A dynamic dose-response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

Optimization of energy efficiency and COVID-19 pandemic control in different indoor environments

The COVID-19 pandemic has led to considerable morbidity and mortality, and consumed enormous resources (e.g. energy) to control and prevent the disease. It is crucial to balance infection risk and energy consumption when reducing the spread of infection. In this study, a quantitative human, behavior-based, infection risk-energy consumption model for different indoor environments was developed. An optimal balance point for each indoor environment can be obtained using the anti-problem method. For this study we selected Wangjing Block, one of the most densely populated places in Beijing, as an example. Under the current ventilation standard (30 m³/h/person), prevention and control of the COVID-19 pandemic would be insufficient because the basic reproduction number (R₀ ) for students, workers and elders are greater than 1. The optimal required fresh air ventilation rates in most indoor environments are near or below 60 m³/h/person, after considering the combined effects of multiple mitigation measures. In residences, sports buildings and restaurants, the demand for fresh air ventilation rate is relatively high. After our global optimization of infection risk control (R₀  ≤ 1), energy consumption can be reduced by 13.7% and 45.1% on weekdays and weekends, respectively, in contrast to a strategy of strict control (R₀  = 1 for each indoor environment).

A quantitative microbial risk assessment for touchscreen user interfaces using an asymmetric transfer gradient transmission mode

The ubiquitous use of public touchscreen user interfaces for commercial applications has created a credible risk for fomite-mediated disease transmission. This paper presents results from a stochastic simulation designed to assess this risk. The model incorporates a queueing network to simulate people flow and touchscreen interactions. It also describes an updated model for microbial transmission using an asymmetric gradient transfer assumption that incorporates literature reviewed empirical data concerning touch-transfer efficiency between fingers and surfaces. In addition to natural decay/die-off, pathogens are removed from the system by simulated cleaning / disinfection and personal-touching rates (e.g. face, dermal, hair and clothing). The dose response is implemented with an exponential moving average filter to model the temporal dynamics of exposure. Public touchscreens were shown to pose a considerable infection risk (∼3%) using plausible default simulation parameters. Sensitivity of key model parameters, including the rate of surface disinfection is examined and discussed. A distinctive and important advancement of this simulation was its ability to distinguish between infection risk from a primary contaminated source and that due to the re-deposition of pathogens onto secondary, initially uncontaminated touchscreens from sequential use. The simulator is easily configurable and readily adapted to more general fomite-mediated transmission modelling and may provide a valuable framework for future research.

Estimating the Risk of Human Herpesvirus 6 and Cytomegalovirus Transmission to Ugandan Infants from Viral Shedding in Saliva by Household Contacts

Human herpesvirus 6 (HHV-6) and cytomegalovirus (CMV) infections are common in early childhood. In a prospective Ugandan birth cohort study, most infants acquired HHV-6 (24/31; 77%) and CMV (20/30; 67%) during follow-up. To assess the transmission risk, we modeled a dose-response relationship between infant HHV-6 and CMV infections and weekly oral viral shedding by mothers and all other ("secondary") children in the home. Oral viral loads that were shed by mothers and secondary children were significantly associated with HHV-6 but not CMV transmission. While secondary children had higher and more frequent HHV-6 shedding than their mothers, they had a lower per-exposure transmission risk, suggesting that transmission to maternal contacts may be more efficient. HHV-6 transmission was relatively inefficient, occurring after <25% of all weekly exposures. Although HHV-6 transmission often occurs following repeated, low dose exposures, we found a non-linear dose-response relationship in which infection risk markedly increases when exposures reached a threshold of > 5 log₁₀ DNA copies/mL. The lack of association between oral CMV shedding and transmission is consistent with breastfeeding being the dominant route of infant infection for that virus. These affirm saliva as the route of HHV-6 transmission and provide benchmarks for developing strategies to reduce the risk of infection and its related morbidity.

A dose response model for quantifying the infection risk of antibiotic-resistant bacteria

Quantifying the human health risk of microbial infection helps inform regulatory policies concerning pathogens, and the associated public health measures. Estimating the infection risk requires knowledge of the probability of a person being infected by a given quantity of pathogens, and this relationship is modeled using pathogen specific dose response models (DRMs). However, risk quantification for antibiotic-resistant bacteria (ARB) has been hindered by the absence of suitable DRMs for ARB. A new approach to DRMs is introduced to capture ARB and antibiotic-susceptible bacteria (ASB) dynamics as a stochastic simple death (SD) process. By bridging SD with data from bench experiments, we demonstrate methods to (1) account for the effect of antibiotic concentrations and horizontal gene transfer on risk; (2) compute total risk for samples containing multiple bacterial types (e.g., ASB, ARB); and (3) predict if illness is treatable with antibiotics. We present a case study of exposure to a mixed population of Gentamicin-susceptible and resistant Escherichia coli and predict the health outcomes for varying Gentamicin concentrations. Thus, this research establishes a new framework to quantify the risk posed by ARB and antibiotics.

Modeling Rabbit Responses to Single and Multiple Aerosol Exposures of Bacillus anthracis Spores

Survival models are developed to predict response and time-to-response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple-dose data set to predict the probability of death through specifying functions of dose response and the time between exposure and the time-to-death (TTD). Among the models developed, the best-fitting survival model (baseline model) is an exponential dose-response model with a Weibull TTD distribution. Alternative models assessed use different underlying dose-response functions and use the assumption that, in a multiple-dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this article. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high-dose rabbit data sets. More accurate survival models depend upon future development of dose-response data sets specifically designed to assess potential multiple-dose effects on response and time-to-response. The process used in this article to develop the best-fitting survival model for exposure of rabbits to multiple aerosol doses of B. anthracis spores should have broad applicability to other host-pathogen systems and dosing schedules because the empirical modeling approach is based upon pathogen-specific empirically-derived parameters.

Dose-response relationships for environmentally mediated infectious disease transmission models

Environmentally mediated infectious disease transmission models provide a mechanistic approach to examining environmental interventions for outbreaks, such as water treatment or surface decontamination. The shift from the classical SIR framework to one incorporating the environment requires codifying the relationship between exposure to environmental pathogens and infection, i.e. the dose-response relationship. Much of the work characterizing the functional forms of dose-response relationships has used statistical fit to experimental data. However, there has been little research examining the consequences of the choice of functional form in the context of transmission dynamics. To this end, we identify four properties of dose-response functions that should be considered when selecting a functional form: low-dose linearity, scalability, concavity, and whether it is a single-hit model. We find that i) middle- and high-dose data do not constrain the low-dose response, and different dose-response forms that are equally plausible given the data can lead to significant differences in simulated outbreak dynamics; ii) the choice of how to aggregate continuous exposure into discrete doses can impact the modeled force of infection; iii) low-dose linear, concave functions allow the basic reproduction number to control global dynamics; and iv) identifiability analysis offers a way to manage multiple sources of uncertainty and leverage environmental monitoring to make inference about infectivity. By applying an environmentally mediated infectious disease model to the 1993 Milwaukee Cryptosporidium outbreak, we demonstrate that environmental monitoring allows for inference regarding the infectivity of the pathogen and thus improves our ability to identify outbreak characteristics such as pathogen strain.

Unveiling time in dose-response models to infer host susceptibility to pathogens

The biological effects of interventions to control infectious diseases typically depend on the intensity of pathogen challenge. As much as the levels of natural pathogen circulation vary over time and geographical location, the development of invariant efficacy measures is of major importance, even if only indirectly inferrable. Here a method is introduced to assess host susceptibility to pathogens, and applied to a detailed dataset generated by challenging groups of insect hosts (Drosophila melanogaster) with a range of pathogen (Drosophila C Virus) doses and recording survival over time. The experiment was replicated for flies carrying the Wolbachia symbiont, which is known to reduce host susceptibility to viral infections. The entire dataset is fitted by a novel quantitative framework that significantly extends classical methods for microbial risk assessment and provides accurate distributions of symbiont-induced protection. More generally, our data-driven modeling procedure provides novel insights for study design and analyses to assess interventions.

While control options for plant, animal, and human pathogens are emerging rapidly, reliable assessment of the effect of interventions in biological systems presents many challenges. A major question is how to connect laboratory experiments and measurements with the relevant process in natural settings, where hosts are subject to pathogen exposures that vary in time and geographical location. With this aim, measures of protection that are invariant under varying exposure intensity need to be developed and integrated with mathematical models. In this article, we introduce a method to assess host susceptibility to pathogens, and apply it to survival of Drosophila melanogaster challenged with different doses of Drosophila C virus. By replicating the procedure in groups of flies that carry the symbiont Wolbachia, we are able to estimate how the viral protection induced by this intracellular bacterium is distributed in the host population. Our results disentangle host infection status from observed mortality, accounting naturally for time since exposure. The multiple-dose design proposed challenges traditional study designs to assess interventions.

Herpes simplex virus-2 transmission probability estimates based on quantity of viral shedding

Herpes simplex virus (HSV)-2 is periodically shed in the human genital tract, most often asymptomatically, and most sexual transmissions occur during asymptomatic shedding. It would be helpful to identify a genital viral load threshold necessary for transmission, as clinical interventions that maintain viral quantity below this level would be of high utility. However, because viral expansion, decay and re-expansion kinetics are extremely rapid during shedding episodes, it is impossible to directly measure genital viral load at the time of sexual activity. We developed a mathematical model based on reproducing shedding patterns in transmitting partners, and median number of sex acts prior to transmission in discordant couples, to estimate infectivity of single viral particles in the negative partner's genital tract. We then inferred probability estimates for transmission at different levels of genital tract viral load in the transmitting partner. We predict that transmission is unlikely at viral loads less than 10(4) HSV DNA copies. Moreover, most transmissions occur during prolonged episodes with high viral copy numbers. Many shedding episodes that result in transmission do not reach the threshold of clinical detection, because the ulcer remains very small, highlighting one reason why HSV-2 spreads so effectively within populations.

Deterministic models of inhalational anthrax in New Zealand white rabbits

Computational models describing bacterial kinetics were developed for inhalational anthrax in New Zealand white (NZW) rabbits following inhalation of Ames strain B. anthracis. The data used to parameterize the models included bacterial numbers in the airways, lung tissue, draining lymph nodes, and blood. Initial bacterial numbers were deposited spore dose. The first model was a single exponential ordinary differential equation (ODE) with 3 rate parameters that described mucociliated (physical) clearance, immune clearance (bacterial killing), and bacterial growth. At 36 hours postexposure, the ODE model predicted 1.7×10⁷ bacteria in the rabbit, which agreed well with data from actual experiments (4.0×10⁷ bacteria at 36 hours). Next, building on the single ODE model, a physiological-based biokinetic (PBBK) compartmentalized model was developed in which 1 physiological compartment was the lumen of the airways and the other was the rabbit body (lung tissue, lymph nodes, blood). The 2 compartments were connected with a parameter describing transport of bacteria from the airways into the body. The PBBK model predicted 4.9×10⁷ bacteria in the body at 36 hours, and by 45 hours the model showed all clearance mechanisms were saturated, suggesting the rabbit would quickly succumb to the infection. As with the ODE model, the PBBK model results agreed well with laboratory observations. These data are discussed along with the need for and potential application of the models in risk assessment, drug development, and as a general aid to the experimentalist studying inhalational anthrax.

Quantitative models of the dose-response and time course of inhalational anthrax in humans

Anthrax poses a community health risk due to accidental or intentional aerosol release. Reliable quantitative dose-response analyses are required to estimate the magnitude and timeline of potential consequences and the effect of public health intervention strategies under specific scenarios. Analyses of available data from exposures and infections of humans and non-human primates are often contradictory. We review existing quantitative inhalational anthrax dose-response models in light of criteria we propose for a model to be useful and defensible. To satisfy these criteria, we extend an existing mechanistic competing-risks model to create a novel Exposure–Infection–Symptomatic illness–Death (EISD) model and use experimental non-human primate data and human epidemiological data to optimize parameter values. The best fit to these data leads to estimates of a dose leading to infection in 50% of susceptible humans (ID₅₀) of 11,000 spores (95% confidence interval 7,200–17,000), ID₁₀ of 1,700 (1,100–2,600), and ID₁ of 160 (100–250). These estimates suggest that use of a threshold to human infection of 600 spores (as suggested in the literature) underestimates the infectivity of low doses, while an existing estimate of a 1% infection rate for a single spore overestimates low dose infectivity. We estimate the median time from exposure to onset of symptoms (incubation period) among untreated cases to be 9.9 days (7.7–13.1) for exposure to ID₅₀, 11.8 days (9.5–15.0) for ID₁₀, and 12.1 days (9.9–15.3) for ID₁. Our model is the first to provide incubation period estimates that are independently consistent with data from the largest known human outbreak. This model refines previous estimates of the distribution of early onset cases after a release and provides support for the recommended 60-day course of prophylactic antibiotic treatment for individuals exposed to low doses.

Anthrax poses a potential community health risk due to accidental or intentional aerosol release. We address the need for a transparent and defensible quantitative dose-response model for inhalational anthrax that is useful for risk assessors in estimating the magnitude and timeline of potential public health consequences should a release occur. Our synthesis of relevant data and previous modeling efforts identifies areas of improvement among many commonly cited dose-response models and estimates. To address those deficiencies, we provide a new model that is based on clear, transparent assumptions and published data from human and non-human primate exposures. Our resulting estimates provide important insight into the infectivity to humans of low inhaled doses of anthrax spores and the timeline of infections after an exposure event. These insights are critical to assessment of the impacts of delays in responding to a large scale aerosol release, as well as the recommended course of antibiotic administration to those potentially exposed.