An Advanced Risk Modeling Method to Estimate Legionellosis Risks Within a Diverse Population
Abstract
:1. Introduction
1.1. Fundamental Background of L. pneumophila and Disease Endpoints
1.2. The Evolution of L. pneumophila Causes Water Systems Control Challenges and Drives Pathogenesis
1.3. Health Effects Within Diverse Populations Are Not Equal
1.4. QMRA Can Optimize L. pneumophila Interventions
1.5. Current QMRA Modeling Methods Are Inadequate for L. pneumophila
- The host is exposed to an average dose in the environment (d), modeled as a random discrete Poisson dose (red in Equation (1)).
- From this d, there are j pathogens that are delivered to a susceptible location within the host, for example, alveoli for L. pneumophila.
- From those j organisms, k survive to initiate an infection, which is a Boolean outcome and, thus, the binomial distribution (blue in Equation (1)). These likelihoods are coupled to develop the joint probability that d will result in an infection, which is then simplified to the exponential dose-response function at the far right (green in Equation (1)).
1.6. Scope and Purpose of Research
2. Modeling Methods
2.1. Two-Dimensional Simulation for Risk Modeling
2.2. Exposure Model and Probability of Infection
- Concentration of L. pneumophila in the premise plumbing water;
- Concentration of L. pneumophila in the air during showering, within a shower duration;
- Generation of aerosols sized ≤5 µm;
- Delivered dose to alveoli of human lungs, accounting for intermediate losses in the previous two regions of the respiratory system.
2.3. Risk Characterization: Probability of Illness and DALYs
2.4. Method to Estimate Morbidity Ratio Proxies and Dynamic Health Effect QMRA Models
3. Results
3.1. Effects of Flow Rate
3.2. Age Demographic Risks
3.3. Race Demographic Risks
3.4. Sex Demographic Risks
4. Discussion
4.1. Interpretation of Results
4.2. Model Limitations
4.3. Other Potential Methods for Future Research
4.4. Broader Impacts of This Research
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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Model Parameter | Distribution Variability or Uncertainty a; AICw | Value(s) | Units | Citation |
---|---|---|---|---|
Hmix | Truncated Normal b—V AICw = 0.350 | µ c = 0.5778; σ d = 0.0399 UB e = 0.5094; LB f = 0.6472 | Unitless | Estimated in this research |
Cmix | Cauchy—V AICw = 0.65 | Location = 0.363; Scale = 0.0217 | ||
AFQ1H | Triangular—V AICw = NA h | Min = 0.0097; Median = 0.0013 Max = 0.0069 | Distribution optimized in this research, data used for optimization from [46] | |
AFQ2H | Triangular—V AICw = NA h | Min = 0.0014; Median = 0.0027 Max = 0.0128 | ||
AFQ3H | Triangular—V AICw = NA h | Min = 0.0010; Median = 0.0015 Max = 0.0061 | ||
AFQ1C | Truncated Weibull—V AICw = 0.349 | Scale = 2.754; shape = 0.0308 UB = 0.0478; LB = 1(10−15) | ||
AFQ2C | Truncated Weibull—V AICw = 0.460 | Scale = 4.125; shape = 0.0373 UB = 0.0473; LB = 1(10−15) | ||
AFQ3C | Triangular—V AICw = NA h | Min = 0.0097; Median = 0.0128 Max = 0.0173 | ||
Cw | Uniform—U AICw = NA h | Min = 1; Max = 1(106) | CFU L−1 | Min [47], Max [48] |
PC | Uniform—V AICw = NA h | Min = 0.25; Max = 0.65 | Unitless | Value from [29] |
ts | Uniform—V AICw = NA h | Min = 0.0333; Max = 0.25 | Hours | Estimated in this research |
RI,Child | Triangular—V AICw = NA h | Min = 0.0076; Median = 0.0111 Max = 0.013 | m3 h−1 | Distributions chosen in this research, data from US EPA exposure factors handbook [35] |
RI,Adult | Triangular—V AICw = NA h | Min = 0.012; Median = 0.0124 Max = 0.013 | ||
RI,Elderly | Point value—V AICw = NA h | 0.012 | ||
DF1 | Truncated Logistic b—U AICw = 0.525 | Location = 0.06777; Scale = 0.04305 UB = 0.01; LB = 0.195 | Unitless | Distributions from this research, data from [49] |
DF2 | Truncated Weibull b—U AICw = 0.658 | Scale = 0.4134; shape = 0.2102 UB = 0.00; LB = 0.41 | ||
DF3 | Truncated lognormal b—U AICw = 0.429 | µ = –1.052; σ = 0.4350 UB = 0.159; LB = 0.62 | ||
k | Triangular—U AICw = NA h | Median = 0.00599; Min = 0.00326; Max = 0.131 | Distribution from this research. Values from [43] | |
;;g | Point values AICw = NA h | 0.0077; 0.097; 0.75 for Child Adult and Elderly respectively | Calculated in this research Data from [50] | |
;;;;g | Point values AICw = NA h | 0.0025; 0.010; 0.15; 0.61; 1.4 (10−5) for American Indian; Asian; Black; White and Other races respectively | ||
;g | Point Values AICw = NA h | 0.64; 0.36 for male and female respectively | ||
DWM | Triangular—U AICw = NA h | Min = 0.039; median = 0.051; max = 0.06 | Distributions from this research data from [51] | |
DWP | Triangular—U AICw = NA h | Min = 0.104; median = 0.125; max = 0.152 | ||
DWS | Triangular—U AICw = NA h | Min = 0.179; median = 0.217; max = 0.251 |
Demographic Group | Statistic | Pinf a | Pill b | MDALY c | SDALY d | PDALY e |
---|---|---|---|---|---|---|
Child | U95 f | 7.29 (10−6) | 2.39 (10−7) | 1.20 (10−8) | 3.03 (10−8) | 6.36 (10−8) |
M g | 2.61 (10−6) | 4.98 (10−8) | 2.48 (10−9) | 6.28 (10−9) | 1.32 (10−8) | |
L95 h | 2.69 (10−7) | 4.19 (10−9) | 2.08 (10−10) | 5.28 (10−10) | 1.11 (10−9) | |
Adult | U95 | 7.93 (10−6) | 1.84 (10−6) | 9.30 (10−8) | 2.36 (10−6) | 4.88 (10−7) |
M | 2.84 (10−6) | 3.85 (10−7) | 1.91 (10−8) | 4.87 (10−8) | 1.02 (10−7) | |
L95 | 2.93 (10−7) | 3.24 (10−8) | 1.60 (10−9) | 4.09 (10−9) | 8.53 (10−9) | |
Elderly | U95 | 7.57 (10−6) | 2.64 (10−5) | 1.33 (10−6) | 3.37 (10−6) | 7.00 (10−6) |
M | 2.71 (10−6) | 5.54 (10−6) | 2.75 (10−7) | 7.03 (10−7) | 1.47 (10−6) | |
L95 | 2.79 (10−7) | 4.65 (10−7) | 2.30 (10−8) | 5.88 (10−8) | 1.23 (10−7) | |
Combined Ages | U95 | 5.95 (10−5) | Not Modeled j | |||
M | 1.25 (10−5) | |||||
L95 | 1.05 (10−6) | |||||
American Indian | U95 | NA i | 8.34 (10−6) | 4.20 (10−7) | 1.07 (10−6) | 2.21 (10−6) |
M | 1.75 (10−6) | 8.70 (10−8) | 2.21 (10−7) | 4.65 (10−7) | ||
L95 | 1.47 (10−7) | 7.27 (10−9) | 1.86 (10−8) | 3.91 (10−8) | ||
Asian | U95 | 5.56 (10−6) | 2.80 (10−7) | 7.05 (10−7) | 1.48 (10−6) | |
M | 1.16 (10−6) | 5.78 (10−8) | 1.48 (10−7) | 3.09 (10−7) | ||
L95 | 9.80 (10−8) | 4.86 (10−9) | 1.24 (10−8) | 2.60 (10−8) | ||
Black | U95 | 3.45 (10−5) | 1.74 (10−6) | 4.9 (10−6) | 9.19 (10−6) | |
M | 7.24 (10−6) | 3.63 (10−7) | 9.15 (10−7) | 1.92 (10−6) | ||
L95 | 6.09 (10−7) | 3.04 (10−8) | 7.68 (10−8) | 1.62 (10−7) | ||
White | U95 | 2.34 (10−5) | 1.71 (10−6) | 2.97 (10−6) | 6.20 (10−6) | |
M | 4.91 (10−6) | 2.45 (10−7) | 6.21 (10−7) | 1.30 (10−6) | ||
L95 | 4.13 (10−7) | 2.04 (10−8) | 5.21 (10−8) | 1.10 (10−7) | ||
Other | U95 | 1.48 (10−7) | 7.38 (10−9) | 1.87 (10−8) | 3.93 (10−8) | |
M | 3.10 (10−8) | 1.55 (10−9) | 3.91 (10−9) | 8.22 (10−9) | ||
L95 | 2.61 (10−9) | 1.30 (10−10) | 3.29 (10−10) | 6.90 (10−10) | ||
Female | U95 | 2.10 (10−5) | 1.06 (10−6) | 2.69 (10−6) | 5.61 (10−6) | |
M | 4.41 (10−6) | 2.19 (10−7) | 5.59 (10−7) | 1.17 (10−6) | ||
L95 | 3.71 (10−7) | 1.84 (10−8) | 4.69 (10−8) | 9.80 (10−8) | ||
Male | U95 | 3.85 (10−5) | 1.92 (10−6) | 4.93 (10−6) | 1.02 (10−5) | |
M | 8.07 (10−6) | 4.03 (10−7) | 1.02 (10−6) | 2.14 (10−6) | ||
L95 | 6.79 (10−7) | 3.37 (10−8) | 8.56 (10−8) | 1.79 (10−7) |
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Weir, M.H.; Mraz, A.L.; Mitchell, J. An Advanced Risk Modeling Method to Estimate Legionellosis Risks Within a Diverse Population. Water 2020, 12, 43. https://doi.org/10.3390/w12010043
Weir MH, Mraz AL, Mitchell J. An Advanced Risk Modeling Method to Estimate Legionellosis Risks Within a Diverse Population. Water. 2020; 12(1):43. https://doi.org/10.3390/w12010043
Chicago/Turabian StyleWeir, Mark H., Alexis L. Mraz, and Jade Mitchell. 2020. "An Advanced Risk Modeling Method to Estimate Legionellosis Risks Within a Diverse Population" Water 12, no. 1: 43. https://doi.org/10.3390/w12010043