Choices and trade-offs in inference with infectious disease models

Examining the impact of ICU population interaction structure on modeled colonization dynamics of Staphylococcus aureus

Background

Complex transmission models of healthcare-associated infections provide insight for hospital epidemiology and infection control efforts, but they are difficult to implement and come at high computational costs. Structuring more simplified models to incorporate the heterogeneity of the intensive care unit (ICU) patient-provider interactions, we explore how methicillin-resistant Staphylococcus aureus (MRSA) dynamics and acquisitions may be better represented and approximated.

Methods

Using a stochastic compartmental model of an 18-bed ICU, we compared the rates of MRSA acquisition across three ICU population interaction structures: a model with nurses and physicians as a single staff type (SST), a model with separate staff types for nurses and physicians (Nurse-MD model), and a Metapopulation model where each nurse was assigned a group of patients. The proportion of time spent with the assigned patient group (γ) within the Metapopulation model was also varied.

Results

The SST, Nurse-MD, and Metapopulation models had a mean of 40.6, 32.2 and 19.6 annual MRSA acquisitions respectively. All models were sensitive to the same parameters in the same direction, although the Metapopulation model was less sensitive. The number of acquisitions varied non-linearly by values of γ, with values below 0.40 resembling the Nurse-MD model, while values above that converged toward the Metapopulation structure.

Discussion

Inclusion of complex population interactions within a modeled hospital ICU has considerable impact on model results, with the SST model having more than double the acquisition rate of the more structured metapopulation model. While the direction of parameter sensitivity remained the same, the magnitude of these differences varied, producing different colonization rates across relatively similar populations. The non-linearity of the model’s response to differing values of a parameter gamma (γ) suggests simple model approximations are appropriate in only a narrow space of relatively dispersed nursing assignments.

Conclusion

Simplifying assumptions around how a hospital population is modeled, especially assuming random mixing, may overestimate infection rates and the impact of interventions. In many, if not most, cases more complex models that represent population mixing with higher granularity are justified.

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease's natural history and individuals' behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland's first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.

Planning as Inference in Epidemiological Dynamics Models

In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policy-making could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.

A runtime alterable epidemic model with genetic drift, waning immunity and vaccinations

We present methods for building a Java Runtime-Alterable-Model Platform (RAMP) of complex dynamical systems. We illustrate our methods by building a multivariant SEIR (epidemic) RAMP. Underlying our RAMP is an individual-based model that includes adaptive contact rates, pathogen genetic drift, waning and cross-immunity. Besides allowing parameter values, process descriptions and scriptable runtime drivers to be easily modified during simulations, our RAMP can used within R-Studio and other computational platforms. Process descriptions that can be runtime altered within our SEIR RAMP include pathogen variant-dependent host shedding, environmental persistence, host transmission and within-host pathogen mutation and replication. They also include adaptive social distancing and adaptive application of vaccination rates and variant-valency of vaccines. We present simulation results using parameter values and process descriptions relevant to the current COVID-19 pandemic. Our results suggest that if waning immunity outpaces vaccination rates, then vaccination rollouts may fail to contain the most transmissible variants, particularly if vaccine valencies are not adapted to deal with escape mutations. Our SEIR RAMP is designed for easy use by others. More generally, our RAMP concept facilitates construction of highly flexible complex systems models of all types, which can then be easily shared as stand-alone application programs.

Possible future waves of SARS-CoV-2 infection generated by variants of concern with a range of characteristics

Viral reproduction of SARS-CoV-2 provides opportunities for the acquisition of advantageous mutations, altering viral transmissibility, disease severity, and/or allowing escape from natural or vaccine-derived immunity. We use three mathematical models: a parsimonious deterministic model with homogeneous mixing; an age-structured model; and a stochastic importation model to investigate the effect of potential variants of concern (VOCs). Calibrating to the situation in England in May 2021, we find epidemiological trajectories for putative VOCs are wide-ranging and dependent on their transmissibility, immune escape capability, and the introduction timing of a postulated VOC-targeted vaccine. We demonstrate that a VOC with a substantial transmission advantage over resident variants, or with immune escape properties, can generate a wave of infections and hospitalisations comparable to the winter 2020-2021 wave. Moreover, a variant that is less transmissible, but shows partial immune-escape could provoke a wave of infection that would not be revealed until control measures are further relaxed.

Comparison between one and two dose SARS-CoV-2 vaccine prioritization for a fixed number of vaccine doses

The swift development of SARS-CoV-2 vaccines has been met with worldwide commendation. However, in the context of an ongoing pandemic there is an interplay between infection and vaccination. While infection can grow exponentially, vaccination rates are generally limited by supply and logistics. With the first SARS-CoV-2 vaccines receiving medical approval requiring two doses, there has been scrutiny on the spacing between doses; an elongated period between doses allows more of the population to receive a first vaccine dose in the short-term generating wide-spread partial immunity. Focusing on data from England, we investigated prioritization of a one dose or two dose vaccination schedule given a fixed number of vaccine doses and with respect to a measure of maximizing averted deaths. We optimized outcomes for two different estimates of population size and relative risk of mortality for at-risk groups within the Phase 1 vaccine priority order. Vaccines offering relatively high protection from the first dose favour strategies that prioritize giving more people one dose, although with increasing vaccine supply eventually those eligible and accepting vaccination will receive two doses. While optimal dose timing can substantially reduce the overall mortality risk, there needs to be careful consideration of the logistics of vaccine delivery.

Modeling transmission of pathogens in healthcare settings

PURPOSE OF REVIEW

Mathematical, statistical, and computational models provide insight into the transmission mechanisms and optimal control of healthcare-associated infections. To contextualize recent findings, we offer a summative review of recent literature focused on modeling transmission of pathogens in healthcare settings.

RECENT FINDINGS

The COVID-19 pandemic has led to a dramatic shift in the modeling landscape as the healthcare community has raced to characterize the transmission dynamics of SARS-CoV-2 and develop effective interventions. Inequities in COVID-19 outcomes have inspired new efforts to quantify how structural bias impacts both health outcomes and model parameterization. Meanwhile, developments in the modeling of methicillin-resistant Staphylococcus aureus, Clostridioides difficile, and other nosocomial infections continue to advance. Machine learning continues to be applied in novel ways, and genomic data is being increasingly incorporated into modeling efforts.

SUMMARY

As the type and amount of data continues to grow, mathematical, statistical, and computational modeling will play an increasing role in healthcare epidemiology. Gaps remain in producing models that are generalizable to a variety of time periods, geographic locations, and populations. However, with effective communication of findings and interdisciplinary collaboration, opportunities for implementing models for clinical decision-making and public health decision-making are bound to increase.

Real-time tracking and prediction of COVID-19 infection using digital proxies of population mobility and mixing

Digital proxies of human mobility and physical mixing have been used to monitor viral transmissibility and effectiveness of social distancing interventions in the ongoing COVID-19 pandemic. We develop a new framework that parameterizes disease transmission models with age-specific digital mobility data. By fitting the model to case data in Hong Kong, we are able to accurately track the local effective reproduction number of COVID-19 in near real time (i.e., no longer constrained by the delay of around 9 days between infection and reporting of cases) which is essential for quick assessment of the effectiveness of interventions on reducing transmissibility. Our findings show that accurate nowcast and forecast of COVID-19 epidemics can be obtained by integrating valid digital proxies of physical mixing into conventional epidemic models.

Real-time tracking and prediction of COVID-19 infection using digital proxies of population mobility and mixing

Digital proxies of human mobility and physical mixing have been used to monitor viral transmissibility and effectiveness of social distancing interventions in the ongoing COVID-19 pandemic. We develop a new framework that parameterizes disease transmission models with age-specific digital mobility data. By fitting the model to case data in Hong Kong, we are able to accurately track the local effective reproduction number of COVID-19 in near real time (i.e., no longer constrained by the delay of around 9 days between infection and reporting of cases) which is essential for quick assessment of the effectiveness of interventions on reducing transmissibility. Our findings show that accurate nowcast and forecast of COVID-19 epidemics can be obtained by integrating valid digital proxies of physical mixing into conventional epidemic models.

Digital proxies of human mobility can be used to monitor social distancing, and therefore have potential to infer COVID-19 dynamics. Here, the authors integrate travel card data from Hong Kong into a transmission model and show that it can be used to track transmissibility in near real-time.

Development and dissemination of infectious disease dynamic transmission models during the COVID-19 pandemic: what can we learn from other pathogens and how can we move forward?

The current COVID-19 pandemic has resulted in the unprecedented development and integration of infectious disease dynamic transmission models into policy making and public health practice. Models offer a systematic way to investigate transmission dynamics and produce short-term and long-term predictions that explicitly integrate assumptions about biological, behavioural, and epidemiological processes that affect disease transmission, burden, and surveillance. Models have been valuable tools during the COVID-19 pandemic and other infectious disease outbreaks, able to generate possible trajectories of disease burden, evaluate the effectiveness of intervention strategies, and estimate key transmission variables. Particularly given the rapid pace of model development, evaluation, and integration with decision making in emergency situations, it is necessary to understand the benefits and pitfalls of transmission models. We review and highlight key aspects of the history of infectious disease dynamic models, the role of rigorous testing and evaluation, the integration with data, and the successful application of models to guide public health. Rather than being an expansive history of infectious disease models, this Review focuses on how the integration of modelling can continue to be advanced through policy and practice in appropriate and conscientious ways to support the current pandemic response.

Tooling-up for infectious disease transmission modelling

In this introduction to the Special Issue on methods for modelling of infectious disease epidemiology we provide a commentary and overview of the field. We suggest that the field has been through three revolutions that have focussed on specific methodological developments; disease dynamics and heterogeneity, advanced computing and inference, and complexity and application to the real-world. Infectious disease dynamics and heterogeneity dominated until the 1980s where the use of analytical models illustrated fundamental concepts such as herd immunity. The second revolution embraced the integration of data with models and the increased use of computing. From the turn of the century an emergence of novel datasets enabled improved modelling of real-world complexity. The emergence of more complex data that reflect the real-world heterogeneities in transmission resulted in the development of improved inference methods such as particle filtering. Each of these three revolutions have always kept the understanding of infectious disease spread as its motivation but have been developed through the use of new techniques, tools and the availability of data. We conclude by providing a commentary on what the next revoluition in infectious disease modelling may be.