Conceived and designed the experiments: IHS JSK MN JMP SL JNSE. Performed the experiments: IHS JMP JNSE. Analyzed the data: IHS JSK JNSE. Wrote the paper: IHS JSK JMP SL JNSE.
The authors have declared that no competing interests exist.
Influenza can be transmitted through respirable (small airborne particles), inspirable (intermediate size), direct-droplet-spray, and contact modes. How these modes are affected by features of the virus strain (infectivity, survivability, transferability, or shedding profiles), host population (behavior, susceptibility, or shedding profiles), and environment (host density, surface area to volume ratios, or host movement patterns) have only recently come under investigation. A discrete-event, continuous-time, stochastic transmission model was constructed to analyze the environmental processes through which a virus passes from one person to another via different transmission modes, and explore which factors increase or decrease different modes of transmission. With the exception of the inspiratory route, each route on its own can cause high transmission in isolation of other modes. Mode-specific transmission was highly sensitive to parameter values. For example, droplet and respirable transmission usually required high host density, while the contact route had no such requirement. Depending on the specific context, one or more modes may be sufficient to cause high transmission, while in other contexts no transmission may result. Because of this, when making intervention decisions that involve blocking environmental pathways, generic recommendations applied indiscriminately may be ineffective; instead intervention choice should be contextualized, depending on the specific features of people, virus strain, or venue in question.
We model the transmission of influenza through the environment assuming four possible transmission routes: respiratory (small particle inhalation), inspiratory (medium particle inhalation), direct-droplet-spray (large particle spray directly to susceptible tissue), and contact-mediated (when large particles settle in the environment, are picked up, and self-inoculated). There is much disagreement in the literature with regard to the dominant route of influenza transmission. Using empirical estimates where possible, we vary 18 parameters which are relevant to these transmission routes. These parameters are features of the agent, host, or environment. Depending on these features, a specific route or routes may be operating at a high intensity. Thus, it is unlikely there is a single universal dominant influenza transmission route. Therefore, interventions which target only one of these routes will not be optimal in all settings. It is important to understand the context in terms of the agent, host, and environment in order to develop optimal environmental intervention strategies.
On June 11, 2009 the WHO declared the H1N1 influenza virus a pandemic. Health organizations worldwide were prompted to escalate their efforts to minimize transmission within their jurisdictions. Airports began to monitor incoming passengers while schools increased their already intensive surveillance activities. Recommendations were established with regard to masks, hygiene, decontamination, and isolation of suspected cases. This interest in intervention and control of person-to-person transmitted illnesses with multiple potential routes of transmission began to intensify during the emergence of SARS and later the H5N1 (avian influenza) virus. Heightened awareness of the potential for another pandemic influenza led to increased funding to study non-pharmaceutical interventions by the CDC as well as increased efforts in modeling influenza transmission. These studies were funded in order to better understand optimal intervention and control strategies. Much insight was gained into influenza mitigation strategies such as border closure, social distancing, antiviral prophylaxis, restriction of public transportation, and school closure
This manuscript explores potential effects of these unknown factors by presenting: 1) a transmission model structure that explicitly describes the environmental processes through which viruses pass from one person to another, thereby distinguishing the different modes of transmission; and 2) an analytical approach that explores which factors increase or decrease different modes of transmission under the given model structure. The model analyzed is an environmental infection transmission system model that elaborates the approach to such models by Li et al.
To inform relevant intervention options for influenza, we consider four potential modes of transmission: respirable, inspirable, direct-droplet-spray, and contact mediated transmission
For example, different viruses may have different infectivity, survivability, transferability, or shedding profiles. Similarly, among different populations who have different behaviors, susceptibility profiles, or shedding profiles, the same virus may have different effects depending on the type of population present. Finally, even with identical viral strains and human populations, environmental venues may have variable host densities, surface area to volume ratios, or host movement patterns that can generate different population level infection outcomes. These diverse sources of heterogeneity that we address form the corners of the epidemiologic triad (
Specific features are listed in each corner that are relevant to either the agent (specific virus strain), host, and environmental venue.
We assess the effects of these sources of heterogeneity on relative magnitude of influenza transmission modes in a scenario where all individuals move randomly in an identical fashion. We construct a detailed stochastic individual based model of environmental influenza transmission. We use values from empirical literature as well as expert judgment to parameterize this model. We apply upper and lower parameter constraints to 18 parameters, and obtain a Latin hypercube sample of this constrained parameter space. We analyze the resulting outcome space with respect to how different transmission modes are more or less important in specific contexts.
With this work we contribute to the body of literature discussing the dominant mode of influenza transmission
We model environmental influenza transmission in a venue by considering infections resulting from contact-mediated, respirable, inspirable, and droplet exposures. We model a single uniform abstract venue with no variation in space with regard to fomites or behavior in order to seek simple general insights. This venue homogeneity helps us identify sources of heterogeneity in transmission attributable to the factors we study in the epidemiological triad (
Relevant governing parameters of transmission are listed below each phase. Viral inactivation occurs in the air, on surfaces, and on fingertips (not explicitly shown). Moving from the left to the right of the diagram, viral excretion magnitude is determined by the shedding rate, volume, and concentration. Where these viruses go is determined by the size of the particle they adhere to during excretion. Based on cough particle size distribution data, these are divided proportionally. Viruses on small particles are well mixed, and are assumed to either inactivate or be inhaled (respiratory exposure) before settling would occur. Viruses on medium particles may either inactivate, settle to the local surfaces, or be inhaled (inspiratory exposure). Some viruses on large particles may be utilized initially in droplet exposure, proportional to the target facial membrane surface area multiplied by the number of susceptible collocated with the shedder. Viruses on larger particles not utilized in droplet exposure is assumed to settle immediately to the local surface environment. Here it may inactivate, or be picked up on fingertips. Once on fingertips, the virus may inactivate, be deposited back to a surface environment, or be used in contact exposure via self-inoculation. Respiratory exposure assumes lower respiratory penetration and uses an ID50 specific to this region. Inspiratory, droplet, and contact exposure assumes the potential for infection only occurs in the upper respiratory tract and all use the same ID50 specific to this region. For simplicity, we assume exponential dose-response relationship.
We assume virus on particles >10µm and <100µm remain in the local environment of the shedder because these particles would be too large to invoke the well mixed room assumption. These may inactivate, settle to the local surface environment, or result in inspiratory exposure in the upper respiratory tract. These particles are too large to penetrate to the lung alveoli.
We assume particles >100µm that are not involved in droplet exposure settle immediately to the shedder's local surface environment evenly spread. Here, the virus may inactivate, be picked up as people touch this surface, and then generate contact exposure via self-inoculation. For the sake of simplicity, we assume that no excreted virus adheres to the shedder's hands (as might happen if a cough or sneeze were covered with a hand). For greater model detail refer to the supporting material.
We vary 18 parameters relevant to influenza transmission related to the host, pathogen, and venue (
Parameter | Description | Unit | Lower Constraint |
Upper Constraint |
Resulting Median |
Reference |
μA | Inactivation rate–air | Min−1 | 0.001 | 0.036 | 0.0060 | |
μS | Inactivation rate–surfaces | Min−1 | 0.0005 | 0.2 | 0.010 | |
μH | Inactivation rate–hands | Min−1 | 0.62 | 1.22 | 0.92 | |
τS-H-S | Transfer efficiency (surface to hand to surface) | 0.0167 | 0.6 | 0.10 | ||
τF-T | Transfer proportion (eyes/nose/mouth to target mucous membranes) | 0.05 | 0.25 | 0.15 | ||
τL | Lung deposition fraction | 0.083 | 0.75 | 0.42 | ||
πL | Lower respiratory HID50 | TCID50 | 0.067 | 6.7 | 0.67 | |
πU | Upper respiratory HID50 | TCID50 | 50 | 5000 | 500 | |
αMag | Shedding magnitude | 0.005 | 0.075 | 0.019 | ||
αResp | Viral proportion to respirable air | 1.4E-7 | 1.4E-5 | 1.4E-6 | ||
αInsp | Viral proportion to inspirable air | 0.00353 | 0.016 | 0.0095 | ||
ρInoc | Rate of self inoculation | Min−1 | 0.02 | 0.32 | 0.080 | |
ρtouch | Rate of surface touching | Min−1 | 0.19 | 3 | 0.75 | |
ρmove | Rate of changing location | Min−1 | 0.00083 | 3 | 0.050 | |
ρbreath | Rate of breathing | Min−1 | 10 | 22 | 16 | |
εsettle | Medium particle settling rate | Min−1 | 4.6 | 11 | 7.6 | |
εSA∶V | Surface area to volume ratio | m |
1 | 5 | 3.0 | |
εdensity | Host density | people/m |
0.056 | 5.6 | 0.2 |
NOTE: HID50 = quantity of virus required to cause infection in 50% of humans.
Either symmetric constraints or constraints which were symmetric when observed after a log transform were applied, so that half of the sampled values would be below the defined median and half above.
Median values were defined either from the literature or from expert judgment. We sampled from the constrained parameter space using Latin hypercube sampling with uniform probability distributions for each parameter.
For each trial, we use a special simulation design: when each new infection takes place, that individual is immediately replaced with a new susceptible in their place. This allows us to observe directly the number of new infections transmitted from one infected person over the course of their infection in the presence of a completely susceptible population of constant size—which is one definition of the basic reproductive number, R0
To examine transmission mode dominance we categorize regions of the full 10,000 unit space into regions where one or more transmission modes have a mode-specific R0 above 1.7 (a plausible value of the 1918 influenza pandemic R0
Aggregated over all 10,000 parameter sets, the contact mode has the highest average mode-specific R0, 1.7. The droplet, respiratory, and inspiratory routes followed with mode-specific R0's 0.27, 0.05, and 0.006 respectively. While this aggregate measure is often all that is reported in the literature, it ignores the heterogeneous effects of different contexts in inducing shifts in transmission mode dominance and intensity; that is to say, contact transmission is not necessarily dominant in all settings.
We divide the entire 10,000 unit space into mutually exclusive categories based on whether one or more transmission modes individually have a mode-specific R0>1.7. The contact, respiratory, and droplet transmission routes all have parameter sets which yield high transmission (mode-specific R0>1.7) via each mode in isolation of all other modes. There are 3079 sets where contact was high with nothing else, 121 for the respiratory mode, and 66 for droplet (
Numbers in different regions reflect the number of parameter sets which yield mode-specific R0>1.7. Overlap indicates that more than one transmission mode has a mode-specific R0>1.7. The 4765 parameter sets outside these three categories indicate that none of these three modes had high mode-specific transmission in these parameter sets. Note, that of these 4765 parameter sets with no single dominant mode, 577 parameter sets still yielded a total-R0>1.7 when summed across all modes. The inspiratory transmission mode did not yield any parameter sets in which it alone dominated, and only 26 parameter sets in which it ever had mode-specific R0>1.7.
Additionally, there was considerable overlap, where multiple modes each have a mode-specific R0>1.7. In these 1969 parameter sets no single mode dominates over the other modes; rather multiple modes transmit at a high intensity simultaneously. Our analysis henceforth ignores the inspiratory route as it only caused high transmission in 26 parameter sets, never occurring alone. The extent of overlap differs by transmission mode (
Host density (
Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
To gain insight into how parameter combinations affect the intensity of each transmission mode separately, we performed CART analyses. For each route, we classified the full 10000 unit space as to whether each mode had high (mode-specific R0>1.7) or low transmission. The CART algorithm then grouped similar regions of this outcome by making parametric divisions. We show the CART figure of the contact route, differentiating between high and low contact mediated transmission in
Numbers in ovals and rectangles are the proportions of parameter sets have mode-specific R0>1.7 which meet the parameterization criteria shown on edges. Numbers at the bottom of each terminal node reflect the number of simulations which meet that classification criteria. Three parameters differentiate between areas of high versus low contact transmission: upper respiratory ID50 (
Terminal node numeral | ||||||
Mode-specific R0 | i | ii | iii | iv | v | vi |
Contact | 0.72 | 1.34 | 4.84 | 0.60 | 5.87 | 20.76 |
Respiratory | 0.47 | 0.22 | 0.88 | 0.13 | 0.65 | 0.54 |
Inspiratory | 0.01 | 0.00 | 0.02 | 0.02 | 0.11 | 0.09 |
Droplet | 0.37 | 0.18 | 0.63 | 1.07 | 4.85 | 3.77 |
Total-R0 | 1.82 | 1.74 | 6.37 | 2.83 | 11.47 | 25.16 |
NOTE. CART = Classification and Regression Tree Algorithm. Data represent the average values for domains in each terminal node of
Turning to the plausibility of terminal node vi, two parameter constraints were required to yield high contact transmission in 86% of settings: first, a minimally constrained upper respiratory infectivity
From similar CART analyses, the droplet mediated transmission mode intensity is differentiated by three parameters: upper respiratory ID50, host density, and shedding magnitude. Respiratory transmission mode intensity is differentiated by five parameters: host density, viral proportion respirable, shedding magnitude, lower respiratory ID50, and lung deposition fraction. To test whether tree structure is sensitive to the cut point of R0 = 1.7, we also construct CART figures using a cut point of 1.2. All resulting tree structures are robust, retaining similar structure, with only minor changes in the parameter values used to divide non-terminal nodes. See the supplemental material for complete discussion of the respiratory, inspiratory, and droplet CART analyses (
This work highlights many parameters which can alter transmission mode dominance. By learning more about these transmission modes, we can better predict which modes are operating in specific scenarios. This insight can eventually help lead to definitions of 1) those factors that will enable us to predict how much transmission could take place via different modes and 2) effective interventions that can interrupt such transmissions. We have further shown that the relative importance of different influenza transmission modes may vary based on features related to the pathogen, host, or mixing venue (
For example, high host density leads to conditions where either droplet, respiratory, or multiple transmission routes simultaneously operate at a high intensity (
Our results should be interpreted with the following caveats. First, the distribution of parameter sets we used does not necessarily represent the probabilistic distribution of parameter sets in all of the real world settings. Thus it would not be appropriate to say that the contact route is most important in the vast majority of real contexts. Going further, if different parameter constraints were used, the shape of the Venn diagram in
With this work, we can make several recommendations for future empirical work. The two influenza dose-response datasets study two different sites of infection using two different influenza strains. It is not clear whether all influenza strains would display a similar site-specific differential (upper versus lower respiratory tract infectivity). Empirical work examining site-specific infectivity first with one strain, and then with another would be quite valuable. This could help tease apart the relationship between innate variability of infectivity of virus strain, whether this varies by site of infection, and if this variability is similar across different strains. Another feature important to learn more about that could sway transmission dominance, is the shedding process. Specifically, examining particle size distributions and excretion rates based on type of excretion (cough, sneeze, normal breathing, speaking), examining how viral concentration varies by particle size, and quantifying how much saliva dilutes infectious nasal fluid in different types of excretions at different stages of infection would be useful.
Data uncertainty resulting from weakness of the data used for specific parameters is another motivation for future work. The surface inactivation rate, hand inactivation rate, all transfer efficiencies (as well as both infectivity parameters) are all based on datasets which contain a minimal number of data-points. If the value of these parameters lies outside of the ranges considered, these could also become quite important in altering transmission mode dominance and therefore optimal intervention choice. For this reason, more work examining these parameters would be worthwhile.
Although these results inform transmission mode dominance, this alone does not allow policy makers to make completely informed intervention decisions. Even if most transmission taking place in a given scenario is through the contact route, this does not indicate hand hygiene as the best intervention decision solely because it targets the contact route exclusively. For example, it is possible that specific features of the scenario which relate to how hand hygiene interacts with pathogens in the environment could render a hand hygiene intervention ineffective, despite the contact route operating at a high intensity if there are substantial pathogen levels in the environment thereby allowing hands to be re-contaminated as soon as future surface touching occurs. A study similar to this could be extended to include the modeling of specific interventions, and be used to characterize a specific scenario. Doing so would be part of an overall site-specific microbial risk assessment. This would involve taking into account specific features of the environment, host, and pathogen strain as well as their dynamic interactions.
Conclusions from previous work of others may differ from our work, since we considered a broad set of parameter ranges, rather than point estimates. Previous work of Atkinson and Wein (AW)
With this work it was our goal to highlight that there may not be one and only one dominant influenza transmission route in all settings. We are no more in the aerosol camp than the contact camp. We suggest that this is influenced by features related to the host, pathogen and environment. Depending on the specific situation one or more modes may be sufficient to cause high transmission, while in others no transmission may result. It will be important to extend this work to examine the effect of realistic interventions which aim to block or attenuate the environmental pathways included here. Additionally, similar model extensions could also address the importance of different modes of transmission in a more complex setting, such as multiple venues modeled simultaneously, that can address the network-like potential of certain venues as infection disseminators to a broader population.
The respiratory-route CART diagram. Numbers in ovals and rectangles are the proportions of parameter sets have mode-specific R0>1.7 which meet the parameterization criteria shown on edges. Five parameters differentiate between areas of high versus low respiratory transmission: host density (edensity), viral proportion respirable (aresp), lower respiratory ID50 (piL), shedding magnitude (amag), and lung deposition fraction (tL),. Terminal nodes are given roman numerals for ease of reference.
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The droplet-route CART diagram. Numbers in ovals and rectangles are the proportions of parameter sets have mode-specific R0>1.7 which meet the parameterization criteria shown on edges. Three parameters differentiate between areas of high versus low respiratory transmission: host density (edensity), upper respiratory ID50 (piL), and shedding magnitude (amag). Terminal nodes are given roman numerals for ease of reference.
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Distribution of the airborne viral inactivation rate parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the surface viral inactivation rate parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the skin viral inactivation rate parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the finger-surface transfer efficiency parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the lower respiratory infectivity parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the upper respiratory infectivity parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the lung deposition parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the host movement rate parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the viral proportion respirable parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the surface touching rate parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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Distribution of the transfer proportion from self inoculation site to target site parameter for different categories of transmission mode dominance. Droplet, respiratory, and contact refer to parameter sets which only yielded high transmission by these routes alone. Multiple refers to parameter sets where more than one transmission route was causing high transmission. Combined refers to parameter sets which did not contain a single dominant transmission mode, but did cause high transmission by multiple modes combined, and none refers to parameter sets which both had no dominant modes of transmission and also did not combine to cause high transmission.
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This document includes greater detail of the model structure, model parameterization, description of additional analyses, and a discussion comparing this work to previous relevant modeling works.
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