal/RPE function. Analysis of a and b waves from scotopic and photopic ERG showed no difference between either low or high dose of HNG and sham injection at 4 WAFI. However, at 4 WAFI, the visual acuity in rats treated with high dose HNG showed significant improvement as compared to the rats treated with low dose of HNG or saline. Most significantly, our findings support that HNG administered IP can modulate RPE/neuroretina cells and improve vision, thus may be a potential treatment for retinal degeneration diseases.

We introduce a spectral existence criterion for the evolution of cooperation in the form of the inequality{lambda} maxb > c, where{lambda} max is the leading eigenvalue of an interaction operator encoding population structure, and b and c represent benefit and cost tradeoffs, respectively. Nowaks five rules for the evolution of cooperation correspond to cases in which the cooperation condition reduces to a scalar assortment coefficient. These results follow from the Price equation, which sheds light on a long-standing debate on the role of inclusive fitness and evolutionary dynamics in explaining the evolution of cooperation.

The basic reproduction number of an infectious disease is known to depend on the structure of contacts between individuals in a population. This relationship has been explored mathematically through two well-known models: one which depends on a matrix of contact rates between different demographic groups, and another which depends on the variability of contact rates over the population. Here we introduce a model that combines and generalises these two approaches. We derive a formula for the basic reproduction number and validate it through comparisons to simulated outbreaks. Applying this method to contact survey data collected in Belgium between 2020 and 2022, we find that our model produces higher estimates of the basic reproduction number and larger relative changes over periods when social contact behaviour was changing during the COVID-19 pandemic. Our analysis suggests some practical considerations when using contact data in models of infectious disease transmission.

Infectious disease dynamics are strongly shaped by human mobility, social structure, and heterogeneous contact patterns, yet many epidemic models do not jointly capture these features. This study develops a spatial metapopulation epidemic model incorporating recurrent group-switch interactions to represent real-world transmission processes. Building on the Movement-Interaction-Return framework, the model integrates household structure, age-stratified contacts, and mobility between locations within a single SEIR framework. Using UK demographic, mobility, and social contact data, the model quantifies how within- and between-group interactions, mobility rates, and location connectivity influence epidemic spread. Both deterministic and stochastic simulations are implemented to analyse outbreak dynamics, variability, and fade-out probabilities for COVID-19-like and Ebola-like infections. Results shows that highly connected locations drive faster transmission, earlier epidemic peaks, and greater difficulty in containment, whereas larger but less connected locations tend to produce slower, more localised outbreaks despite their population size. Comparative analysis reveals that COVID-19-like infections spread rapidly and remain difficult to control even under interventions, while Ebola-like infections exhibit slower dynamics and are more effectively contained, particularly under targeted measures. Non-pharmaceutical interventions, particularly widespread closures, substantially reduce infections, hospitalisations, and deaths, although effectiveness depends on timing and pathogen characteristics. These findings highlight the importance of integrating mobility, clustering, and demographic heterogeneity to inform targeted and effective epidemic control strategies.

Malaria persists worldwide, exerting its greatest impact in sub-Saharan Africa. This study develops and uses a mathematical model to assess how sub-optimum versus optimum treatment of malaria drives asymptomatic infections, immunity build-up, and sustained transmission, providing insights for effective control. Fitted to case data from Kenya and Nigeria, the framework is used to quantify the burden of malaria and the additional cost associated with sub-optimum treatment. Global sensitivity analysis identifies mosquito demographic parameters, biting rates, and malaria treatment rate among major disease drivers under sub-optimum treatment, emphasizing the need for integrated strategies that improve access to optimum treatment and reduce mosquito-human contact. Model simulations show that sub-optimum treatment amplifies asymptomatic prevalence, sustaining/increasing malaria transmission and burden. Further simulations reveal that optimum treatment could avert more than one-third of infections and deaths, while asymptomatic infections contribute up to $96%$ ($75%$) of malaria-related Years Lived with Disability in Kenya (Nigeria). Cost analysis shows that optimum treatment lowers malaria burden significantly and can reduce annual total treatment costs by $\approx $12$ million, underscoring the substantial economic and public health gains of limiting sub-optimum care. This study demonstrates that effective and sustained malaria control requires strengthening adherence to treatment, minimizing sub-optimum treatment, reducing mosquito-human contact, and targeting asymptomatic carriers to curb hidden transmission and reduce long-term health and economic losses.

Mainland China experienced multiple waves of COVID19 pandemic during 2020 2022, driven by emerging variants and changes in public health and social measures (PHSMs). We developed a hypergraph-based Susceptible Vaccinated Exposed Infectious Recovered Susceptible (SVEIRS) model to reconstruct epidemic dynamics across 31 provinces, capturing transmission heterogeneity associated with clustered contacts. We assessed key characteristics of transmission at national and provincial levels during four outbreak periods: initial, localized predelta, Delta, and widespread Omicron, which accounted for 96.7% of all infections. We found significant diversity in transmission contributions across cluster sizes, with a small fraction of larger clusters responsible for a disproportionate share of infections. Counterfactual analyses showed that reducing clustersize heterogeneity, while holding overall exposure constant, could have lowered national infections by 11.70 to 30.79%, with the largest effects during Omicron period. Ascertainment rates increased over time but remained spatially heterogeneous with a range: (14.40, 71.93)%. Population susceptibility declined following mass vaccination (to 42.49% in Aug 2021, nationally) and rebounded (to 89.89% in Nov 2022) due to waning immunity with variations across the provinces. Effective reproduction numbers displayed marked temporal and spatial variability, with higher estimates during Omicron. Overall, these results highlight critical role of group contact heterogeneity in shaping epidemic dynamics.

Scrub typhus remains a persistent public health concern with strong spatial and temporal variability. This study analyses the spatio-temporal distribution, clustering patterns, and forecasting of scrub typhus across five districts, Chittoor, Ranipet, Tirupattur, Vellore, and Tiruvannamalai, using long-term surveillance data from May 2005 to May 2024. We applied spatio-temporal exploratory analysis to identify trends, seasonal behaviour, and inter-district heterogeneity in disease incidence. Hotspot analysis was conducted using the Getis-Ord Gi* statistics to detect statistically significant hotspots and coldspot clusters and examine their evolution over time. To support decision-making, we developed statistical, machine learning (ML), and deep learning (DL) based forecasting models using monthly scrub typhus and climatic features. Root mean square error (RMSE), and R-square error (R2) evaluation metrics are used to compare the performance of the prediction model. Scrub typhus shows clear and recurring seasonal peaks across all five districts, and incidence increases are associated with precipitation, dew point, relative humidity, and vegetation cover. Temperature shows a strong negative correlation, while relative humidity and normalized difference vegetation index (NDVI) show strong positive correlations in all districts. Hotspot analysis identifies Vellore and Chittoor as persistent core transmission zones, with weaker clustering in surrounding districts. Forecasting results indicate that model performance varies by location. The results reveal persistent hotspots, clear seasonal signals, and short-term forecasts across districts. This integrated spatiotemporal and forecasting framework provides actionable insights for targeted surveillance and timely intervention strategies to control scrub typhus.

An effective vaccine capable of inducing sterile protection against Plasmodium, the causative agent of malaria, is critical to aid global eradication. Whole-organism vaccines using liver-infective sporozoites provide high levels of sterile protection against pre-erythrocytic infection. Yet, determinants of sporozoite immunogenicity remain poorly characterized. Using rodent models of vaccination, we demonstrate that the ability of Plasmodium sporozoites to actively migrate through multiple host cells prior to infecting hepatocytes is required for sterilizing immunity, regardless of the time of intrahepatic development of immunizing parasites. We further establish that host cell traversal is sufficient to trigger robust protection against Plasmodium hepatic infection. Impaired cell traversal precludes protective liver-resident memory CD8 T cell responses following vaccination, but not the production of anti-plasmodial antibodies. Our findings challenge the prevailing notion that intrahepatic parasite development is the sole determinant of whole-sporozoite vaccination-induced protection, and highlight parasite behavior traits as critical immunogenic events shaping sterilizing cellular immunity against Plasmodium liver stages.

Have European gray wolves recovered? Despite an increase to [~]21,000 wolves (Canis lupus), our genomic analyses reveal significant risks to their long-term viability. We analyzed over 200 whole-genomes spanning five major European populations. Rather than a single recovering population, European wolves form a mosaic of isolated, independently evolving lineages, mostly diverging in the late Pleistocene. All lineages have contemporary effective population sizes below the threshold for long-term viability (Ne [&ge;] 500) and show extensive inbreeding. Runs of homozygosity reveal population-specific inbreeding histories spanning recent to deep timeframes. Most lineages exhibit higher realized than masked genetic load, indicating emerging inbreeding depression. These findings challenge claims that downlisting European wolves is biologically warranted: none of these populations currently meets thresholds associated with favorable conservation status.