Schedule for: 22w5058 - Preparing for the next pandemic

Ideally, a top down preparation for the unknown should yield a flexible family of models that are qualitatively understood and can be bottom up adjusted quantitatively to whatever information becomes available. In this spirit, KM (Kermack and McKendrick) introduced in 1927 a RE (Renewal Equation) formulation of a wide class of models of an outbreak of an infectious disease in a closed population. Unfortunately, the persistent misconception is that their paper is devoted to the SIR compartmental model. And in the wake of that misconception, the rather restricted class of compartmental models became predominant. The aim of the lecture is to advertise the KM RE approach for epidemic model formulation by highlighting recent variations and extensions, in particular a discrete time variant and a version that incorporates various forms of (static) heterogeneity.

We are interested in estimating the changing distribution of immunity, from infection and vaccination, against a pathogen over time. In this talk, I will introduce our mathematical modelling framework of immunity. I will also discuss in-host modelling activities that we have used to inform our immunity outcome assumptions in the population-level model. Examples of model output will focus on COVID-19 in Canada.

Timely drug development is crucial in influencing the outcome of a pandemic. In this talk, I will give a brief overview of the drug development pipeline and how modeling and simulation can play a key role in expediting the various stages or in assuring drug safety. In preparing for the next pandemic, modeling and simulation should be a part of the strategy to decrease the time it takes for drugs to reach the populations at risk.

The COVID-19 pandemic has highlighted the urgent need to develop reliable tools to forecast the trajectory of epidemics and pandemics in near real-time. In this talk I introduce and apply an ensemble n-sub-epidemic modeling framework for forecasting the trajectory of epidemics and pandemics. We systematically assess its calibration and short-term forecasting performance in weekly 10-30 days ahead forecasts in the context of the COVID-19 pandemic in the USA from late April 2020 to late February 2022 and compare its performance with two commonly used statistical ARIMA models. This framework demonstrated reliable forecasting performance and substantially outcompeted the ARIMA models. In particular, forecasting performance consistently improved for the ensemble sub-epidemic models that incorporated a higher number of top-ranking sub-epidemic models. The ensemble model incorporating the top four ranking sub-epidemic models consistently yielded the best performance, particularly in terms of the coverage rate of the 95% prediction interval and the weighted interval score. This framework could be applied to forecast other growth processes found in nature and society including the spread of information through social media.

Chemical reaction networks depict a biological system as a graph with 1. nodes (complexes) created by a combination of variables (constituent species) and 2. directed edges (reactions) such as as A+B -> C. One of the major problems in this literature is to derive qualitative behaviors of the dynamical system associated with a reaction network using its network structural conditions. In this talk, we will discuss how network structural conditions can be used to study infection disease models desribed with reaction networks. As an example, we will consider infection disease models on small communities such as school or campus, that can have various underlying network structures.

In the simplest epidemic models, the population reaches herd immunity once a certain fraction of individuals have gained immunity. While a single number suffices in homogenous populations, in a heterogeneous population, a number is needed for every category. In August 2020, Ball, Britton, and Trapman used a 6 age level 3 activity level model to show that population heterogeneity can substantially reduce the total number of immune people needed for herd immunity. In this talk, we discuss how heterogeneity affects herd immunity in simpler models.

During the COVID-19 pandemic, a range of mathematical models were applied to data in real-time in order to predict of project the future course, estimate key parameters, and understand important new features such as the transmissibility of emerging variants. Here I will describe our efforts in these areas, with a particular focus on the predictive ability of mathematical models in the context of attempting to inform policy. I will discuss the challenges we encountered, and use them to reflect on lessons learned that could help better prepare for future pandemics.

Efforts to forecast the COVID-19 pandemic proliferated rapidly in early 2020, building on previous forecasting work for other pathogens. The lack of historical data, evolving data streams, dynamic participation, role of variants, and scope and scale of mitigation measures all presented new challenges to forecasting science. Major collaborative efforts have provided operational forecasts for many jurisdictions with some documented success. For example, ensemble forecasts continue to provide more reliable information than most individual team forecasts and scenario projections have helped inform decision making at horizons for which forecasts are unreliable. Nonetheless, critical scientific challenges remain to improve forecast reliability, further reduce uncertainty, and extend forecast horizons.

In the past decade, human mobility data has become increasingly available with the introduction of smartphone devices. Not only did communication between acquaintances and access to information become easier; smartphones provide clues on the movement patterns of individuals throughout their day. Incorporating mobility data into an epidemiological model can offer valuable insight for implementing control strategies. In this talk, we will present analytical tools for approximating the basic reproduction number for a SIS-SI vector-borne disease network model. We will use cell phone data to estimate the movement patterns of individuals between different regions with the objective of understanding how the network structure influences vector-borne disease dynamics.

In the COVID-19 pandemic, the primary tools used to analyze the spread of infection were based on epidemic curves of reported incident infections and population-level models of transmission. While these methods might be useful for short-term predictions, they do not yield reliable insights into risks, rates, and mechanisms of transmission that can be used to design interventions---the measurements are too coarse to support modeling robust and accurate enough for causal inference. Careful measurement and modeling of transmission in close-contact settings such as households, congregate living facilities, hospitals, classrooms, and workplaces is our most promising method of producing such insights. Such studies must be done more often and in more locations, and they must be analyzed using methods such as chain binomial models or pairwise survival analysis. They have the potential to incorporate information about pathogen genomes to improve accuracy and precision, and they have the potential to relate pathogen mutations directly to changes in transmissibility. However, there are important practical and logistical problems to solve in terms of recruitment, high frequency testing, and data collection. Conducting household studies of influenza, coronavirus, cholera, and other infectious diseases will lay a foundation for the effective deployment and analysis of these studies in a future pandemic. Through the shared concept of the contact interval distribution, pairwise survival analysis methods can inform and be informed by dynamical survival analysis (DSA) models for the population-level spread of infection. Combined, these methods provide a novel multi-scale approach to the epidemiology of communicable diseases.

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as “frailty variation”. Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being crucial to protect vulnerable individuals from severe outcomes as the virus becomes endemic.

Epidemic control is perhaps the most debated topic in infectious diseases in these times. Defining and implementing social distancing protocols is a significant challenge with economical, political, and scientific considerations. The definition of a clear or optimal goal remains unclear. The main question is which policies should be employed to make sure that the healthcare system is not overwhelmed as the epidemic spreads, while at the same time ensuring that harsh measures such as lockdowns are not maintained more than what is deemed as strictly necessary. In this context, modelling is a powerful tool to investigate the likely impact of different measures. While, in the era of big data, high complexity models are the gold-standard when addressing country-specific questions, simpler models remain important to understand the core ideas behind different policy choices. In this talk we will explore several possibilities, from one-shot interventions to the problem of controlling an outbreak through its whole course, with particular attention to the possible issues of model misspecification.

The role of children in SARS-CoV-2 transmission has been uncertain throughout the pandemic. While early in the pandemic, it has been suggested that children might have a lower susceptibility to infection and contribute less to onward transmission, this hypothesis has been challenged by their unique social behavior and contact network as well as the emergence of new variants. It has become clear that understanding the effect of age structure on the epidemic dynamics is crucial for guiding public health policies. In this talk, I will give a broad overview of what we have learned about the role of school-age children in the current pandemic. I will focus on the contribution of mathematical modeling to understanding the SARS-CoV-2 transmission dynamics within schools and the potential effect of school-based interventions.

Even as our attempts to predict all twists and turns of the global COVID-19 pandemic over last 2 years have exposed severe shortcomings in our traditional methodology of analyzing ecological systems, they also led to many new interesting scientific ideas and a broader discussion about the role of mathematicians in shaping public health policies. This talk will review some of the experiences from my last years of working on pandemic modeling in the state of Ohio focusing on possible new modeling directions combining agent-based and population-level models.

Dynamic Survival Analysis combines classical dynamical systems theory and survival analysis to provide a probabilistic interpretation of mean-field equations for population dynamics. In essence, it turns an ecological model into an agent-based model by interpreting the mean-field ordinary or partial differential equations as describing probability laws of individual trajectories. One can then write efficient algorithms for likelihood-based parameter inference for both Markov as well as non-Markov models. Because of its foundation in survival analysis, the method can handle aggregation (over time and individuals), censoring and truncation of data in a principled way. The talk will provide several examples to highlight the incredible flexibility of the method.

The calculus is the fact that changing variables in an SIR model for the competition of two infections leads to a logistic. This observation “explains” the rapid takeover by new more transmissible covid variants. We apply this observation to data on te transition from beta to delta to the micron family of variants.

We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erd˝os-R´enyi and Barab´asi-Albert networks. It is known that the contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, in this case at the population-level, contain information about the underlying network. This information, in turn, is useful for predicting the future course of an ongoing epidemic. To exploit this in a prediction framework, the exact high-dimensional stochastic model of an SIS epidemic on a network is approximated by a lower-dimensional surrogate model. The surrogate model is based on a birth-and-death process; the effect of the underlying network is described by a parametric model for the birth rates. We demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. As long as the population-level data is available over a long-enough period, even if not sampled frequently, the model leads to excellent predictions where the underlying network is correctly identified and prediction uncertainty mainly reflects the intrinsic stochasticity of the spreading epidemic. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty. The proposed method relies on minimal data at population-level, which is always likely to be available. This, combined with its numerical efficiency, makes the proposed method attractive to be used either as a standalone inference and prediction scheme or in conjunction with other inference and/or predictive models.

Many of the policy responses to the COVID-19 pandemic have involved restricting people’s behavior. Often these have been associated with penalties to induce compliance. When designing a policy, ethical considerations suggest that the penalties for an action should be proportional to the harm caused by that action. In this talk, I will explore the expected impact on the final size of an epidemic of a single individual changing behavior as well as the combined impact of a group. Due to the convexity of the final size relation, the marginal benefit of an individual changing behavior to prevent transmission is increased if others are also taking actions to prevent transmission. This benefit is largest when the reproduction number is close to 1. This talk will also have an introduction to the use of Probability Generating Functions in modeling infectious disease transmission.

We consider the minimization of the total number of infected individuals over the course of an epidemic in which the rate of infectious contacts can be reduced by time-dependent nonpharmaceutical interventions. The societal and economic costs of interventions are taken into account using a linear budget constraint which imposes a trade-off between short-term heavy interventions and long-term light interventions. We search for an optimal intervention strategy in an infinite-dimensional space of controls containing multiple consecutive lockdowns, gradually imposed and lifted restrictions, and various heuristic controls based for example on tracking the effective reproduction number. We derive the optimal strategy among all interventions not exceeding a pre-specified maximal cost. It is further proven that, rather counterintuitively, adding restrictions prior to the start of the optimal strategy may even increase the total incidence.

The emergence of new infectious diseases, particularly vector-borne diseases, has increased over the last few decades and this trend is predicted to continue due to a now rapidly changing climate. Our goal is to develop an architecture that integrates large, heterogeneous datasets into global-scale Earth system models coupled to local-scale mechanistic models. Developing this model will require integrating biological, demographic, infrastructural, epidemiological, hydrological, and ecological drivers. Our continental-scale model, the Climate Integrated Model of Mosquito-borne Infectious Diseases (CIMMID), is the first ever process-based mosquito-borne disease model that integrates all of the critical processes of hydrology, vegetation, mosquito, human, and disease transmission. Mechanistic models using highly heterogeneous datasets at multiple scales are essential for our predictive understanding of global security risk and predicting nonlinear human-natural systems. We use model-driven data fusion approach integrating large, heterogeneous data to predict mosquito-borne disease spread. A key innovation of CIMMID, suitable for both seasonal and decadal prediction of disease risks, is our development of the “HydroPop unit” which couples the DOE’s Energy Exascale Earth System Model processes with our existing local disease transmission models by subdividing E3SM grid cells into mosquito habitat units. The long-term goal of this project is to develop a model-driven data fusion platform that we can extend to predict relevant risks by swapping in relevant models of those processes globally.

Real-time forecasting of infectious diseases is a crucial component of decision support during a public health emergency. In the face of uncertainty, it allows stakeholders to visualize the potential paths an outbreak may take. The need for forecasting was highlighted early in the COVID-19 pandemic following its rapid global spread, and later as behavioral changes made anticipating transmission levels difficult. In March 2020, we built a flexible forecasting model that projects cumulative COVID-19 cases and deaths six weeks ahead at multiple spatial scales: globally at the national level, for every state/territory in the United States (US), and for US counties with more than 3,000 individuals. The world’s understanding of SARS-CoV2 and COVID-19 has grown significantly since 2020. Similarly, our understanding of what is and isn’t important for COVID-19 forecasting has also evolved and improved. In this talk, I will describe Los Alamos National Laboratory’s forecasting model and then discuss how COVID-19 forecasting efforts have evolved since the start of the pandemic, highlighting trends of the forecasting community at-large as well as our own experience. COVID-19 is the first pandemic that has been forecasted in real-time at scale. By reflecting on what went right, what went wrong, and what needs to be improved, we can be better prepared next time.

Environmental pathogen surveillance is a promising disease surveillance modality that has been widely adopted for SARS-CoV-2 monitoring. The highly variable nature of environmental pathogen data is a challenge for integrating these data into public health response. One source of this variability is heterogeneous infection both within an individual over the course of infection, as well as between individuals in their pathogen shedding over time. We present a mechanistic modeling and estimation framework for connecting environmental pathogen data to infection prevalence. Infected individuals are modeled as shedding pathogen into the environment via a Poisson process whose rate parameter $\lambda_t$ varies over the course of their infection. These shedding curves $\lambda_t$ are themselves random, allowing for variation between individuals. We show that this results in a Poisson process for environmental pathogen levels with rate parameter a function of infection prevalence, total shedding over the course of infection, and pathogen removal from the environment. Theoretical results include determination of identifiable parameters for the model from environmental pathogen data, and simple, explicit formulas for the likelihood for particular choices of individual shedding curves. We give a two-step Bayesian inference framework, where the first step corresponds to calibration from data where prevalence is known, followed by an estimation step from environmental surveillance data when prevalence is unknown. We apply this modeling and estimation framework to synthetic data, as well as to an empirical case study of SARS-CoV-2 in environmental dust collected from isolation rooms housing university students. Both the synthetic data and empirical case study indicate high inter-individual variation in shedding, leading to wide credible intervals for prevalence. We examine how uncertainty in prevalence estimates from environmental pathogen levels scales with true infection prevalence and model misspecification.

Covid-19 has thrown up various interesting research questions for infectious disease modellers. In this talk I will briefly discuss two that I have worked on. The first, is what does the (partial) observation of the times at which individuals show symptoms tell us about the number of individuals infected in a population? The second, is what affect do superspreader events have on disease dynamics? (joint work with Frank Ball)

Serial intervals are a fundamental quantity in infectious disease control; however, their estimation requires knowledge of individuals' contacts and exposures, typically obtained through resource-intensive contact tracing efforts. I will present a new approach that instead uses virus sequences to inform who infected whom and thereby estimate serial intervals. The statistical model takes incomplete sampling into account as the method is intended to be applied at a broader scale than typical contact-based approaches, for example to track population-level changes in the serial interval through time. I will describe an application to COVID-19 data from Victoria, Australia, in which we compare estimates of the serial interval from different case clusters and across contact sites such as schools and healthcare.

In preparing for the next pandemic, it is necessary to have a fundamental understanding of how disease is transmitted, and what factors limit its eradication. In the case of COVID-19, the situation remains particularly severe. Gaps in our knowledge included: (1) Failure to understand the physics of transmission, in particular that COVID-19 is airborne. (2) Failure of epidemic modeling to capture the interplay between social activity and disease spreading. (3) Failure to appreciate that evolution can be rapid. Many other factors, including social, behavioural, medical and economic contribute to the difficulty for society to respond effectively. In this talk, I report on our successes and failures in modeling social activity along with COVID-19 transmission, extending epidemic models to include stochastic social activity. I also report on the way that modeling was able to help design, set up and run a large-scale COVID-19 mitigation effort at the University of Illinois at Urbana-Champaign, starting in summer 2020. Modeling was performed at the agent level as well as the population level, and the former included the physics of COVID-19 transmission by aerosols. Mitigation was based on surveillance testing using PCR on saliva samples, collected from a population of ~50,000 at two to three times a week. Modeling and real-time data analytics were required to prevent runaway exponential growth of COVID-19 in the community. During 2020, the outcomes of the latter include: (1) R frequently in 0.75-0.85, daily case positivity mostly ~0.5%, reaching a highly-publicised maximum of 2.86% on only one day. The local pandemic was controlled with no out of control exponential growth, and the university remained open. (2) Highly social undergraduate student cases were essentially uncorrelated with faculty/staff and Champaign County residents (excluding the students), so our university did not drive cases within the surrounding community. (3) Among all 251 US counties with universities with enrollment > 15,000, Champaign County had 32% reduction in cases and 4-fold reduction in mortality compared to expectation. These results show that a major systematic approach to pandemic mitigation is possible locally and can achieve good outcomes. However, significant resources, training and collaboration between public health officials and scientists is required.