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The Susceptible-Infected-Recovered/Removed model is a standard model for epidemiological spread of disease through vulnerable populations. In this paper we show how SIR network dynamics can be implemented using spiking neurons.
Animal movement plays a critical role in disease transmission between farms. However, in the United States, the lack of available animal shipment data, sometimes coupled with a lack of detailed information about farm demographics and characteristics, presents great challenges for epidemic modeling and prediction. In this study, we proposed a new method based on the maximum entropy to generate “synthetic” animal movement networks, considering available statistics about the premises operation type, operation size, and the distance between premises. We illustrated our method for the swine movement networks in Iowa and performed network analyses to gain insights into the swine industry. We then applied the generated networks to a network-based epidemic model to identify potential system vulnerabilities in terms of disease transmission. The model was parameterized for African Swine Fever (ASF) as the US swine industry is quite concerned about this disease. Results show that premises with a central role in the network are more vulnerable to disease outbreaks and play an important role in disease spread. Simulations with outbreaks starting from random farms reveal no significant large outbreaks, indicating the system’s relative robustness against arbitrary disease introductions. However, outbreaks originating from high out-degree farms can lead to large epidemic sizes. This underscores the importance for stakeholders and policymakers to continue improving animal movement records and traceability programs in the US and the value of making that data available to epidemiologists and modelers to better understand risk and inform strategies aimed to cost-effectively prevent and control disease transmission. Our approach could be easily adapted to estimate movement networks in other animal production systems and to inform disease spread models for various infectious diseases.
We develop and analyze a stage-progression compartmental model to study the emerging invasive nontyphoidal Salmonella (iNTS) epidemic in sub-Saharan Africa. iNTS bloodstream infections are often fatal, and the diverse and non-specific clinical features of iNTS make it difficult to diagnose. We focus our study on identifying approaches that can reduce the incidence of new infections. In sub-Saharan Africa, transmission and mortality are correlated with the ongoing HIV epidemic and severe malnutrition. We use our model to quantify the impact that increasing antiretroviral therapy (ART) for HIV infected adults and reducing malnutrition in children would have on mortality from iNTS in the population. We consider immunocompromised subpopulations in the region with major risk factors for mortality, such as malaria and malnutrition among children and HIV infection and ART coverage in both children and adults. We parameterize the progression rates between infection stages using the branching probabilities and estimated time spent at each stage. We interpret the basic reproduction number R 0 as the total contribution from an infinite infection loop produced by the asymptomatic carriers in the infection chain. The results indicate that the asymptomatic HIV+ adults without ART serve as the driving force of infection for the iNTS epidemic. We conclude that the worst disease outcome is among the pediatric population, which has the highest infection rates and death counts. Our sensitivity analysis indicates that the most effective strategies to reduce iNTS mortality in the studied population are to improve the ART coverage among high-risk HIV+ adults and reduce malnutrition among children.
Here we propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ~ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.
Monkeypox, a zoonotic disease, is emerging as a potential sexually transmitted infection/disease, with underlying transmission mechanisms still unclear. We devised a risk-structured, compartmental model, incorporating sexual behavior dynamics. We compared different strategies targeting the high-risk population: a scenario of control policies geared toward the use of condoms and/or sexual abstinence (robust control strategy) with risk compensation behavior change, and a scenario of control strategies with behavior change in response to the doubling rate (adaptive control strategy). Monkeypox's basic reproduction number is 1.464, 0.0066, and 1.461 in the high-risk, low-risk, and total populations, respectively, with the high-risk group being the major driver of monkeypox spread. Policies imposing condom use or sexual abstinence need to achieve a 35% minimum compliance rate to stop further transmission, while a combination of both can curb the spread with 10% compliance to abstinence and 25% to condom use. With risk compensation, the only option is to impose sexual abstinence by at least 35%. Adaptive control is more effective than robust control where the daily sexual contact number is reduced proportionally and remains constant thereafter, shortening the time to epidemic peak, lowering its size, facilitating disease attenuation, and playing a key role in controlling the current outbreak.
Abstract The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is important for designing effective disease mitigation approaches. We combine a run-and-tumble self-propelled active matter system with an S-I-R model to capture the effects of spatial disorder. Working in the motility-induced phase separation regime both with and without quenched disorder, we find two epidemic regimes. For low transmissibility, quenched disorder lowers the frequency of epidemics and increases their average duration. For high transmissibility, the epidemic spreads as a front and the epidemic curves are less sensitive to quenched disorder; however, within this regime it is possible for quenched disorder to enhance the contagion by creating regions of higher particle densities. We discuss how this system could be realized using artificial swimmers with mobile optical traps operated on a feedback loop.
In the face of the COVID-19 pandemic, the literature saw a spike in publications for epidemic models, and a renewed interest in capturing contact networks and geographic movement of populations. There remains a general lack of consensus in the modeling community around best practices for spatiotemporal epi-modeling, specifically as it pertains to the infection rate formulation and the underlying contact or mixing model. We mathematically verify several common modeling assumptions in the literature, to prove when certain choices can provide consistent results across different geographic resolutions, population densities and patterns, and mixing assumptions. The most common infection rate formulation, a computationally low cost per capita infection rate assumption, fails the consistency tests for heterogeneous populations and gravity-weighting assumptions. Future modeling efforts in spatiotemporal disease modeling should be wary of this limitation, particularly when working with more heterogeneous or sparse populations. Our results provide guidance for testing that a model preserves desirable properties even when model inputs mask potential problems due to symmetry or homogeneity. We also provide a recipe for performing this type of verification, strengthening decision support tools.
The susceptible-infected (SI) and susceptible-infected-recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by whether or not the number of susceptibles always drops to zero at long times. Here, in this study, we introduce a new active matter epidemic model, the “susceptible-cleric-zombie-recovered” (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability γ via interaction with a cleric. Upon colliding with a zombie, both susceptibles and clerics enter the zombie state with probability β and α, respectively. By changing the initial fraction of clerics or their healing ability rate γ, we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which a finite number of clerics and susceptibles survive at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection.
We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network. We contrast the pros and cons of the different types of surrogate models and the effort involved in learning them. Importantly, the proposed framework reveals that, around the tipping points, the emergent dynamics of both benchmark examples can be effectively described by a one-dimensional stochastic differential equation, thus revealing the intrinsic dimensionality of the normal form of the specific type of the tipping point. This allows a significant reduction in the computational cost of the tasks of interest.
In this paper, we present a method for estimating the infection-rate of a disease as a spatial-temporal field. Our data comprises time-series case-counts of symptomatic patients in various areal units of a region. We extend an epidemiological model, originally designed for a single areal unit, to accommodate multiple units. The field estimation is framed within a Bayesian context, utilizing a parameterized Gaussian random field as a spatial prior. We apply an adaptive Markov chain Monte Carlo method to sample the posterior distribution of the model parameters condition on COVID-19 case-count data from three adjacent counties in New Mexico, USA. Our results suggest that the correlation between epidemiological dynamics in neighboring regions helps regularize estimations in areas with high variance (i.e., poor quality) data. Using the calibrated epidemic model, we forecast the infection-rate over each areal unit and develop a simple anomaly detector to signal new epidemic waves. Our findings show that anomaly detector based on estimated infection-rates outperforms a conventional algorithm that relies solely on case-counts.
Abstract Research into network dynamics of spreading processes typically employs both discrete and continuous time methodologies. Although each approach offers distinct insights, integrating them can be challenging, particularly when maintaining coherence across different time scales. This review focuses on the Microscopic Markov Chain Approach (MMCA), a probabilistic f ramework originally designed for epidemic modeling. MMCA uses discrete dynamics to compute the probabilities of individuals transitioning between epidemiological states. By treating each time step—usually a day—as a discrete event, the approach captures multiple concurrent changes within this time frame. The approach allows to estimate the likelihood of individuals or populations being in specific states, which correspond to distinct epidemiological compartments. This review synthesizes key findings from the application of this approach, providing a comprehensive overview of its utility in understanding epidemic spread.
Vaccination and the alternative behavior, vaccine refusal, are a classic example of manifesting behaviors driven by social norms and norm violations. Establishing how norms emerge, and under what circumstances people choose to violate them are key issues to understand in modeling epidemics. Interactions between individuals can lead to large-scale patterning of behavior (emergent phenomena). As norm violations are revealed through human behavior, drawing on psychological theory and principles to predict those violations is a viable approach for more human-constrained epidemiological models. As an example of the implications at scale, vaccine refusal is correlated with the spread of mis/disinformation about vaccine side-effects. Considering the complexities of network dynamics, the downstream effects means that if even a small group within a population are persuaded against vaccination, there is a reservoir from which disease and disease outbreaks can propagate. This work will attempt to identify those psychological indicators, to define circumstances that predict health behaviors, and identify potentially modifiable antecedents of health behavior, and factors that influence changes toward health protective behaviors.
Human mobility insights guide domain experts in an array of decisions, including critical infrastructure design, disaster response, epidemic modeling, national security, and policy making. Due to the inherent noise and privacy concerns in real-world individual-level mobility data, it is often preferred to leverage simulators that generate synthetic mobility data instead. However, it is critical to inspect and validate the output of such simulators to ensure the synthetic data is aligned with the characteristics of the population and the area of interest known to domain experts. While there exist many quantitative approaches for validating synthetic data, we argue it is also important to also validate such data qualitatively to capture aspects that are known to domain experts but difficult to quantify. In this work, we demonstrate a visual analytic platform that empowers domain experts to interact with their simulation outputs along spatial and temporal dimensions. By augmenting automated techniques and human skills, our visual analytic platform is a step towards interactive capabilities for model steering and quality control of mobility simulators.
Long-distance dispersal (LDD) pathogens pose substantial challenges for epidemic control due to their ability to generate new infection foci at great distances. While various modeling approaches have been developed to understand and manage such outbreaks, little work has compared how models of different structures behave under shared conditions. Here, in this study, we compare four structurally distinct epidemiological models — EPIMUL, GEMF, PoPS, and Warwick — each adapted to simulate the spread of wheat stripe rust (WSR), a wind-dispersed LDD pathogen, under identical epidemiological parameters and dispersal kernel. Using data from a controlled field experiment, we evaluate the ability of each model to replicate disease prevalence under nine intervention scenarios that vary in timing and culling area. While the models differ substantially in design — ranging from spatial grid-based to network-based and raster-based frameworks — the shared dispersal kernel allowed for close alignment in their predictions. All models accurately captured general epidemic trends, particularly the strong effect of early intervention on disease suppression. We qualitatively compared their behavioral responses across scenarios and also evaluated an ensemble prediction by averaging across model outputs. Our findings highlight how integrating shared epidemiological components into distinct modeling frameworks can improve consistency and accuracy, while reinforcing the importance of early culling in managing LDD pathogen outbreaks.
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We study the problem of designing scalable algorithms to find effective intervention strategies for controlling stochastic epidemic processes on networks. This is a common problem arising in agent based models for epidemic spread. Previous approaches to this problem focus on either heuristics with no guarantees or approximation algorithms that scale only to networks corresponding to county-sized populations, typically, with less than a million nodes. In particular, the mathematical-programming based approaches need to solve the Linear Program (LP) relaxation of the problem using an LP solver, which restricts the scalability of this approach. In this work, we overcome this restriction by designing an algorithm that adapts the multiplicative weights update (MWU) framework, along with the sample average approximation (SAA) technique, to approximately solve the linear program (LP) relaxation for the problem. To scale this approach further, we provide a memory-efficient algorithm that enables scaling to large networks, corresponding to country-size populations, with over 300 million nodes and 30 billion edges. Furthermore, we show that this approach provides near-optimal solutions to the LP in practice.
In this paper, we use modified versions of the SIAR model for epidemics to propose two ways of understanding and quantifying the effect of non-compliance to non-pharmaceutical intervention measures on the spread of an infectious disease. The SIAR model distinguishes between symptomatic infected (I) and asymptomatic infected (A) populations. One modification, which is simpler, assumes a known proportion of the population does not comply with government mandates such as quarantining and social-distancing. In a more sophisticated approach, the modified model treats non-compliant behavior as a social contagion. We theoretically explore different scenarios such as the occurrence of multiple waves of infections. Local and asymptotic analyses for both models are also provided.
In simulation-based studies and analyses of epidemics, a major challenge lies in resolving the conflict between fidelity of models and the speed of their simulation. Another related challenge arises in dealing with the large number of what–if scenarios that need to be explored. Here, we describe new computational methods that together provide an approach to dealing with both challenges. A mesoscopic modeling approach is described that strikes a middle ground between macroscopic models based on coupled differential equations and microscopic models built on fine-grained behaviors at the individual entity level. The mesoscopic approach offers the ability to incorporate complex compositions of multiple layers of dynamics even while retaining the potential for aggregate behaviors at varying levels. It also is an excellent match to the accelerator-based architectures of modern computing platforms in which graphical processing units (GPUs) can be exploited for fast simulation via the parallel execution mode of single instruction multiple thread (SIMT). The challenge of simulating a large number of scenarios is addressed via a method of sharing model state and computation across a tree of what–if scenarios that are localized, incremental changes to a large base simulation. A combination of the mesoscopic modeling approach and the incremental what–if scenario tree evaluation has been implemented in the software on modern GPUs. Synthetic simulation scenarios are presented to demonstrate the computational characteristics of our approach. Results from the experiments with large population data, including USA, UK, and India, illustrate the modeling methodology and computational performance on thousands of synthetically generated what–if scenarios. Execution of our implementation scaled to 8192 GPUs of supercomputing platforms demonstrates the ability to rapidly evaluate what–if scenarios several orders of magnitude faster than the conventional methods.