The anterior cingulate cortex (ACC) is important for higher-order cognitive functions, emotional responses, and monitoring internal states. ACC dysfunction has been implicated in an array of psychiatric and neurodegenerative disorders which have a bidirectional relationship with the metabolic disorder Type 2 diabetes (T2D). T2D is a chronic disease characterized by hyperglycemia, loss of insulin signaling, neuroinflammation, and increased morbidity and mortality chances. To better understand the functional effects of T2D on ACC information processing, we delivered an intermittent, low-dose streptozotocin (STZ) protocol to rats (all male due to female insensitivity to STZ) which led to lasting hyperglycemia and recorded single neurons during a delayed alternation task. We observed changes in spatial and reward processing in spite of no differences in overall behavioral accuracy, though we did find hyperglycemic animals spent less time at the reward site. Hyperglycemic animal (n = 5) ACC neurons had higher spatial information scores and changes in the allotment of spatial coding assets. Specifically, the hyperglycemic group had greatest spatial information during the reward approach, while in controls (n = 3) it was uniformly distributed. We found that state space separation and decoding accuracy were greater in control ensembles at the reward location. Furthermore, control hippocampal theta phase-locked cells had the strongest reward coding, and this effect was absent in hyperglycemic animals, leading to a muted reward location representation, despite increased reward approach coding. T2D inferred a nuanced and layered effect on ACC activity, leading to reward coding deficits, a reduced post-reinforcement pause, and a differential change in spatial coding properties.

Arboviral diseases remain a major public health concern, particularly in tropical and subtropical regions where mosquito populations thrive. One promising strategy to curb transmission is the release of Aedes aegypti mosquitoes infected with Wolbachia, a bacterium that reduces their ability to spread viruses. However, past large-scale releases have not always been successful, especially in complex urban settings, where restricted access to certain areas often leads to infection establishment failures and wasted resources. To address this, we developed and analyzed a partial differential equation model that simulates how Wolbachia-infected mosquitoes are established in different urban environments. We also explored strategies to improve their success under constraints on release size and the efficacy level of insecticide used for pre-release interventions. Our findings suggest that targeted releases are most effective in areas with limited mosquito movement without additional insecticide use. In higher mosquito dispersal areas, reducing at least 35 wild mosquitoes before release significantly improves establishment within nine months. Additionally, distributing releases over 2-5 weekly batches enhances success more than a single large release, even without other interventions. These findings offer practical insights for designing cost-effective and efficient Wolbachia-based mosquito control programs, reducing the burden of mosquito-borne diseases on vulnerable communities.

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict, a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software ( https://github.com/gchowell/forecasting_growthmodels ), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

Many infectious disease forecasting models in the United States (US) are built with data partitioned into geopolitical regions centered on human activity as opposed to regions defined by natural ecosystems; although useful for data collection and intervention, this has the potential to mask biological relationships between the environment and disease. We explored this concept by analyzing the correlations between climate and West Nile virus (WNV) case data aggregated to geopolitical and ecological regions. We compared correlations between minimum, maximum, and mean annual temperature; precipitation; and annual WNV neuroinvasive disease (WNND) case data from 2005 to 2019 when partitioned into (a) climate regions defined by the National Oceanic and Atmospheric Administration (NOAA) and (b) Level I ecoregions defined by the Environmental Protection Agency (EPA). We found that correlations between climate and WNND in NOAA climate regions and EPA ecoregions were often contradictory in both direction and magnitude, with EPA ecoregions more often supporting previously established biological hypotheses and environmental dynamics underlying vector-borne disease transmission. Using ecological regions to examine the relationships between climate and disease cases can enhance the predictive power of forecasts at various scales, motivating a conceptual shift in large-scale analyses from geopolitical frameworks to more ecologically meaningful regions.

Vaccine hesitancy threatens to reverse the progress in tackling vaccine-preventable diseases. We used an $ SIS $ model with a game theory model for vaccination and parameters from the COVID-19 pandemic to study how vaccine hesitancy impacts epidemic dynamics. The system showed three asymptotic behaviors: total rejection of vaccinations, complete acceptance, and oscillations. With increasing fear of infection, stable endemic states become periodic oscillations. Our results suggest that managing fear of infection relative to vaccination is vital to successful mass vaccinations.

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy's partial differential equation (PDE) for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the PDE for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical PDE solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(n log n) instead of the typical O(n^3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy's equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy's equation with a random permeability field, the framework broadly applies to solutions of other PDE with random coefficients.

Abstract We present an ensemble transfer learning method to predict suicide from Veterans Affairs (VA) electronic medical records (EMR). A diverse set of base models was trained to predict a binary outcome constructed from reported suicide, suicide attempt, and overdose diagnoses with varying choices of study design and prediction methodology. Each model used twenty cross-sectional and 190 longitudinal variables observed in eight time intervals covering 7.5 years prior to the time of prediction. Ensembles of seven base models were created and fine-tuned with ten variables expected to change with study design and outcome definition in order to predict suicide and combined outcome in a prospective cohort. The ensemble models achieved c-statistics of 0.73 on 2-year suicide risk and 0.83 on the combined outcome when predicting on a prospective cohort of $$\sim$$ ∼ 4.2 M veterans. The ensembles rely on nonlinear base models trained using a matched retrospective nested case-control (Rcc) study cohort and show good calibration across a diversity of subgroups, including risk strata, age, sex, race, and level of healthcare utilization. In addition, a linear Rcc base model provided a rich set of biological predictors, including indicators of suicide, substance use disorder, mental health diagnoses and treatments, hypoxia and vascular damage, and demographics.

Anterior cingulate cortex (ACC) activity is important for operations that require the ability to integrate multiple experiences over time, such as rule learning, cognitive flexibility, working memory, and long-term memory recall. To shed light on this, we analyzed neuronal activity while rats repeated the same behaviors during hour-long sessions to investigate how activity changed over time. We recorded neuronal ensembles as rats performed a decision-free operant task with varying reward likelihoods at three different response ports ( n = 5). Neuronal state space analysis revealed that each repetition of a behavior was distinct, with more recent behaviors more similar than those further apart in time. ACC activity was dominated by a slow, gradual change in low-dimensional representations of neural state space aligning with the pace of behavior. Temporal progression, or drift, was apparent on the top principal component for every session and was driven by the accumulation of experiences and not an internal clock. Notably, these signals were consistent across subjects, allowing us to accurately predict trial numbers based on a model trained on data from a different animal. We observed that non-continuous ramping firing rates over extended durations (tens of minutes) drove the low-dimensional ensemble representations. 40% of ACC neurons' firing ramped over a range of trial lengths and combinations of shorter duration ramping neurons created ensembles that tracked longer durations. These findings provide valuable insights into how the ACC, at an ensemble level, conveys temporal information by reflecting the accumulation of experiences over extended periods.

An ensemble n-sub-epidemic modeling framework that integrates sub-epidemics to capture complex temporal dynamics has demonstrated powerful forecasting capability in previous works. This modeling framework can characterize complex epidemic patterns, including plateaus, epidemic resurgences, and epidemic waves characterized by multiple peaks of different sizes. In this tutorial paper, we introduce and illustrate SubEpiPredict, a user-friendly MATLAB toolbox for fitting and forecasting time series data using an ensemble n-sub-epidemic modeling framework. The toolbox can be used for model fitting, forecasting, and evaluation of model performance of the calibration and forecasting periods using metrics such as the weighted interval score (WIS). We also provide a detailed description of these methods including the concept of the n-sub-epidemic model, constructing ensemble forecasts from the top-ranking models, etc. For the illustration of the toolbox, we utilize publicly available daily COVID-19 death data at the national level for the United States. The MATLAB toolbox introduced in this paper can be very useful for a wider group of audiences, including policymakers, and can be easily utilized by those without extensive coding and modeling backgrounds.

Background Dynamical mathematical models defined by a system of differential equations are typically not easily accessible to non-experts. However, forecasts based on these types of models can help gain insights into the mechanisms driving the process and may outcompete simpler phenomenological growth models. Here we introduce a friendly toolbox, SpatialWavePredict, to characterize and forecast the spatial wave sub-epidemic model, which captures diverse wave dynamics by aggregating multiple asynchronous growth processes and has outperformed simpler phenomenological growth models in short-term forecasts of various infectious diseases outbreaks including SARS, Ebola, and the early waves of the COVID-19 pandemic in the US. Results This tutorial-based primer introduces and illustrates a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using an ensemble spatial wave sub-epidemic model based on ordinary differential equations. Scientists, policymakers, and students can use the toolbox to conduct real-time short-term forecasts. The five-parameter epidemic wave model in the toolbox aggregates linked overlapping sub-epidemics and captures a rich spectrum of epidemic wave dynamics, including oscillatory wave behavior and plateaus. An ensemble strategy aims to improve forecasting performance by combining the resulting top-ranked models. The toolbox provides a tutorial for forecasting time-series trajectories, including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. Conclusions We have developed the first comprehensive toolbox to characterize and forecast time-series data using an ensemble spatial wave sub-epidemic wave model. As an epidemic situation or contagion occurs, the tools presented in this tutorial can facilitate policymakers to guide the implementation of containment strategies and assess the impact of control interventions. We demonstrate the functionality of the toolbox with examples, including a tutorial video, and is illustrated using daily data on the COVID-19 pandemic in the USA.

Wolbachia infection in Anopheles albimanus mosquitoes can render mosquitoes less capable of spreading malaria. We developed and analyzed a mechanistic compartmental ordinary differential equation model to evaluate the effectiveness of Wolbachia-based vector control strategies among wild Anopheles mosquitoes in Haiti. The model tracks the mosquito life stages, including egg, larva, and adult (male and female). It also accounts for critical biological effects, such as the maternal transmission of Wolbachia through infected females and cytoplasmic incompatibility, which effectively sterilizes uninfected females when they mate with infected males. We derive and interpret dimensionless numbers, including the basic reproductive number and next-generation numbers. The proposed system presents a backward bifurcation, which indicates a threshold infection that needs to be exceeded to establish a stable Wolbachia infection. The sensitivity analysis ranks the relative importance of the epidemiological parameters at baseline. We simulate different intervention scenarios, including prerelease mitigation using larviciding and thermal fogging before the release, multiple releases of infected populations, and different release times of the year. Our simulations show that the most efficient approach to establishing Wolbachia is to release all the infected mosquitoes immediately after the prerelease mitigation process. Moreover, the model predicts that it is more efficient to release during the dry season than the wet season.

All animals use two different strategies to navigate: idiothetic or movement-based navigation, and allothetic or landmark-based navigation. A new study reveals that compromised idiothetic navigation underlies disrupted grid cell coding in an early stage Alzheimer’s disease mouse model.

Background Simple dynamic modeling tools can be useful for generating real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. Results In this tutorial-based primer, we introduce and illustrate a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to various audiences, including students training in time-series forecasting, dynamic growth modeling, parameter estimation, parameter uncertainty and identifiability, model comparison, performance metrics, and forecast evaluation, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 2-parameter generalized-growth model, which has proved useful to characterize and forecast the ascending phase of epidemic outbreaks, and the Gompertz model as well as the 3-parameter generalized logistic-growth model and the Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. The toolbox provides a tutorial for forecasting time-series trajectories that include the full uncertainty distribution, derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. Conclusions We have developed the first comprehensive toolbox to characterize and forecast time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can facilitate policymaking to guide the implementation of control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and is illustrated using weekly data on the monkeypox epidemic in the USA.

Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of infection among the mosquitoes must exceed a threshold level for the infection to persist. To capture this threshold, it is critical to consider the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes, which is created by the local release of the infected mosquitoes. We develop and analyze partial differential equation (PDE) models to study the invasion dynamics of Wolbachia infection among mosquitoes in the field. Our reaction-diffusion-type models account for both the complex vertical transmission and the spatial mosquito dispersion. We characterize the threshold for a successful invasion, which is a bubble-shaped profile, called the"critical bubble". The critical bubble is optimal in its release size compared to other spatial profiles in a one-dimensional landscape. The fraction of infection near the release center is higher than the threshold level for the corresponding homogeneously mixing ODE models. We show that the proposed spatial models give rise to the traveling waves of Wolbachia infection when above the threshold. We quantify how the threshold condition and traveling-wave velocity depend on the diffusion coefficients and other model parameters. Numerical studies for different scenarios are presented to inform the design of release strategies.

While the number of human cases of mosquito-borne diseases has increased in North America in the last decade, accurate modeling of mosquito population density has remained a challenge. Longitudinal mosquito trap data over the many years needed for model calibration, and validation is relatively rare. In particular, capturing the relative changes in mosquito abundance across seasons is necessary for predicting the risk of disease spread as it varies from year to year. We developed a discrete, semi-stochastic, mechanistic process-based mosquito population model that captures life-cycle egg, larva, pupa, adult stages, and diapause for Culex pipiens (Diptera, Culicidae) and Culex restuans (Diptera, Culicidae) mosquito populations. This model combines known models for development and survival into a fully connected age-structured model that can reproduce mosquito population dynamics. Mosquito development through these stages is a function of time, temperature, daylight hours, and aquatic habitat availability. The time-dependent parameters are informed by both laboratory studies and mosquito trap data from the Greater Toronto Area. The model incorporates city-wide water-body gauge and precipitation data as a proxy for aquatic habitat. This approach accounts for the nonlinear interaction of temperature and aquatic habitat variability on the mosquito life stages. We demonstrate that the full model predicts the yearly variations in mosquito populations better than a statistical model using the same data sources. This improvement in modeling mosquito abundance can help guide interventions for reducing mosquito abundance in mitigating mosquito-borne diseases like West Nile virus.

We analyze an ensemble of n -sub-epidemic modeling for forecasting the trajectory of epidemics and pandemics. These ensemble modeling approaches, and models that integrate sub-epidemics to capture complex temporal dynamics, have demonstrated powerful forecasting capability. This modeling framework can characterize complex epidemic patterns, including plateaus, epidemic resurgences, and epidemic waves characterized by multiple peaks of different sizes. We systematically assess their calibration and short-term forecasting performance in short-term forecasts for the COVID-19 pandemic in the USA from late April 2020 to late February 2022. We compare their performance with two commonly used statistical ARIMA models. The best fit sub-epidemic model and three ensemble models constructed using the top-ranking sub-epidemic models consistently outperformed the ARIMA models in terms of the weighted interval score (WIS) and the coverage of the 95% prediction interval across the 10-, 20-, and 30-day short-term forecasts. In our 30-day forecasts, the average WIS ranged from 377.6 to 421.3 for the sub-epidemic models, whereas it ranged from 439.29 to 767.05 for the ARIMA models. Across 98 short-term forecasts, the ensemble model incorporating the top four ranking sub-epidemic models (Ensemble(4)) outperformed the (log) ARIMA model 66.3% of the time, and the ARIMA model, 69.4% of the time in 30-day ahead forecasts in terms of the WIS. Ensemble(4) consistently yielded the best performance in terms of the metrics that account for the uncertainty of the predictions. This framework can be readily applied to investigate the spread of epidemics and pandemics beyond COVID-19, as well as other dynamic growth processes found in nature and society that would benefit from short-term predictions.

Mathematical models have been widely used to understand the dynamics of the ongoing coronavirus disease 2019 (COVID-19) pandemic as well as to predict future trends and assess intervention strategies. The asynchronicity of infection patterns during this pandemic illustrates the need for models that can capture dynamics beyond a single-peak trajectory to forecast the worldwide spread and for the spread within nations and within other sub-regions at various geographic scales. Here, we demonstrate a five-parameter sub-epidemic wave modeling framework that provides a simple characterization of unfolding trajectories of COVID-19 epidemics that are progressing across the world at different spatial scales. We calibrate the model to daily reported COVID-19 incidence data to generate six sequential weekly forecasts for five European countries and five hotspot states within the United States. The sub-epidemic approach captures the rise to an initial peak followed by a wide range of post-peak behavior, ranging from a typical decline to a steady incidence level to repeated small waves for sub-epidemic outbreaks. We show that the sub-epidemic model outperforms a three-parameter Richards model, in terms of calibration and forecasting performance, and yields excellent short- and intermediate-term forecasts that are not attainable with other single-peak transmission models of similar complexity. Overall, this approach predicts that a relaxation of social distancing measures would result in continuing sub-epidemics and ongoing endemic transmission. We illustrate how this view of the epidemic could help data scientists and policymakers better understand and predict the underlying transmission dynamics of COVID-19, as early detection of potential sub-epidemics can inform model-based decisions for tighter distancing controls.

We describe an approach to generate a heterosexual network with a prescribed joint-degree distribution embedded in a prescribed large-scale social contact network. The structure of a sexual network plays an important role in how all sexually transmitted infections (STIs) spread. Generating an ensemble of networks that mimics the real-world is crucial to evaluating robust mitigation strategies for controlling STIs. Most of the current algorithms to generate sexual networks only use sexual activity data, such as the number of partners per month, to generate the sexual network. Real-world sexual networks also depend on biased mixing based on age, location, and social and work activities. We describe an approach to use a broad range of social activity data to generate possible heterosexual networks. We start with a large-scale simulation of thousands of people in a city as they go through their daily activities, including work, school, shopping, and activities at home. We extract a social network from these activities where the nodes are the people, and the edges indicate a social interaction, such as working in the same location. This social network captures the correlations between people of different ages, living in different locations, their economic status, and other demographic factors. We use the social contact network to define a bipartite heterosexual network that is embedded within an extended social network. The resulting sexual network captures the biased mixing inherent in the social network, and models based on this pairing of networks can be used to investigate novel intervention strategies based on the social contacts among infected people. We illustrate the approach in a model for the spread of chlamydia in the heterosexual network representing the young sexually active community in New Orleans.