Compartmental Models in Epidemiology

Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time. Here, we find that conventional approaches with this assumption cause serious bias in epidemiological parameter estimation. To address this bias, we developed a Bayesian inference method by adopting more realistic history-dependent disease dynamics. Our method more accurately and precisely estimates the reproduction number than the conventional approaches solely from confirmed cases data, which are easy to obtain through testing. It also revealed how the infectious period distribution changed throughout the COVID-19 pandemic during 2020 in South Korea. We also provide a user-friendly package, IONISE, that automates this method.

Effect of vaccine dose intervals: Considering immunity levels, vaccine efficacy, and strain variants for disease control strategy

In this study, we present an immuno-epidemic model to understand mitigation options during an epidemic break. The model incorporates comorbidity and multiple-vaccine doses through a system of coupled integro-differential equations to analyze the epidemic rate and intensity from a knowledge of the basic reproduction number and time-distributed rate functions. Our modeling results show that the interval between vaccine doses is a key control parameter that can be tuned to significantly influence disease spread. We show that multiple doses induce a hysteresis effect in immunity levels that offers a better mitigation alternative compared to frequent vaccination which is less cost-effective while being more intrusive. Optimal dosing intervals, emphasizing the cost-effectiveness of each vaccination effort, and determined by various factors such as the level of immunity and efficacy of vaccines against different strains, appear to be crucial in disease management. The model is sufficiently generic that can be extended to accommodate specific disease forms.

Enhancing COVID-19 forecasting precision through the integration of compartmental models, machine learning and variants

Predicting epidemic evolution is essential for making informed decisions and guiding the implementation of necessary countermeasures. Computational models are vital tools that provide insights into illness progression and enable early detection, proactive intervention, and targeted preventive measures. This paper introduces Sybil, a framework that integrates machine learning and variant-aware compartmental models, leveraging a fusion of data-centric and analytic methodologies. To validate and evaluate Sybil's forecasts, we employed COVID-19 data from several European and U.S. states. The dataset included the number of new and recovered cases, fatalities, and variant presence over time. We evaluate the forecasting precision of Sybil in periods in which there is a change in the trend of the pandemic evolution or a new variant appears. Results demonstrate that Sybil outperforms conventional data-centric approaches, being able to forecast accurately the changes in the trend, the magnitude of these changes, and the future prevalence of new variants.

Spatiotemporal dynamics of epidemiology diseases: mobility based risk and short-term prediction modeling of COVID-19

Nowadays, epidemiological modeling is applied to a wide range of diseases, communicable and non-communicable, namely AIDS, Ebola, influenza, Dengue, Malaria, Zika. More recently, in the context of the last pandemic declared by the World Health Organization (WHO), several studies applied these models to SARS-CoV-2. Despite the increasing number of researches using spatial analysis, some constraints persist that prevent more complex modeling such as capturing local epidemiological dynamics or capturing the real patterns and dynamics. For example, the unavailability of: (i) epidemiological information such as the frequency with which it is made available; (ii) sociodemographic and environmental factors (e.g., population density and population mobility) at a finer scale which influence the evolution patterns of infectious diseases; or (iii) the number of cases information that is also very dependent on the degree of testing performed, often with severe territorial disparities and influenced by context factors. Moreover, the delay in case reporting and the lack of quality control in epidemiological information is responsible for biases in the data that lead to many results obtained being subject to the ecological fallacy, making it difficult to identify causal relationships. Other important methodological limitations are the control of spatiotemporal dependence, management of non-linearity, ergodicy, among others, which can impute inconsistencies to the results. In addition to these issues, social contact, is still difficult to quantify in order to be incorporated into modeling processes. This study aims to explore a modeling framework that can overcome some of these modeling methodological limitations to allow more accurate modeling of epidemiological diseases. Based on Geographic Information Systems (GIS) and spatial analysis, our model is developed to identify group of municipalities where population density (vulnerability) has a stronger relationship with incidence (hazard) and commuting movements (exposure). Specifically, our framework shows how to operate a model over data with no clear trend or seasonal pattern which is suitable for a short-term predicting (i.e., forecasting) of cases based on few determinants. Our tested models provide a good alternative for when explanatory data is few and the time component is not available, once they have shown a good fit and good short-term forecast ability.

Simple economics of vaccination: public policies and incentives

This paper focuses on the economics of vaccination and, more specifically, analyzes the vaccination decision of individuals using a game-theoretic model combined with an epidemiological SIR model that reproduces the infection dynamics of a generic disease. We characterize the equilibrium individual vaccination rate, and we show that it is below the rate compatible with herd immunity due to the existence of externalities that individuals do not internalize when they decide on vaccination. In addition, we analyze three public policies consisting of informational campaigns to reduce the disutility of vaccination, monetary payments to vaccinated individuals and measures to increase the disutility of non-vaccination. If the public authority uses only one type of policy, herd immunity is not necessarily achieved unless monetary incentives are used. When the public authority is not limited to use only one policy, we find that the optimal public policy should consist only of informational campaigns if they are sufficiently effective, or a combination of informational campaigns and monetary incentives otherwise. Surprisingly, the requirement of vaccine passports or other restrictions on the non-vaccinated are not desirable.

Using an epidemiological model to explore the interplay between sharing and advertising in viral videos

How to exploit social networks to make internet content spread rapidly and consistently is an interesting question in marketing management. Although epidemic models have been employed to comprehend the spread dynamics of internet content, such as viral videos, the effects of advertising and individual sharing on information dissemination are difficult to distinguish. This gap forbids us to evaluate the efficiency of marketing strategies. In this paper, we modify a classic mean-field SIR (susceptible-infected-recovered) model, incorporating the influences of sharing and advertising in viral videos. We mathematically analyze the global stability of the system and propose an agent-based modeling approach to evaluate the efficiency of sharing and advertising. We further provide a case study of music videos on YouTube to show the validity of our model.

Bayesian inference for the onset time and epidemiological characteristics of emerging infectious diseases

Background

Emerging infectious diseases pose a significant threat to global public health. Timely detection and response are crucial in mitigating the spread of such epidemics. Inferring the onset time and epidemiological characteristics is vital for accelerating early interventions, but accurately predicting these parameters in the early stages remains challenging.

Methods

We introduce a Bayesian inference method to fit epidemic models to time series data based on state-space modeling, employing a stochastic Susceptible-Exposed-Infectious-Removed (SEIR) model for transmission dynamics analysis. Our approach uses the particle Markov chain Monte Carlo (PMCMC) method to estimate key epidemiological parameters, including the onset time, the transmission rate, and the recovery rate. The PMCMC algorithm integrates the advantageous aspects of both MCMC and particle filtering methodologies to yield a computationally feasible and effective means of approximating the likelihood function, especially when it is computationally intractable.

Results

To validate the proposed method, we conduct case studies on COVID-19 outbreaks in Wuhan, Shanghai and Nanjing, China, respectively. Using early-stage case reports, the PMCMC algorithm accurately predicted the onset time, key epidemiological parameters, and the basic reproduction number. These findings are consistent with empirical studies and the literature.

Conclusion

This study presents a robust Bayesian inference method for the timely investigation of emerging infectious diseases. By accurately estimating the onset time and essential epidemiological parameters, our approach is versatile and efficient, extending its utility beyond COVID-19.

Forecasting the spread of COVID-19 based on policy, vaccination, and Omicron data

The COVID-19 pandemic caused by the novel SARS-COV-2 virus poses a great risk to the world. During the COVID-19 pandemic, observing and forecasting several important indicators of the epidemic (like new confirmed cases, new cases in intensive care unit, and new deaths for each day) helped prepare the appropriate response (e.g., creating additional intensive care unit beds, and implementing strict interventions). Various predictive models and predictor variables have been used to forecast these indicators. However, the impact of prediction models and predictor variables on forecasting performance has not been systematically well analyzed. Here, we compared the forecasting performance using a linear mixed model in terms of prediction models (mathematical, statistical, and AI/machine learning models) and predictor variables (vaccination rate, stringency index, and Omicron variant rate) for seven selected countries with the highest vaccination rates. We decided on our best models based on the Bayesian Information Criterion (BIC) and analyzed the significance of each predictor. Simple models were preferred. The selection of the best prediction models and the use of Omicron variant rate were considered essential in improving prediction accuracies. For the test data period before Omicron variant emergence, the selection of the best models was the most significant factor in improving prediction accuracy. For the test period after Omicron emergence, Omicron variant rate use was considered essential in deciding forecasting accuracy. For prediction models, ARIMA, lightGBM, and TSGLM generally performed well in both test periods. Linear mixed models with country as a random effect has proven that the choice of prediction models and the use of Omicron data was significant in determining forecasting accuracies for the highly vaccinated countries. Relatively simple models, fit with either prediction model or Omicron data, produced best results in enhancing forecasting accuracies with test data.

Incorporating social vulnerability in infectious disease mathematical modelling: a scoping review

BACKGROUND

Highlighted by the rise of COVID-19, climate change, and conflict, socially vulnerable populations are least resilient to disaster. In infectious disease management, mathematical models are a commonly used tool. Researchers should include social vulnerability in models to strengthen their utility in reflecting real-world dynamics. We conducted a scoping review to evaluate how researchers have incorporated social vulnerability into infectious disease mathematical models.

METHODS

The methodology followed the Joanna Briggs Institute and updated Arksey and O'Malley frameworks, verified by the PRISMA-ScR checklist. PubMed, Clarivate Web of Science, Scopus, EBSCO Africa Wide Information, and Cochrane Library were systematically searched for peer-reviewed published articles. Screening and extracting data were done by two independent researchers.

RESULTS

Of 4075 results, 89 articles were identified. Two-thirds of articles used a compartmental model (n = 58, 65.2%), with a quarter using agent-based models (n = 24, 27.0%). Overall, routine indicators, namely age and sex, were among the most frequently used measures (n = 42, 12.3%; n = 22, 6.4%, respectively). Only one measure related to culture and social behaviour (0.3%). For compartmental models, researchers commonly constructed distinct models for each level of a social vulnerability measure and included new parameters or influenced standard parameters in model equations (n = 30, 51.7%). For all agent-based models, characteristics were assigned to hosts (n = 24, 100.0%), with most models including age, contact behaviour, and/or sex (n = 18, 75.0%; n = 14, 53.3%; n = 10, 41.7%, respectively).

CONCLUSIONS

Given the importance of equitable and effective infectious disease management, there is potential to further the field. Our findings demonstrate that social vulnerability is not considered holistically. There is a focus on incorporating routine demographic indicators but important cultural and social behaviours that impact health outcomes are excluded. It is crucial to develop models that foreground social vulnerability to not only design more equitable interventions, but also to develop more effective infectious disease control and elimination strategies. Furthermore, this study revealed the lack of transparency around data sources, inconsistent reporting, lack of collaboration with local experts, and limited studies focused on modelling cultural indicators. These challenges are priorities for future research.

The Epidemiological and Economic Impact of COVID-19 in Kazakhstan: An Agent-Based Modeling

BACKGROUND

Our study aimed to assess how effective the preventative measures taken by the state authorities during the pandemic were in terms of public health protection and the rational use of material and human resources.

MATERIALS AND METHODS

We utilized a stochastic agent-based model for COVID-19's spread combined with the WHO-recommended COVID-ESFT version 2.0 tool for material and labor cost estimation.

RESULTS

Our long-term forecasts (up to 50 days) showed satisfactory results with a steady trend in the total cases. However, the short-term forecasts (up to 10 days) were more accurate during periods of relative stability interrupted by sudden outbreaks. The simulations indicated that the infection's spread was highest within families, with most COVID-19 cases occurring in the 26-59 age group. Government interventions resulted in 3.2 times fewer cases in Karaganda than predicted under a "no intervention" scenario, yielding an estimated economic benefit of 40%.

CONCLUSION

The combined tool we propose can accurately forecast the progression of the infection, enabling health organizations to allocate specialists and material resources in a timely manner.

Spatial-temporal simulation for hospital infection spread and outbreaks of Clostridioides difficile

Validated and curated datasets are essential for studying the spread and control of infectious diseases in hospital settings, requiring clinical information on patients' evolution and their location. The literature shows that approaches based on Artificial Intelligence (AI) in the development of clinical-support systems have benefits that are increasingly recognized. However, there is a lack of available high-volume data, necessary for trusting such AI models. One effective method in this situation involves the simulation of realistic data. Existing simulators primarily focus on implementing compartmental epidemiological models and contact networks to validate epidemiological hypotheses. Nevertheless, other practical aspects such as the hospital building distribution, shifts or safety policies on infections has received minimal attention. In this paper, we propose a novel approach for a simulator of nosocomial infection spread, combining agent-based patient description, spatial-temporal constraints of the hospital settings, and microorganism behavior driven by epidemiological models. The predictive validity of the model was analyzed considering micro and macro-face validation, parameter calibration based on literature review, model alignment, and sensitive analysis with an expert. This simulation model is useful in monitoring infections and in the decision-making process in a hospital, by helping to detect spatial-temporal patterns and predict statistical data about the disease.

On a two-strain epidemic model involving delay equations

We propose an epidemiological model for the interaction of either two viruses or viral strains with cross-immunity, where the individuals infected by the first virus cannot be infected by the second one, and without cross-immunity, where a secondary infection can occur. The model incorporates distributed recovery and death rates and consists of integro-differential equations governing the dynamics of susceptible, infectious, recovered, and dead compartments. Assuming that the recovery and death rates are uniformly distributed in time throughout the duration of the diseases, we can simplify the model to a conventional ordinary differential equation (ODE) model. Another limiting case arises if the recovery and death rates are approximated by the delta-function, thereby resulting in a new point-wise delay model that incorporates two time delays corresponding to the durations of the diseases. We establish the positiveness of solutions for the distributed delay models and determine the basic reproduction number and an estimate for the final size of the epidemic for the delay model. According to the results of the numerical simulations, both strains can coexist in the population if the disease transmission rates for them are close to each other. If the difference between them is sufficiently large, then one of the strains dominates and eliminates the other one.

Effective population size in simple infectious disease models

Almost all models used in analysis of infectious disease outbreaks contain some notion of population size, usually taken as the census population size of the community in question. In many settings, however, the census population is not equivalent to the population likely to be exposed, for example if there are population structures, outbreak controls or other heterogeneities. Although these factors may be taken into account in the model: adding compartments to a compartmental model, variable mixing rates and so on, this makes fitting more challenging, especially if the population complexities are not fully known. In this work we consider the concept of effective population size in outbreak modelling, which we define as the size of the population involved in an outbreak, as an alternative to use of more complex models. Effective population size is an important quantity in genetics for estimation of genetic diversity loss in populations, but it has not been widely applied in epidemiology. Through simulation studies and application to data from outbreaks of COVID-19 in China, we find that simple SIR models with effective population size can provide a good fit to data which are not themselves simple or SIR.

Scalable parallel and distributed simulation of an epidemic on a graph

We propose an algorithm to simulate Markovian SIS epidemics with homogeneous rates and pairwise interactions on a fixed undirected graph, assuming a distributed memory model of parallel programming and limited bandwidth. This setup can represent a broad class of simulation tasks with compartmental models. Existing solutions for such tasks are sequential by nature. We provide an innovative solution that makes trade-offs between statistical faithfulness and parallelism possible. We offer an implementation of the algorithm in the form of pseudocode in the Appendix. Also, we analyze its algorithmic complexity and its induced dynamical system. Finally, we design experiments to show its scalability and faithfulness. In our experiments, we discover that graph structures that admit good partitioning schemes, such as the ones with clear community structures, together with the correct application of a graph partitioning method, can lead to better scalability and faithfulness. We believe this algorithm offers a way of scaling out, allowing researchers to run simulation tasks at a scale that was not accessible before. Furthermore, we believe this algorithm lays a solid foundation for extensions to more advanced epidemic simulations and graph dynamics in other fields.

Circulation of Respiratory Viruses in the City: Towards an Agent-Based Ecosystem model

Mathematical models play an important role in management of outbreaks of acute respiratory infections (ARI). While such models are generally used to study the spread of a solitary virus, in reality multiple viruses co-circulate in the population. These viruses have been studied in detail, including the course of infection and immune defense mechanisms. We developed an agent-based model, called ABM-ARI, assimilating heterogeneous data and theoretical knowledge into a biologically motivated system, that allows to reproduce the seasonal patterns of ARI incidence and simulate interventions. ABM-ARI uses city-specific data to create a synthetic population and to construct realistic contact networks in different activity settings. Characteristics of infection, immune protection and non-specific resistance were varied between individuals to account for the population heterogeneity. For the calibration, we minimised the normalised mean absolute error between simulated and observed epidemic curves. ABM-ARI was built based on the quantitative assessment of features of predominant respiratory viruses and epidemiological characteristics of the population. It provides a good fit to the observed epidemic curves for different age groups and viruses. We also simulated one-week school closures when student absences were at or above 10%, 20% or 30% and found that only 10% and 20% thresholds resulted in a reduction of the incidence. ABM-ARI has a great potential in tackling the challenge of emerging infections by simulating and evaluating the effectiveness of various interventions.

Getting Jab or Regular Test: Observations from an Impulsive Epidemic COVID-19 Model

Several safe and effective vaccines are available to prevent individuals from experiencing severe illness or death as a result of COVID-19. Widespread vaccination is widely regarded as a critical tool in the fight against the disease. However, some individuals may choose not to vaccinate due to vaccine hesitancy or other medical conditions. In some sectors, regular compulsory testing is required for such unvaccinated individuals. Interestingly, different sectors require testing at various frequencies, such as weekly or biweekly. As a result, it is essential to determine the optimal testing frequency and identify underlying factors. This study proposes a population-based model that can accommodate different personal decision choices, such as getting vaccinated or undergoing regular tests, as well as vaccine efficacies and uncertainties in epidemic transmission. The model, formulated as impulsive differential equations, uses time instants to represent the reporting date for the test result of an unvaccinated individual. By employing well-accepted indices to measure transmission risk, including the basic reproduction number, the peak time, the final size, and the number of severe infections, the study shows that an optimal testing frequency is highly sensitive to parameters involved in the transmission process, such as vaccine efficacy, disease transmission rate, test accuracy, and existing vaccination coverage. The testing frequency should be appropriately designed with the consideration of all these factors, as well as the control objectives measured by epidemiological quantities of great concern.

Self-adapting infectious dynamics on random networks

Self-adaptive dynamics occurs in many fields of research, such as socio-economics, neuroscience, or biophysics. We consider a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the state of the system. This leads to piecewise deterministic Markovian dynamics coupled to a non-Markovian adaptive mechanism. We apply this framework to basic epidemic models (SIS, SIR) on random networks. We consider a co-evolutionary dynamical network where node-states change through the epidemics and network topology changes through the creation and deletion of edges. For a simple threshold base application of lockdown measures, we observe large regions in parameter space with oscillatory behavior, thereby exhibiting one of the most reduced mechanisms leading to oscillations. For the SIS epidemic model, we derive analytic expressions for the oscillation period from a pairwise closed model, which is validated with numerical simulations for random uniform networks. Furthermore, the basic reproduction number fluctuates around one indicating a connection to self-organized criticality.

Stochastic Reaction Networks Within Interacting Compartments

Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on [Formula: see text], and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes, chemical and otherwise, in homogeneous environments. There are multiple avenues for generalizing away from the assumption that the environment is homogeneous, with the proper modeling choice dependent upon the context of the problem being considered. One such generalization was recently introduced in Duso and Zechner (Proc Nat Acad Sci 117(37):22674-22683 , Duso and Zechner (2020)), where the proposed model includes a varying number of interacting compartments, or cells, each of which contains an evolving copy of the stochastic reaction system. The novelty of the model is that these compartments also interact via the merging of two compartments (including their contents), the splitting of one compartment into two, and the appearance and destruction of compartments. In this paper we begin a systematic exploration of the mathematical properties of this model. We (i) obtain basic/foundational results pertaining to explosivity, transience, recurrence, and positive recurrence of the model, (ii) explore a number of examples demonstrating some possible non-intuitive behaviors of the model, and (iii) identify the limiting distribution of the model in a special case that generalizes three formulas from an example in Duso and Zechner (Proc Nat Acad Sci 117(37):22674-22683 , Duso and Zechner (2020)).

A celebration of Fred Brauer's legacy in mathematical biology

Fred Brauer (1932-2021), one of the pioneers of mathematical population biology, shaped generations of researchers through his lines of research, his books which have become key references in the field, and his mentoring of junior researchers. This dedication reviews some of his work in population harvesting and epidemiological modeling, highlighting how this special collection reflects the impact of his legacy through both his research accomplishments and the formation of new researchers.

Epidemic Management via Imperfect Testing: A Multi-criterial Perspective

Diagnostic testing may represent a key component in response to an ongoing epidemic, especially if coupled with containment measures, such as mandatory self-isolation, aimed to prevent infectious individuals from furthering onward transmission while allowing non-infected individuals to go about their lives. However, by its own nature as an imperfect binary classifier, testing can produce false negative or false positive results. Both types of misclassification are problematic: while the former may exacerbate the spread of disease, the latter may result in unnecessary isolation mandates and socioeconomic burden. As clearly shown by the COVID-19 pandemic, achieving adequate protection for both people and society is a crucial, yet highly challenging task that needs to be addressed in managing large-scale epidemic transmission. To explore the trade-offs imposed by diagnostic testing and mandatory isolation as tools for epidemic containment, here we present an extension of the classical Susceptible-Infected-Recovered model that accounts for an additional stratification of the population based on the results of diagnostic testing. We show that, under suitable epidemiological conditions, a careful assessment of testing and isolation protocols can contribute to epidemic containment, even in the presence of false negative/positive results. Also, using a multi-criterial framework, we identify simple, yet Pareto-efficient testing and isolation scenarios that can minimize case count, isolation time, or seek a trade-off solution for these often contrasting epidemic management objectives.

Modeling the drivers of oscillations in COVID-19 data on college campuses

PURPOSE

Incorporating human behavior in a disease model can explain the oscillations in COVID-19 data which occur more rapidly than can be explained by variants alone on college campuses.

METHODS

Dampened oscillations emerge by supplementing a simple disease model with a risk assessment function, which depends on the current number of infected individuals in the student population and the institutional public health policies. After accounting for a rapid disease impulse due to social gatherings, we achieve sustained oscillations that follow the trend of 2020/2021 COVID-19 data as reported on the COVID-19 dashboards of US post-secondary institutions.

RESULTS

This adjustment to the epidemiological model can provide an intuitive way of understanding rapid oscillations based on human risk perception and institutional policies. More risk-averse communities experience lower disease-level equilibria and less oscillations within the system, while communities that are less responsive to changes in the number of infected individuals exhibit larger amplitude and frequency of the oscillations.

CONCLUSIONS

Community risk assessment plays an important role in COVID-19 management in college settings. Improving the ability of individuals to rapidly and conservatively respond to changes in community disease levels may help assist in self-regulating these oscillations to levels well below thresholds for emergency management.

Human behavior in the time of COVID-19: Learning from big data

Since the World Health Organization (WHO) characterized COVID-19 as a pandemic in March 2020, there have been over 600 million confirmed cases of COVID-19 and more than six million deaths as of October 2022. The relationship between the COVID-19 pandemic and human behavior is complicated. On one hand, human behavior is found to shape the spread of the disease. On the other hand, the pandemic has impacted and even changed human behavior in almost every aspect. To provide a holistic understanding of the complex interplay between human behavior and the COVID-19 pandemic, researchers have been employing big data techniques such as natural language processing, computer vision, audio signal processing, frequent pattern mining, and machine learning. In this study, we present an overview of the existing studies on using big data techniques to study human behavior in the time of the COVID-19 pandemic. In particular, we categorize these studies into three groups-using big data to measure, model, and leverage human behavior, respectively. The related tasks, data, and methods are summarized accordingly. To provide more insights into how to fight the COVID-19 pandemic and future global catastrophes, we further discuss challenges and potential opportunities.

How Does Network Structure Impact Socially Reinforced Diffusion?

How does network structure impact the speed and reach of social contagions? The current view holds that random links facilitate “simple” contagion, but when agents require multiple reinforcements for “complex” adoption, clustered networks are better conduits of social influence. We show that in complex contagion, even low probabilities of adoption upon a single contact would activate an exponential contagion process that tilts the balance in favor of random networks. On the other hand, underappreciated but critical to the race between random and clustered networks is how long agents engage with contagion. Switching back to prior practice and the inactivation of senders and especially receivers shorten the window of engagement for convincing distant contacts and weaken the reach of diffusion on random networks. We propose a simplified framework where clustering primarily enables contagion when repetition matters and receivers lose interest quickly; otherwise, diffusion, simple or complex, is faster on random networks than clustered ones. These mechanisms can inform designing social networks, structuring groups, and seeding of ideas and innovations at a time when the increasing inflow of content from various media limits actors’ engagement with each item, whereas expanding network size and connections speeds up diffusion through distant contacts.

Supplemental Material: The e-companion is available at https://doi.org/10.1287/orsc.2023.1658 .

Novel model prediction time-to-event analysis: data validation and estimation of 200 million cases in the global COVID-19 epidemic

OBJECTIVES

Assessment of recuperation and death times of a population inflicted by an epidemic has only been feasible through studying a sample of individuals via time-to-event analysis, which requires identified participants. Therefore, we aimed to introduce an original model to estimate the average recovery/death times of infected population of contagious diseases without the need to undertake survival analysis and just through the data of unidentified infected, recovered and dead cases.

DESIGN

Cross-sectional study.

SETTING

An internet source that asserted from official sources of each government. The model includes two techniques-curve fitting and optimisation problems. First, in the curve fitting process, the data of the three classes are simultaneously fitted to functions with defined constraints to derive the average times. In the optimisation problems, data are directly fed to the technique to achieve the average times. Further, the model is applied to the available data of COVID-19 of 200 million people throughout the globe.

RESULTS

The average times obtained by the two techniques indicated conformity with one another showing p values of 0.69, 0.51, 0.48 and 0.13 with one, two, three and four surges in our timespan, respectively. Two types of irregularity are detectable in the data, significant difference between the infected population and the sum of the recovered and deceased population (discrepancy) and abrupt increase in the cumulative distributions (step). Two indices, discrepancy index (DI) and error of fit index (EI), are developed to quantify these irregularities and correlate them with the conformity of the time averages obtained by the two techniques. The correlations between DI and EI and the quantified conformity of the results were -0.74 and -0.93, respectively.

CONCLUSION

The results of statistical analyses point out that the proposed model is suitable to estimate the average times between recovery and death.

An age-dependent immuno-epidemiological model with distributed recovery and death rates

The work is devoted to a new immuno-epidemiological model with distributed recovery and death rates considered as functions of time after the infection onset. Disease transmission rate depends on the intra-subject viral load determined from the immunological submodel. The age-dependent model includes the viral load, recovery and death rates as functions of age considered as a continuous variable. Equations for susceptible, infected, recovered and dead compartments are expressed in terms of the number of newly infected cases. The analysis of the model includes the proof of the existence and uniqueness of solution. Furthermore, it is shown how the model can be reduced to age-dependent SIR or delay model under certain assumptions on recovery and death distributions. Basic reproduction number and final size of epidemic are determined for the reduced models. The model is validated with a COVID-19 case data. Modelling results show that proportion of young age groups can influence the epidemic progression since disease transmission rate for them is higher than for other age groups.

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.

Agent-based simulation of pedestrian dynamics for exposure time estimation in epidemic risk assessment

Purpose

With the coronavirus disease 2019 (COVID-19) pandemic spreading across the world, protective measures for containing the virus are essential, especially as long as no vaccine or effective treatment is available. One important measure is the so-called physical distancing or social distancing.

Methods

In this paper, we propose an agent-based numerical simulation of pedestrian dynamics in order to assess the behavior of pedestrians in public places in the context of contact transmission of infectious diseases like COVID-19, and to gather insights about exposure times and the overall effectiveness of distancing measures.

Results

To abide by the minimum distance of 1.5 m stipulated by the German government at an infection rate of 2%, our simulation results suggest that a density of one person per 16m² or below is sufficient.

Conclusions

The results of this study give insight into how physical distancing as a protective measure can be carried out more efficiently to help reduce the spread of COVID-19.

Efficient social distancing during the COVID-19 pandemic: Integrating economic and public health considerations

Although social distancing can effectively contain the spread of infectious diseases by reducing social interactions, it may have economic effects. Crises such as the COVID-19 pandemic create dilemmas for policymakers because the long-term implementation of restrictive social distancing policies may cause massive economic damage and ultimately harm healthcare systems. This paper proposes an epidemic control framework that policymakers can use as a data-driven decision support tool for setting efficient social distancing targets. The framework addresses three aspects of the COVID-19 pandemic that are related to social distancing or community mobility data: modeling, financial implications, and policy-making. Thus, we explore the COVID-19 pandemic and concurrent economic situation as functions of historical pandemic data and mobility control. This approach allows us to formulate an efficient social distancing policy as a stochastic feedback control problem that minimizes the aggregated risks of disease transmission and economic volatility. We further demonstrate the use of a deep learning algorithm to solve this control problem. Finally, by applying our framework to U.S. data, we empirically examine the efficiency of the U.S. social distancing policy.

Complex dynamics and control analysis of an epidemic model with non-monotone incidence and saturated treatment

In this manuscript, we consider an epidemic model having constant recruitment of susceptible individuals with non-monotone disease transmission rate and saturated-type treatment rate. Two types of disease control strategies are taken here, namely vaccination for susceptible individuals and treatment for infected individuals to minimize the impact of the disease. We study local as well as global stability analysis of the disease-free equilibrium point and also endemic equilibrium point based on the values of basic reproduction number R 0 . Therefore, disease eradicates from the population if basic reproduction number less than unity and disease persists in the population if basic reproduction number greater than unity. We use center manifold theorem to study the dynamical behavior of the disease-free equilibrium point for R 0 = 1 . We investigate different bifurcations such as transcritical bifurcation, backward bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation of co-dimension 2. The biological significance of all types of bifurcations are described. Some numerical simulations are performed to check the reliability of our theoretical approach. Sensitivity analysis is performed to identify the influential model parameters which have most impact on the basic reproduction number of the proposed model. To control or eradicate the influence of the emerging disease, we need to control the most sensitive model parameters using necessary preventive measures. We study optimal control problem using Pontryagin's maximum principle. Finally using efficiency analysis, we determine most effective control strategy among applied controls.

Vaccine Allocation and Distribution: A Review with a Focus on Quantitative Methodologies and Application to Equity, Hesitancy, and COVID-19 Pandemic

This review focuses on vaccine distribution and allocation in the context of the current COVID-19 pandemic. The implications discussed are in the areas of equity in vaccine distribution and allocation (at a national level as well as worldwide), vaccine hesitancy, game-theoretic modeling to guide decision-making and policy-making at a governmental level, distribution and allocation barriers (in particular in low-income countries), and operations research (OR) mathematical models to plan and execute vaccine distribution and allocation. To conduct this review, we adopt a novel methodology that consists of three phases. The first phase deploys a bibliometric analysis; the second phase concentrates on a network analysis; and the last phase proposes a refined literature review based on the results obtained by the previous two phases. The quantitative techniques utilized to conduct the first two phases allow describing the evolution of the research in this area and its potential ramifications in future. In conclusion, we underscore the significance of operations research (OR)/management science (MS) research in addressing numerous challenges and trade-offs connected to the current pandemic and its strategic impact in future research.

Agent-Based Simulation for Infectious Disease Modelling over a Period of Multiple Days, with Application to an Airport Scenario

With the COVID-19 pandemic, the role of infectious disease spreading in public places has been brought into focus more than ever. Places that are of particular interest regarding the spread of infectious diseases are international airport terminals, not only for the protection of staff and ground crew members but also to help minimize the risk of the spread of infectious entities such as COVID-19 around the globe. Computational modelling and simulation can help in understanding and predicting the spreading of infectious diseases in any such scenario. In this paper, we propose a model, which combines a simulation of high geometric detail regarding virus spreading with an account of the temporal progress of infection dynamics. We, thus, introduce an agent-based social force model for tracking the spread of infectious diseases by modelling aerosol traces and concentration of virus load in the air. We complement this agent-based model to have consistency over a period of several days. We then apply this model to investigate simulations in a realistic airport setting with multiple virus variants of varying contagiousness. According to our experiments, a virus variant has to be at least twelve times more contagious than the respective control to result in a level of infection of more than 30%. Combinations of agent-based models with temporal components can be valuable tools in an attempt to assess the risk of infection attributable to a particular virus and its variants.

SARS-CoV-2 transmission in university classes

We investigate transmission dynamics for SARS-CoV-2 on a real network of classes at Simon Fraser University. Outbreaks are simulated over the course of one semester across numerous parameter settings, including moving classes above certain size thresholds online. Regression trees are used to analyze the effect of disease parameters on simulation outputs. We find that an aggressive class size thresholding strategy is required to mitigate the risk of a large outbreak, and that transmission by symptomatic individuals is a key driver of outbreak size. These findings provide guidance for designing control strategies at other institutions, as well as setting priorities and allocating resources for disease monitoring.

A contact tracing SIR model for randomly mixed populations

Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments.

Investigation of Factors Affecting COVID-19 and Sixth Wave Management Using a System Dynamics Approach

The COVID-19 pandemic has plunged the world into a health and economic crisis never seen before since the Spanish flu pandemic in 1918. The closure of schools and universities, the banning of rallies, and other social distancing in countries have been done to disrupt the transmission of the virus. Governments have planned to reduce restrictions on corona management by implementing vaccination programs. This research aims to better understand the Coronavirus disease's behavior, identify the prevalent factors, and adopt effective policies to control the pandemic. This study examines the different scenarios of releasing the constraints and returning to normal conditions before Corona to analyze the results of different scenarios to prevent the occurrence of subsequent peaks. The system dynamics approach is an effective means of studying COVID-19's behavioral characteristics. The factors that affect Coronavirus disease outbreak and control by expanding the basic SEIR model, interventions, and policies, such as vaccination, were investigated in this research. Based on the obtained results, the most critical factor in reducing the prevalence of the disease is reducing the behavioral risks of people and increasing the vaccination process. Observance of hygienic principles leads to disruption of the transmission chain, and vaccination increases the immunity of individuals against the acute type of infection. In addition, the closure of businesses and educational centers, along with government support for incomes, effectively controls and reduces the pandemic, which requires cooperation between the people and the government. In a situation where a new type of corona has spread, if the implementation of the policy of reducing restrictions and reopening schools and universities is done without planning, it will cause a lot of people to suffer.

Adaptive Sentinel Testing in Workplace for COVID-19 Pandemic

Testing and isolation of infectious employees is one of the critical strategies to make the workplace safe during the pandemic for many organizations. Adaptive testing frequency reduces cost while keeping the pandemic under control at the workplace. However, most models aimed at estimating test frequencies were structured for municipalities or large organizations such as university campuses of highly mobile individuals. By contrast, the workplace exhibits distinct characteristics: employee positivity rate may be different from the local community because of rigorous protective measures at workplace, or self-selection of co-workers with common behavioral tendencies for adherence to pandemic mitigation guidelines. Moreover, dual exposure to COVID-19 occurs at work and home that complicates transmission modeling, as does transmission tracing at the workplace. Hence, we developed bi-modal SEIR (Susceptible, Exposed, Infectious, and Removed) model and R-shiny tool that accounts for these differentiating factors to adaptively estimate the testing frequency for workplace. Our tool uses easily measurable parameters: community incidence rate, risks of acquiring infection from community and workplace, workforce size, and sensitivity of testing. Our model is best suited for moderate-sized organizations with low internal transmission rates, no-outward facing employees whose position demands frequent in-person interactions with the public, and low to medium population positivity rates. Simulations revealed that employee behavior in adherence to protective measures at work and in their community, and the onsite workforce size have large effects on testing frequency. Reducing workplace transmission rate through workplace mitigation protocols and higher sensitivity of the test deployed, although to a lesser extent. Furthermore, our simulations showed that sentinel testing leads to only marginal increase in the number of infections even for high community incidence rates, suggesting that this may be a cost-effective approach in future pandemics. We used our model to accurately guide testing regimen for three campuses of the Jackson Laboratory.

Sequential time-window learning with approximate Bayesian computation: an application to epidemic forecasting

The long duration of the COVID-19 pandemic allowed for multiple bursts in the infection and death rates, the so-called epidemic waves. This complex behavior is no longer tractable by simple compartmental model and requires more sophisticated mathematical techniques for analyzing epidemic data and generating reliable forecasts. In this work, we propose a framework for analyzing complex dynamical systems by dividing the data in consecutive time-windows to be separately analyzed. We fit parameters for each time-window through an approximate Bayesian computation (ABC) algorithm, and the posterior distribution of parameters obtained for one window is used as the prior distribution for the next window. This Bayesian learning approach is tested with data on COVID-19 cases in multiple countries and is shown to improve ABC performance and to produce good short-term forecasting.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11071-022-07865-x.

VGsim: Scalable viral genealogy simulator for global pandemic

Accurate simulation of complex biological processes is an essential component of developing and validating new technologies and inference approaches. As an effort to help contain the COVID-19 pandemic, large numbers of SARS-CoV-2 genomes have been sequenced from most regions in the world. More than 5.5 million viral sequences are publicly available as of November 2021. Many studies estimate viral genealogies from these sequences, as these can provide valuable information about the spread of the pandemic across time and space. Additionally such data are a rich source of information about molecular evolutionary processes including natural selection, for example allowing the identification of new variants with transmissibility and immunity evasion advantages. To our knowledge, there is no framework that is both efficient and flexible enough to simulate the pandemic to approximate world-scale scenarios and generate viral genealogies of millions of samples. Here, we introduce a new fast simulator VGsim which addresses the problem of simulation genealogies under epidemiological models. The simulation process is split into two phases. During the forward run the algorithm generates a chain of population-level events reflecting the dynamics of the pandemic using an hierarchical version of the Gillespie algorithm. During the backward run a coalescent-like approach generates a tree genealogy of samples conditioning on the population-level events chain generated during the forward run. Our software can model complex population structure, epistasis and immunity escape.

We develop a fast and flexible simulation software package VGsim for modeling epidemiological processes and generating genealogies of large pathogen samples. The software takes into account host population structure, pathogen evolution, host immunity and some other epidemiological aspects. The computational efficiency of the package allows to simulate genealogies of tens of millions of samples, which is important, e.g., for SARS-CoV-2 genome studies.

Spatial effects in parasite-induced marine diseases of immobile hosts

Emerging marine infectious diseases pose a substantial threat to marine ecosystems and the conservation of their biodiversity. Compartmental models of epidemic transmission in marine sessile organisms, available only recently, are based on non-spatial descriptions in which space is homogenized and parasite mobility is not explicitly accounted for. However, in realistic scenarios epidemic transmission is conditioned by the spatial distribution of hosts and the parasites' mobility patterns, calling for an explicit description of space. In this work, we develop a spatially explicit individual-based model to study disease transmission by waterborne parasites in sessile marine populations. We investigate the impact of spatial disease transmission through extensive numerical simulations and theoretical analysis. Specifically, the effects of parasite mobility into the epidemic threshold and the temporal progression of the epidemic are assessed. We show that larger values of pathogen mobility imply more severe epidemics, as the number of infections increases, and shorter timescales to extinction. An analytical expression for the basic reproduction number of the spatial model, R ~ 0 , is derived as a function of the non-spatial counterpart, R ₀, which characterizes a transition between a disease-free and a propagation phase, in which the disease propagates over a large fraction of the system.

Model Complexity and Accuracy: A COVID-19 Case Study

When creating mathematical models for forecasting and decision making, there is a tendency to include more complexity than necessary, in the belief that higher-fidelity models are more accurate than simpler ones. In this paper, we analyze the performance of models that submitted COVID-19 forecasts to the U.S. Centers for Disease Control and Prevention and evaluate them against a simple two-equation model that is specified using simple linear regression. We find that our simple model was comparable in accuracy to highly publicized models and had among the best-calibrated forecasts. This result may be surprising given the complexity of many COVID-19 models and their support by large forecasting teams. However, our result is consistent with the body of research that suggests that simple models perform very well in a variety of settings.

Parasite-induced shifts in host movement may explain the transient coexistence of high- and low-pathogenic disease strains

Many parasites induce decreased host movement, known as lethargy, which can impact disease spread and the evolution of virulence. Mathematical models have investigated virulence evolution when parasites cause host death, but disease-induced decreased host movement has received relatively less attention. Here, we consider a model where, due to the within-host parasite replication rate, an infected host can become lethargic and shift from a moving to a resting state, where it can die. We find that when the lethargy and disease-induced mortality costs to the parasites are not high, then evolutionary bistability can arise, and either moderate or high virulence can evolve depending on the initial virulence and the magnitude of mutation. These results suggest, firstly, the coexistence of strains with different virulence, which may explain the transient coexistence of low- and high-pathogenic strains of avian influenza viruses, and secondly, that medical interventions to treat the symptoms of lethargy or prevent disease-induced host deaths can result in a large jump in virulence and the rapid evolution of high virulence. In complement to existing results that show bistability when hosts are heterogeneous at the population level, we show that evolutionary bistability may arise due to transmission heterogeneity at the individual host level.

Modeling pandemic to endemic patterns of SARS-CoV-2 transmission using parameters estimated from animal model data

The contours of endemic coronaviral disease in humans and other animals are shaped by the tendency of coronaviruses to generate new variants superimposed upon nonsterilizing immunity. Consequently, patterns of coronaviral reinfection in animals can inform the emerging endemic state of the SARS-CoV-2 pandemic. We generated controlled reinfection data after high and low risk natural exposure or heterologous vaccination to sialodacryoadenitis virus (SDAV) in rats. Using deterministic compartmental models, we utilized in vivo estimates from these experiments to model the combined effects of variable transmission rates, variable duration of immunity, successive waves of variants, and vaccination on patterns of viral transmission. Using rat experiment-derived estimates, an endemic state achieved by natural infection alone occurred after a median of 724 days with approximately 41.3% of the population susceptible to reinfection. After accounting for translationally altered parameters between rat-derived data and human SARS-CoV-2 transmission, and after introducing vaccination, we arrived at a median time to endemic stability of 1437 (IQR = 749.25) days with a median 15.4% of the population remaining susceptible. We extended the models to introduce successive variants with increasing transmissibility and included the effect of varying duration of immunity. As seen with endemic coronaviral infections in other animals, transmission states are altered by introduction of new variants, even with vaccination. However, vaccination combined with natural immunity maintains a lower prevalence of infection than natural infection alone and provides greater resilience against the effects of transmissible variants.

Impact of implementation timing on the effectiveness of stay-at-home requirement under the COVID-19 pandemic: Lessons from the Italian Case

When a new infectious outbreak emerges, governments must initially rely on non-pharmaceutical interventions (NPIs) to mitigate the impact of the pathogen. Although a strict stay-at-home requirement (i.e., lockdown) presents high effectiveness in reducing patients hospitalized in intensive care units (ICUs), it comes with unintended physical, psychological, and economic damages for the citizens. Using how Italy managed the COVID-19 outbreak from February to September 2020 on a national basis, this study aims at understanding the impact of implementation timing on the effectiveness of NPIs. Our findings may be helpful to avoid the implementation of stay-at-home requirements when it is not strictly necessary. A compartmental SEICRD model was developed to create the baseline scenario without NPIs. Generalized Poisson regressions were applied to study the change in effectiveness over-time of NPIs on Avoided ICUs for each one of the Italian regions. Our study suggests that although the stay-at-home requirement is the most effective measure in reducing ICU hospitalizations in regions encountering the outbreak early, its effectiveness decreases in regions encountering the outbreak later, where a set of other NPIs are more effective. We developed a reference of daily new cases when lockdown should be implemented or avoided, accordingly. Our findings could be useful to support policymakers in contrasting the pandemic and in limiting the societal and economic impact of stringent NPIs.

COVID-19 heterogeneity in islands chain environment

Background

It is critical to capture data and modeling from the COVID-19 pandemic to understand as much as possible and prepare for future epidemics and possible pandemics. The Hawaiian Islands provide a unique opportunity to study heterogeneity and demographics in a controlled environment due to the geographically closed borders and mostly uniform pandemic-induced governmental controls and restrictions.

Objective

The goal of the paper is to quantify the differences and similarities in the spread of COVID-19 among different Hawaiian islands as well as several other archipelago and islands, which could potentially help us better understand the effect of differences in social behavior and various mitigation measures. The approach should be robust with respect to the unavoidable differences in time, as the arrival of the virus and promptness of mitigation measures may vary significantly among the chosen locations. At the same time, the comparison should be able to capture differences in the overall pandemic experience.

Methods

We examine available data on the daily cases, positivity rates, mobility, and employ a compartmentalized model fitted to the daily cases to develop appropriate comparison approaches. In particular, we focus on merge trees for the daily cases, normalized positivity rates, and baseline transmission rates of the models.

Results

We observe noticeable differences among different Hawaiian counties and interesting similarities between some Hawaiian counties and other geographic locations. The results suggest that mitigation measures should be more localized, that is, targeting the county level rather than the state level if the counties are reasonably insulated from one another. We also notice that the spread of the disease is very sensitive to unexpected events and certain changes in mitigation measures.

Conclusions

Despite being a part of the same archipelago and having similar protocols for mitigation measures, different Hawaiian counties exhibit quantifiably different dynamics of the spread of the disease. One potential explanation is that not sufficiently targeted mitigation measures are incapable of handling unexpected, localized outbreak events. At a larger-scale view of the general spread of the disease on the Hawaiian island counties, we find very interesting similarities between individual Hawaiian islands and other archipelago and islands.

Epidemiological modelling in refugee and internally displaced people settlements: challenges and ways forward

The spread of infectious diseases such as COVID-19 presents many challenges to healthcare systems and infrastructures across the world, exacerbating inequalities and leaving the world’s most vulnerable populations at risk. Epidemiological modelling is vital to guiding evidence-informed or data-driven decision making. In forced displacement contexts, and in particular refugee and internally displaced people (IDP) settlements, it meets several challenges including data availability and quality, the applicability of existing models to those contexts, the accurate modelling of cultural differences or specificities of those operational settings, the communication of results and uncertainties, as well as the alignment of strategic goals between diverse partners in complex situations. In this paper, we systematically review the limited epidemiological modelling work applied to refugee and IDP settlements so far, and discuss challenges and identify lessons learnt from the process. With the likelihood of disease outbreaks expected to increase in the future as more people are displaced due to conflict and climate change, we call for the development of more approaches and models specifically designed to include the unique features and populations of refugee and IDP settlements. To strengthen collaboration between the modelling and the humanitarian public health communities, we propose a roadmap to encourage the development of systems and frameworks to share needs, build tools and coordinate responses in an efficient and scalable manner, both for this pandemic and for future outbreaks.

Modeling Social Distancing and Quantifying Epidemic Disease Exposure in a Built Environment

As we transition away from pandemic-induced isolation and social distancing, there is a need to estimate the risk of exposure in built environments. We propose a novel metric to quantify social distancing and the potential risk of exposure to airborne diseases in an indoor setting, which scales with distance and the number of people present. The risk of exposure metric is designed to incorporate the dynamics of particle movement in an enclosed set of rooms for people at different immunity levels, susceptibility due to age, background infection rates, intrinsic individual risk factors (e.g., comorbidities), mask-wearing levels, the half-life of the virus and ventilation rate in the environment. The model parameters have been selected for COVID-19, although the modeling framework applies to other airborne diseases. The performance of the metric is tested using simulations of a real physical environment, combining models for walking, path length dynamics, and air-conditioning replacement action. We have also created a visualization tool to help identify high-risk areas in the built environment. The resulting software framework is being used to help with planning movement and scheduling in a clinical environment ahead of reopening of the facility, for deciding the maximum time within an environment that is safe for a given number of people, for air replacement settings on air-conditioning and heating systems, and for mask-wearing policies. The framework can also be used for identifying locations where foot traffic might create high-risk zones and for planning timetabled transitions of groups of people between activities in different spaces. Moreover, when coupled with individual-level location tracking (via radio-frequency tagging, for example), the exposure risk metric can be used in real-time to estimate the risk of exposure to the coronavirus or other airborne illnesses, and intervene through air-conditioning action modification, changes in timetabling of group activities, mask-wearing policies, or restricting the number of individuals entering a given room/space. All software are provided online under an open-source license.

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

Prioritizing high-contact occupations raises effectiveness of vaccination campaigns

A twenty-year-old idea from network science is that vaccination campaigns would be more effective if high-contact individuals were preferentially targeted. Implementation is impeded by the ethical and practical problem of differentiating vaccine access based on a personal characteristic that is hard-to-measure and private. Here, we propose the use of occupational category as a proxy for connectedness in a contact network. Using survey data on occupation-specific contact frequencies, we calibrate a model of disease propagation in populations undergoing varying vaccination campaigns. We find that vaccination campaigns that prioritize high-contact occupational groups achieve similar infection levels with half the number of vaccines, while also reducing and delaying peaks. The paper thus identifies a concrete, operational strategy for dramatically improving vaccination efficiency in ongoing pandemics.

Mitigating bias in estimating epidemic severity due to heterogeneity of epidemic onset and data aggregation

Outbreaks of infectious diseases, such as influenza, are a major societal burden. Mitigation policies during an outbreak or pandemic are guided by the analysis of data of ongoing or preceding epidemics. The reproduction number, R0, defined as the expected number of secondary infections arising from a single individual in a population of susceptibles is critical to epidemiology. For typical compartmental models such as the Susceptible-Infected-Recovered (SIR) R0 represents the severity of an epidemic. It is an estimate of the early-stage growth rate of an epidemic and is an important threshold parameter used to gain insights into the spread or decay of an outbreak. Models typically use incidence counts as indicators of cases within a single large population; however, epidemic data are the result of a hierarchical aggregation, where incidence counts from spatially separated monitoring sites (or sub-regions) are pooled and used to infer R0. Is this aggregation approach valid when the epidemic has different dynamics across the regions monitored? We characterize bias in the estimation of R0 from a merged data set when the epidemics of the sub-regions, used in the merger, exhibit delays in onset. We propose a method to mitigate this bias, and study its efficacy on synthetic data as well as real-world influenza and COVID-19 data.

A Multi-Agent-Based Simulation Model for the Spreading of Diseases Through Social Interactions During Pandemics

Epidemiological models have a vital and consolidated role in aiding decision-making during crises such as the Coronavirus Disease 2019 (COVID-19) pandemic. However, the influence of social interactions in the spreading of communicable diseases is left aside from the main models in the literature. The main contribution of this work is the introduction of a probabilistic simulation model based on a multi-agent approach that is capable of predicting the spreading of diseases. Our proposal has a simple model for the main source of infections in pandemics of respiratory viruses: social interactions. This simplicity is key for incorporating complex networks topology into the model, which is a more accurate representation for real-world interactions. This flexibility in network structure allows the evaluation of specific phenomena, such as the presence of super-spreaders. We provide the modeling for the dynamical network topology in two different simulation scenarios. Another contribution is the generic microscopic model for infection evolution that enables the evaluation of impact from more specific behaviors and interventions on the overall spreading of the disease. It also enables a more intuitive process for going from data to model parameters. This ease of changing the infection evolution model is key for performing more complete analyses than would be possible in other models from the literature. Further, we give specific parameters for a controlled scenario with quick testing and tracing. We present computational results that illustrate the model utilization for predicting the spreading of COVID-19 in a city. Also, we show the results of applying the model for assessing the risk of resuming on-site activities at a collective use facility.

An agent-based model of spread of a pandemic with validation using COVID-19 data from New York State

We introduce a novel agent based model where each agent carries an effective viral load that captures the instantaneous state of infection of the agent. We simulate the spread of a pandemic and subsequently validate it by using publicly available COVID-19 data. Our simulation tracks the temporal evolution of a virtual city or community of agents in terms of contracting infection, recovering asymptomatically, or getting hospitalized. The virtual community is divided into family groups with 2-6 individuals in each group. Agents interact with other agents in virtual public places like at grocery stores, on public transportation and in offices. We initially seed the virtual community with a very small number of infected individuals and then monitor the disease spread and hospitalization over a period of fifty days, which is a reasonable time-frame for the initial spread of a pandemic. An uninfected or asymptomatic agent is randomly selected from a random family group in each simulation step for visiting a random public space. Subsequently, an uninfected agent contracts infection if the public place is occupied by other infected agents. We have calibrated our simulation rounds according to the size of the population of the virtual community for simulating realistic exposure of agents to a contagion. Our simulation results are consistent with the publicly available hospitalization and ICU patient data from three distinct regions of varying sizes in New York state. Our model can predict the trend in epidemic spread and hospitalization from a set of simple parameters and could be potentially useful in predicting the disease evolution based on available data and observations about public behavior. Our simulations suggest that relaxing the social distancing measures may increase the hospitalization numbers by some 30% or more.