Projecting COVID-19 cases and hospital burden in Ohio.

As the Coronavirus 2019 disease (COVID-19) started to spread rapidly in the state of Ohio, the Ecology, Epidemiology and Population Health (EEPH) program within the Infectious Diseases Institute (IDI) at The Ohio State University (OSU) took the initiative to offer epidemic modeling and decision analytics support to the Ohio Department of Health (ODH). This paper describes the methodology used by the OSU/IDI response modeling team to predict statewide cases of new infections as well as potential hospital burden in the state. The methodology has two components: (1) A Dynamical Survival Analysis (DSA)-based statistical method to perform parameter inference, statewide prediction and uncertainty quantification. (2) A geographic component that down-projects statewide predicted counts to potential hospital burden across the state. We demonstrate the overall methodology with publicly available data. A Python implementation of the methodology is also made publicly available. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Second-pandemic strain of Vibrio cholerae from the Philadelphia cholera outbreak of 1849.

In the 19th century, there were several major cholera pandemics in the Indian subcontinent, Europe, and North America. The causes of these outbreaks and the genomic strain identities remain a mystery. We used targeted high-throughput sequencing to reconstruct the Vibrio cholerae genome from the preserved intestine of a victim of the 1849 cholera outbreak in Philadelphia, part of the second cholera pandemic. This O1 biotype strain has 95 to 97% similarity with the classical O395 genome, differing by 203 single-nucleotide polymorphisms (SNPs), lacking three genomic islands, and probably having one or more tandem cholera toxin prophage (CTX) arrays, which potentially affected its virulence. This result highlights archived medical remains as a potential resource for investigations into the genomic origins of past pandemics.

Model distinguishability and inference robustness in mechanisms of cholera transmission and loss of immunity.

Mathematical models of cholera and waterborne disease vary widely in their structures, in terms of transmission pathways, loss of immunity, and a range of other features. These differences can affect model dynamics, with different models potentially yielding different predictions and parameter estimates from the same data. Given the increasing use of mathematical models to inform public health decision-making, it is important to assess model distinguishability (whether models can be distinguished based on fit to data) and inference robustness (whether inferences from the model are robust to realistic variations in model structure). In this paper, we examined the effects of uncertainty in model structure in the context of epidemic cholera, testing a range of models with differences in transmission and loss of immunity structure, based on known features of cholera epidemiology. We fit these models to simulated epidemic and long-term data, as well as data from the 2006 Angola epidemic. We evaluated model distinguishability based on fit to data, and whether the parameter values, model behavior, and forecasting ability can accurately be inferred from incidence data. In general, all models were able to successfully fit to all data sets, both real and simulated, regardless of whether the model generating the simulated data matched the fitted model. However, in the long-term data, the best model fits were achieved when the loss of immunity structures matched those of the model that simulated the data. Two parameters, one representing person-to-person transmission and the other representing the reporting rate, were accurately estimated across all models, while the remaining parameters showed broad variation across the different models and data sets. The basic reproduction number (R0) was often poorly estimated even using the correct model, due to practical unidentifiability issues in the waterborne transmission pathway which were consistent across all models. Forecasting efforts using noisy data were not successful early in the outbreaks, but once the epidemic peak had been achieved, most models were able to capture the downward incidence trajectory with similar accuracy. Forecasting from noise-free data was generally successful for all outbreak stages using any model. Our results suggest that we are unlikely to be able to infer mechanistic details from epidemic case data alone, underscoring the need for broader data collection, such as immunity/serology status, pathogen dose response curves, and environmental pathogen data. Nonetheless, with sufficient data, conclusions from forecasting and some parameter estimates were robust to variations in the model structure, and comparative modeling can help to determine how realistic variations in model structure may affect the conclusions drawn from models and data.

Disease invasion on community networks with environmental pathogen movement.

The ability of disease to invade a community network that is connected by environmental pathogen movement is examined. Each community is modeled by a susceptible-infectious-recovered (SIR) framework that includes an environmental pathogen reservoir, and the communities are connected by pathogen movement on a strongly connected, weighted, directed graph. Disease invasibility is determined by the basic reproduction number R(0) for the domain. The domain R(0) is computed through a Laurent series expansion, with perturbation parameter corresponding to the ratio of the pathogen decay rate to the rate of water movement. When movement is fast relative to decay, R(0) is determined by the product of two weighted averages of the community characteristics. The weights in these averages correspond to the network structure through the rooted spanning trees of the weighted, directed graph. Clustering of disease "hot spots" influences disease invasibility. In particular, clustering hot spots together according to a generalization of the group inverse of the Laplacian matrix facilitates disease invasion.

Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease.

Cholera and many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. An important epidemiological question is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine whether parameters for a differential equation model of waterborne disease transmission dynamics can be identified, both in the ideal setting of noise-free data (structural identifiability) and in the more realistic setting in the presence of noise (practical identifiability). We used a differential algebra approach together with several numerical approaches, with a particular emphasis on identifiability of the transmission rates. To examine these issues in a practical public health context, we apply the model to a recent cholera outbreak in Angola (2006). Our results show that the model parameters-including both water and person-to-person transmission routes-are globally structurally identifiable, although they become unidentifiable when the environmental transmission timescale is fast. Even for water dynamics within the identifiable range, when noisy data are considered, only a combination of the water transmission parameters can practically be estimated. This makes the waterborne transmission parameters difficult to estimate, leading to inaccurate estimates of important epidemiological parameters such as the basic reproduction number (R0). However, measurements of pathogen persistence time in environmental water sources or measurements of pathogen concentration in the water can improve model identifiability and allow for more accurate estimation of waterborne transmission pathway parameters as well as R0. Parameter estimates for the Angola outbreak suggest that both transmission pathways are needed to explain the observed cholera dynamics. These results highlight the importance of incorporating environmental data when examining waterborne disease.

COVID-19 dynamics in an Ohio prison.

Incarcerated individuals are a highly vulnerable population for infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Understanding the transmission of respiratory infections within prisons and between prisons and surrounding communities is a crucial component of pandemic preparedness and response. Here, we use mathematical and statistical models to analyze publicly available data on the spread of SARS-CoV-2 reported by the Ohio Department of Rehabilitation and Corrections (ODRC). Results from mass testing conducted on April 16, 2020 were analyzed together with time of first reported SARS-CoV-2 infection among Marion Correctional Institution (MCI) inmates. Extremely rapid, widespread infection of MCI inmates was reported, with nearly 80% of inmates infected within 3 weeks of the first reported inmate case. The dynamical survival analysis (DSA) framework that we use allows the derivation of explicit likelihoods based on mathematical models of transmission. We find that these data are consistent with three non-exclusive possibilities: (i) a basic reproduction number >14 with a single initially infected inmate, (ii) an initial superspreading event resulting in several hundred initially infected inmates with a reproduction number of approximately three, or (iii) earlier undetected circulation of virus among inmates prior to April. All three scenarios attest to the vulnerabilities of prisoners to COVID-19, and the inability to distinguish among these possibilities highlights the need for improved infection surveillance and reporting in prisons.

Cholera models with hyperinfectivity and temporary immunity.

A mathematical model for cholera is formulated that incorporates hyperinfectivity and temporary immunity using distributed delays. The basic reproduction number R(0) is defined and proved to give a sharp threshold that determines whether or not the disease dies out. The case of constant temporary immunity is further considered with two different infectivity kernels. Numerical simulations are carried out to show that when R(0) > 1, the unique endemic equilibrium can lose its stability and oscillations occur. Using cholera data from the literature, the quantitative effects of hyperinfectivity and temporary immunity on oscillations are investigated numerically.

Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networks.

We examine how spatial heterogeneity combines with mobility network structure to influence vector-borne disease dynamics. Specifically, we consider a Ross-Macdonald-type disease model on n spatial locations that are coupled by host movement on a strongly connected, weighted, directed graph. We derive a closed form approximation to the domain reproduction number using a Laurent series expansion, and use this approximation to compute sensitivities of the basic reproduction number to model parameters. To illustrate how these results can be used to help inform mitigation strategies, as a case study we apply these results to malaria dynamics in Namibia, using published cell phone data and estimates for local disease transmission. Our analytical results are particularly useful for understanding drivers of transmission when mobility sinks and transmission hot spots do not coincide.

Sentinel node approach to monitoring online COVID-19 misinformation.

Understanding how different online communities engage with COVID-19 misinformation is critical for public health response. For example, misinformation confined to a small, isolated community of users poses a different public health risk than misinformation being consumed by a large population spanning many diverse communities. Here we take a longitudinal approach that leverages tools from network science to study COVID-19 misinformation on Twitter. Our approach provides a means to examine the breadth of misinformation engagement using modest data needs and computational resources. We identify a subset of accounts from different Twitter communities discussing COVID-19, and follow these 'sentinel nodes' longitudinally from July 2020 to January 2021. We characterize sentinel nodes in terms of a linked domain preference score, and use a standardized similarity score to examine alignment of tweets within and between communities. We find that media preference is strongly correlated with the amount of misinformation propagated by sentinel nodes. Engagement with sensationalist misinformation topics is largely confined to a cluster of sentinel nodes that includes influential conspiracy theorist accounts. By contrast, misinformation relating to COVID-19 severity generated widespread engagement across multiple communities. Our findings indicate that misinformation downplaying COVID-19 severity is of particular concern for public health response. We conclude that the sentinel node approach can be an effective way to assess breadth and depth of online misinformation penetration.

Projecting COVID-19 Cases and Subsequent Hospital Burden in Ohio.

As the Coronavirus 2019 (COVID-19) disease started to spread rapidly in the state of Ohio, the Ecology, Epidemiology and Population Health (EEPH) program within the Infectious Diseases Institute (IDI) at the Ohio State University (OSU) took the initiative to offer epidemic modeling and decision analytics support to the Ohio Department of Health (ODH). This paper describes the methodology used by the OSU/IDI response modeling team to predict statewide cases of new infections as well as potential hospital burden in the state. The methodology has two components: 1) A Dynamic Survival Analysis (DSA)-based statistical method to perform parameter inference, statewide prediction and uncertainty quantification. 2) A geographic component that down-projects statewide predicted counts to potential hospital burden across the state. We demonstrate the overall methodology with publicly available data. A Python implementation of the methodology has been made available publicly. Highlights: We present a novel statistical approach called Dynamic Survival Analysis (DSA) to model an epidemic curve with incomplete data. The DSA approach is advantageous over standard statistical methods primarily because it does not require prior knowledge of the size of the susceptible population, the overall prevalence of the disease, and also the shape of the epidemic curve.The principal motivation behind the study was to obtain predictions of case counts of COVID-19 and the resulting hospital burden in the state of Ohio during the early phase of the pandemic.The proposed methodology was applied to the COVID-19 incidence data in the state of Ohio to support the Ohio Department of Health (ODH) and the Ohio Hospital Association (OHA) with predictions of hospital burden in each of the Hospital Catchment Areas (HCAs) of the state.

Multiple transmission pathways and disease dynamics in a waterborne pathogen model.

Multiple transmission pathways exist for many waterborne diseases, including cholera, Giardia, Cryptosporidium, and Campylobacter. Theoretical work exploring the effects of multiple transmission pathways on disease dynamics is incomplete. Here, we consider a simple ODE model that extends the classical SIR framework by adding a compartment (W) that tracks pathogen concentration in the water. Infected individuals shed pathogen into the water compartment, and new infections arise both through exposure to contaminated water, as well as by the classical SIR person-person transmission pathway. We compute the basic reproductive number ([Symbol: see text](0)), epidemic growth rate, and final outbreak size for the resulting "SIWR" model, and examine how these fundamental quantities depend upon the transmission parameters for the different pathways. We prove that the endemic disease equilibrium for the SIWR model is globally stable. We identify the pathogen decay rate in the water compartment as a key parameter determining when the distinction between the different transmission routes in the SIWR model is important. When the decay rate is slow, using an SIR model rather than the SIWR model can lead to under-estimates of the basic reproductive number and over-estimates of the infectious period.

Modeling the role of carrier and mobile herds on foot-and-mouth disease virus endemicity in the Far North Region of Cameroon.

Foot and mouth disease virus (FMDV) is an RNA virus that infects cloven-hoofed animals, often produces either epidemic or endemic conditions, and negatively affects agricultural economies worldwide. FMDV epidemic dynamics have been extensively studied, but understanding of drivers of disease persistence in areas in which FMDV is endemic, such as most of sub-Saharan Africa, is lacking. We present a spatial stochastic model of disease dynamics that incorporates a spatial transmission kernel in a modified Gillespie algorithm, and use it to evaluate two hypothesized drivers of endemicity: asymptomatic carriers and the movement of mobile herds. The model is parameterized using data from the pastoral systems in the Far North Region of Cameroon. Our computational study provides evidence in support of the hypothesis that asymptomatic carriers, but not mobile herds, are a driver of endemicity.

Parameter estimation for bursting neural models.

This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the estimation algorithms to the space of bursting periodic orbits when trying to fit periodic burst data. These geometrical ideas are combined with automatic differentiation to accurately compute parameter sensitivities for the burst timing and period. In addition to being of inherent interest, these sensitivities are used in standard gradient-based optimization algorithms to fit model burst duration and period to data. As an application, we fit Butera et al.'s (Journal of Neurophysiology 81, 382-397, 1999) model of preBötzinger complex neurons to empirical data both in control conditions and when the neuromodulator norepinephrine is added (Viemari and Ramirez, Journal of Neurophysiology 95, 2070-2082, 2006). The results suggest possible modulatory mechanisms in the preBötzinger complex, including modulation of the persistent sodium current.

The large graph limit of a stochastic epidemic model on a dynamic multilayer network.

We consider a Markovian SIR-type (Susceptible → Infected → Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model where edges in different layers correspond to potentially infectious contacts of different types. We assume that the graph structure evolves in response to the epidemic via activation or deactivation of edges of infectious nodes. We derive a large graph limit theorem that gives a system of ordinary differential equations (ODEs) describing the evolution of quantities of interest, such as the proportions of infected and susceptible vertices, as the number of nodes tends to infinity. Analysis of the limiting system elucidates how the coupling of edge activation and deactivation to infection status affects disease dynamics, as illustrated by a two-layer network example with edge types corresponding to community and healthcare contacts. Our theorem extends some earlier results describing the deterministic limit of stochastic SIR processes on static, single-layer configuration model graphs. We also describe precisely the conditions for equivalence between our limiting ODEs and the systems obtained via pair approximation, which are widely used in the epidemiological and ecological literature to approximate disease dynamics on networks. The flexible modeling framework and asymptotic results have potential application to many disease settings including Ebola dynamics in West Africa, which was the original motivation for this study.

Network-based analysis of a small Ebola outbreak.

We present a method for estimating epidemic parameters in network-based stochastic epidemic models when the total number of infections is assumed to be small. We illustrate the method by reanalyzing the data from the 2014 Democratic Republic of the Congo (DRC) Ebola outbreak described in Maganga et al. (2014).

Modeling the trade-off between transmissibility and contact in infectious disease dynamics.

Symptom severity affects disease transmission both by impacting contact rates, as well as by influencing the probability of transmission given contact. This involves a trade-off between these two factors, as increased symptom severity will tend to decrease contact rates, but increase the probability of transmission given contact (as pathogen shedding rates increase with symptom severity). This paper explores this trade-off between contact and transmission given contact, using a simple compartmental susceptible-infected-recovered type model. Under mild assumptions on how contact and transmission probability vary with symptom severity, we give sufficient, biologically intuitive criteria for when the basic reproduction number varies non-monotonically with symptom severity. Multiple critical points are possible. We give a complete characterization of the region in parameter space where multiple critical points are located in the special case where contact rate decreases exponentially with symptom severity. We consider a multi-strain version of the model with complete cross-immunity and no super-infection. In this model, we prove that the strain with highest basic reproduction number drives the other strains to extinction. This has both evolutionary and epidemiological implications, including the possibility of an intervention paradoxically resulting in increased infection prevalence.

The impact of spatial arrangements on epidemic disease dynamics and intervention strategies.

The role of spatial arrangements on the spread and management strategies of a cholera epidemic is investigated. We consider the effect of human and pathogen movement on optimal vaccination strategies. A metapopulation model is used, incorporating a susceptible-infected-recovered system of differential equations coupled with an equation modelling the concentration of Vibrio cholerae in an aquatic reservoir. The model compared spatial arrangements and varying scenarios to draw conclusions on how to effectively manage outbreaks. The work is motivated by the 2010 cholera outbreak in Haiti. Results give guidance for vaccination strategies in response to an outbreak.

Prostaglandin H synthases: members of a class of quasi-linear threshold switches.

Prostaglandin H synthase (PTGS or COX) enzymes catalyze rate-limiting steps in the synthesis of potent prostanoids, including various prostaglandins, thromboxane, and prostacyclin. Mechanisms that have evolved for regulating prostanoid biosynthesis reflect a tension between achieving a rapid but measured response to cellular signals while minimizing spurious activation by signal noise. We found through mathematical modeling that the PTGS enzymes can be thought of as regulatory switches with approximately linear output above an adjustable threshold. In vivo synthesis allows continuous production while signal remains above threshold. Different isoforms show specific adaptions reflecting their physiological roles as constitutive or inducible enzymes. Mathematical modeling helps explain how these adaptations enable the PTGS1 and PTGS2 enzymes to maintain their physiological roles while avoiding potentially damaging consequences.

Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source.

Many factors influencing disease transmission vary throughout and across populations. For diseases spread through multiple transmission pathways, sources of variation may affect each transmission pathway differently. In this paper we consider a disease that can be spread via direct and indirect transmission, such as the waterborne disease cholera. Specifically, we consider a system of multiple patches with direct transmission occurring entirely within patch and indirect transmission via a single shared water source. We investigate the effect of heterogeneity in dual transmission pathways on the spread of the disease. We first present a 2-patch model for which we examine the effect of variation in each pathway separately and propose a measure of heterogeneity that incorporates both transmission mechanisms and is predictive of R(0). We also explore how heterogeneity affects the final outbreak size and the efficacy of intervention measures. We conclude by extending several results to a more general n-patch setting.