# Using Nodal Infection Risks to Guide Interventions Following Accidental Intrusion due to Sustained Low Pressure Events in a Drinking Water Distribution System

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

**Modeling of water quality under pressure deficient conditions.**Integration of pressure-driven hydraulic analysis into QMRA models is required for a more accurate risk analysis of water contamination resulting from accidental intrusion under sustained pressure-deficient conditions (PDCs). In such conditions, a reliable estimation of intrusion points, contamination mass rate entering the DS, and fate/transport of contamination through the network cannot be achieved using traditional demand driven-analysis (DDA) models such as EPANET 2 [3]. Pressure-driven analysis (PDA) was coupled to single species water quality modeling to optimize management strategies (e.g., flushing and isolation actions) by minimizing the mass of consumed contaminant [4,5,6]. A more detailed literature review on hydraulic and water quality modeling under sustained PDCs can be found elsewhere [7].

**Applications of QMRA to drinking water DSs.**Despite evidence of drinking water DS deficiencies causing infectious waterborne diseases [8,9], the majority of QMRA work has been devoted to assessing risk of drinking water treatment failures [2]. Viñas et al. [10] and Hamouda et al. [11] presented detailed literature reviews on QMRA models applied to microbial contaminants in drinking water DSs. Besner et al. [12] developed a conceptual model to assess the public health risk associated with intrusion events. QMRA models have been applied to real DSs to evaluate the infection risk associated with the presence of viruses resulting from intrusion events caused from transient PDCs [13,14,15]. Standard QMRA models consider the water is consumed randomly at any time or at fixed times during the day [14,16,17]. The timing of water withdrawals for drinking purpose is an important factor when assessing the probability of infection as a result of intrusion events and may not be the same as the timing of the total consumption [17,18]. An improved QMRA that integrates the consumer’s behavior (probability density functions (PDFs) of the numbers of glasses and the volume consumed, and kitchen tap use) was developed and applied to assess the infection risk associated with contamination after main repairs [18,19]. They investigated the impact of different parameters such as the location of contamination and the times of valve openings on the infection risk with various pathogens (Campylobacter, Cryptosporidium, Giardia and rotavirus), in the absence of any disinfectant residual. Schijven et al. [20] also considered consumer behavior to estimate the infection risk from ingestion of contaminated water or inhalation of contaminated aerosol droplets in the case of intentional contamination of different durations and seeding concentrations in a DS.

## 2. Methodology

#### 2.1. Exposure Analysis

#### 2.1.1. Hydraulic and Water Quality Analysis

#### 2.1.2. Consumption Events

#### 2.2. Calculation of Infection Risk

## 3. Results

**Estimating ingress volumes.**Histograms of nodal pressures and demand satisfaction ratios (DSRs: available nodal demand divided by the required demand) using PDA are illustrated in Figure 2. Fewer than 1% of the nodes (93 nodes) were prone to intrusion as they experienced pressures less than 1 m under PDCs, which corresponded to the set pressure head above pipes. For about 30% of the nodes, the pressure was less than or equal to the required pressure value assumed in this study for full demand satisfaction (15 m). The DSRs for these nodes are shown in Figure 2b, excluding nodes with no required demand. Figure 2b shows that 1103 nodes have a DSR of less than 50% during depressurization.

**Concentrations of pathogens in sewage.**To cover different consumption behaviors, 200 Monte Carlo simulations were carried out for each scenario of Cryptosporidium concentration in sewage (1, 6, 26, and 560 oocysts/L). The resulting cumulative probability distributions of the number of infected people are plotted in Figure 4. In this figure, the solid lines correspond to the median infection risk, and the dotted lines are the maximum infection risk. For all concentrations, the number of infected people associated to the maximum infection risk was increased by about two folds compared to the median infection risk. For the concentration of 560 oocysts/L, 50% of the consumption events led to at least 1378 (2652) infected people considering the median (maximum) infection risk. As expected, the number of infected people increased when the Cryptosporidium concentration increases from 1 to 560 oocysts/L.

**Consumption behavior.**Figure 5 shows the sensitivity of the number of infected people over the four-day observation period to the volume of consumption (300 mL, 500 mL or 1 L per day per person) and number of glasses per day (1, 3, or 10). A total of nine scenarios were considered with a Cryptosporidium concentration of 560 oocysts/L and 24 h of PDCs. As expected, lower volumes of unboiled tap drinking water per person per day largely reduced the infection risk. By decreasing the volume by half (500 mL), the number of infected people decreased by 40%; decreasing the volume to 300 mL reduced the risk further by about 60%. By increasing the number of glasses per day from 1 to 3, 19 more people were likely to be infected for a 300 mL volume, and this value became 62 for a 1 L consumption volume per day per person (based on the values of F(x) = 1).

**Duration.**Shorter duration PDCs can take place in real networks because of WTP shutdowns, pipe breaks or fire flows. The cumulative probability distribution of the number of infected people for 200 random consumption behaviors is shown for different durations of PDCs: 1, 10, and 24 h (Figure 6). In all scenarios, the timing of the event was adjusted so that the network experienced low/negative pressures at the peak consumption time (i.e., 19:00) of the first day. A significant dependence of the infection risk with the intrusion duration was observed: a lower maximum number of infected people (84) was observed for a 1-h intrusion compared to 502 and 1410 for 10 and 24 h intrusion events, respectively.

**Spatial distribution of nodal infection risk.**Besides the number of infected people under PDCs, the temporal and geographical distribution of infection risk is also essential in defining appropriate preventive/corrective actions. In this regard, the probability of infection of the individuals who were assigned to the same node were summed up to predict the nodal risk. Figure 7 shows the spatial distribution of risk for above-mentioned scenarios corresponding to the consumption events with the maximum number of infected people (F(x) = 1 in Figure 6). As shown, with increasing duration of intrusion event, not only the nodal risks are were, but also larger areas were at risk.

**Daily risk for the 1-h event with daily demand patterns.**For the prior analyses, demand was considered constant during the day and equal to the peak hour demand (i.e., 19:00) in the hydraulic model. The reason is that adjusting different intrusion volumes and nodes at each hour of the duration of PDCs using PDA would be computationally intensive. However, we investigated a 1 h PDCs/intrusion using the daily water consumption pattern in the hydraulic model to assess its impact on the infection risk. Over four days of observation, the maximum number of infected people increased to 99 (Figure S3) with demand patterns compared to 84 with a constant demand in the hydraulic model (Figure 6, 1 h).

^{−7}at 29,754 nodes and higher than 1 × 10

^{−4}at 123 nodes. Only 16 of the nodes showed total nodal risks equivalent to more than one person. On Day 2, the total number of infected people through the whole network decreases to 29 compared to 71 for Day 1, but the number of nodes with an infection risk ≤ 1 × 10

^{−7}was lower compared to Day 1. The reason is that Cryptosporidium oocysts reached more nodes in the network on Day 2, but at lower concentrations as the ingress volume became diluted and flushed out. On Day 2, the nodal infection risk was more than one only at four nodes. On Days 3 and 4, the nodal infection risk was below one for all the nodes.

**Impact of demand satisfaction ratio on risk.**In all simulations, when the DSR (pressure ≤ 0) became zero at a node, the kitchen tap use was set to zero. To study the influence of the DSR (shown in Figure 2b) on the risk, the situation where no consumption happened at nodes with a DSR less than 5% was also modeled (Figure 10). For this investigation, the number of infected people following a 1-h PDCs/intrusion was computed on the day that intrusion occurred. As expected, the number of infected people decreased when the consumption only occurred at the nodes with a DSR ≥ 5% during low/negative pressure conditions (Figure 10).

## 4. Discussion

**Impact of event duration on the spatial distribution of risk in the network.**During an intrusion event, the intrusion risk was determined by several factors such as the intrusion volume, pathogen concentration, network hydraulics, fate and transport of the contaminants and consumers’ behavior. The volume of contaminated water entering the network is a function of the duration of the event. For the events with 1, 10 and 24 h of sustained depressurization, the estimated intrusion volumes through all leak openings were 0.8, 8 and 19 m

^{3}, respectively. Using the orifice equation, some studies have produced estimates of the intrusion volumes through leakage points for transient PDCs [1,13,22]. The total intrusion volumes resulting from a momentary pump shutdown for different intrusion conditions through leakage orifices and submerged air vacuum valves (AVVs) ranged from 10 to 360 L in the same network [22]. In contrast, these authors also showed that the maximum volume entering through a single submerged AVV during a transient could be about 95 times larger than the maximum volume entering through a single leakage orifice (227 L versus 2.4 L). In their study, the modeled intrusion volume was driven by the global leakage rate (5% versus 40%) and pressure differential. However, as these authors also stated, the orifice size at a given node should reflect the local leakage demand. Using Monte Carlo simulations, Gibson et al. [23] investigated the impact of head differences, diameter of orifices, pipe age (number of holes), and low pressure duration on the intrusion volumes during transient negative pressure events. For a 25-year-old pipe, the probability of an intrusion volume greater than 10 L was low (1%), while it increased to 70% for a 150-year-old pipe.

^{−3}), which are not plotted in Figure 7 for clarity.

**Concentration of Cryptosporidium in ingress water.**There are scarce data on the actual concentrations of pathogens in ingress water. Concentrations of pathogens in ingress water could range from those found in wastewater, representing a high-risk scenario of ingress directly from undiluted sewage [26], to the much lower concentrations measured in trench water, urban groundwater or runoff [32,33]. The number of infected people increased from 6 to 1410 when Cryptosporidium concentrations increased from 1 to 560 oocysts/L (Figure 4, median) for the worst-case consumption event (out of 200) (F(x) = 1). In agreement with our results, the contaminant concentration outside the pipe ranked among the top factors in previous QMRA studies [13,15,18,34]. When using the maximum dose–response relationship rather than the median relationship to account for uncertainties, the maximum number of infected people increased about two folds (Figure 4). The magnitude of differences between the median and maximum dose–response relationships is a critical factor to consider as recent evidence suggests that even higher dose–response values for C. hominis should be considered [2,25]. Therefore, both the concentrations and the selection of the dose–response will contribute to uncertainty [2].

**Consumption behavior.**Standard QMRA models usually consider only one consumption event per day [14,15] or a constant volume of consumption per day for every person at fixed hours [16,21]. For the 24 h scenario, the amount of water consumed daily from the kitchen tap had a huge impact on the maximum number of infected people, with decreases of ~40% and 60% when consumption was reduced from a baseline of 1 L/day to 500 mL/day and 300 mL/day, respectively. The model was also sensitive, but to a lesser degree, to the number of glasses per day for a fixed volume (Figure 5). Increasing the number of glasses per day from 1 to 10 increased the overall infection risk (by up to 2%) for the 24-h scenario. This rise was more pronounced for larger consumption volumes (Figure 5). Impact of the number of glasses per day was most noticeable when switching from a single consumption event to 3 or 10 consumption events. Blokker et al. [18] and Van Abel et al. [35] also observed that three ingestion volumes per day result in higher numbers of infected people compared to only one withdrawal of the total volume per day.

**Impact of daily demand.**The diurnal consumption patterns result in variable intrusion volumes and numbers of intrusion nodes during different hours of the day because of the variations in nodal pressure values. In this study, the demand was set to peak hour demand, which could lead to overestimation of intrusion volumes if system pressure was not decreased for night flows. On the other hand, fixed peak water demand overestimated the flushing of contaminants from the network by leakage, commercial, industrial, institutional demands, etc. during periods of low human consumption, resulting in an underestimation of the risk. With the scenario of 1 h PDCs/intrusion which incorporates daily demand patterns in the hydraulic model, it was shown that the underestimation was about 15%, which we consider to be acceptable (Figure 6 compared to Figure S3).

**Integrating demand availability from PDCs.**The novelty of this work lies in the coupling of the PDA and QMRA. Unlike DDA, PDA permits identification of areas with demand shortage, allowing for more realistic estimations of consumption based on water availability at the tap during pressure losses. For example, consuming at a DSR of 5% and less would mean that the filling time would increase by more than 20-fold. As shown on Figure 10, the number of infected people on Day 1 decreased sharply from 71 to 24 (65%) if only consumers at nodes with DSR >5% during low/negative pressures were considered. It should be noted that limitations to consumption only occur during the low-pressure conditions. Furthermore, the extent of these differences depends on the consumption time, and the duration and timing of the event. The results shos that restricting drinking water consumption during periods of low or intermittent flow would greatly reduce risks. Therefore, utilities and health authorities could consider educating people not to consume water during these periods of low flow. Further study is needed to define a minimal DSR criteria based on the amount of reduction in infection risk.

**Implication for risk management.**The nodal risks considered the contaminant transport in the network and the probability of coincidence of passage of contaminants at the tap and consumption. However, the spatial and temporal distribution of total nodal risks also reflected the distribution of the population between nodes (Figure 7 and Figure 9). The areas in which to issue a BWA, and those where corrective actions (e.g., flushing) would be effective, can be determined using nodal risk values in reference to an acceptable risk level.

^{−4}) [37]. Issuing a system-wide BWA that decreased by 80% the average number of glasses of unboiled water consumed led to a four-fold reduction in the number of infected people [18].

## 5. Conclusions

- An approach is proposed to couple QMRA and water quality calculations based on pressure-driven hydraulic analysis to assess the infection risk under sustained low/negative pressure events, causing accidental intrusion of potentially contaminated water surrounding the pipes. The intrusion volume at potential intrusion nodes is adjusted for nodal pressure and pipe state (age and material) using leakage demand.
- By implementing PDA, the pattern of kitchen tap use was dynamically modified to include the impact of demand availability during PDCs in the analysis. During the PDCs, using a higher critical value of the DSR (5% instead of no demand) for drinking water withdrawals led to a significant reduction in the number of infected people (~65% on Day 1 of 1-h PDCs). This reduction in infection risk if contaminated water is not consumed should be considered to guide preventive notices. It shows that customers should be advised not to drink water when flow at the tap is low (i.e., it takes much longer time to fill a glass).
- In this work, depending on the pathogen concentration in sewage, the number of infected people changed by 235-fold, showing the importance of selecting a representative level of contamination in a system. Using raw sewage as the ingress water is a conservative scenario as water surrounding water mains is likely to be less contaminated than sewage.
- Results show that the number of glasses per day (1, 3, or 10) was less important than the consumption volume (300 mL, 500 mL, or 1 L) for the scenario of 24-h PDCs.
- The duration of PDCs/intrusion is a decisive factor in determining the infection risk, issuing sectorial boil water advisories and other preventive/corrective actions. Spatial and temporal distribution of nodal risks presented in this study can help to determine the boundaries and duration of sectorial BWAs.
- A fast response by the utility is key to reducing the infection risk by limiting the contamination area. For a 1-h intrusion, delaying 5 h the necessary preventive/corrective actions from the start of the intrusion may result in the infection of up to 71 people.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Kirmeyer, G.J.; Friedman, M.; Martel, K.; Howie, D.; LeChevallier, M.; Abbaszadegan, M.; Karim, M.; Funk, J.; Harbour, J. Pathogen Intrusion into the Distribution System; 90835; American Water Works Association Research Foundation, American Water Works Association and United States Environmental Protection Agency: Denver, CO, USA, 2001; p. 254. [Google Scholar]
- World Health Organisation (WHO). Quantitative Microbial Risk Assessment: Application for Water Safety Management; World Health Organisation: Geneva, Switzerland, 2016; p. 204. [Google Scholar]
- Rossman, L.A. EPANET 2. User’s Manual; EPA 600-R-00-57; National Risk Management Research Laboratory, Office of Research and Development, United States Environmental Protection Agency (USEPA): Cincinnati, OH, USA, September 2000; p. 200.
- Bashi-Azghadi, S.N.; Afshar, A.; Afshar, M.H. Multi-period response management to contaminated water distribution networks: Dynamic programming versus genetic algorithms. Eng. Optim.
**2017**, 50, 415–429. [Google Scholar] [CrossRef] - Rasekh, A.; Brumbelow, K. Drinking water distribution systems contamination management to reduce public health impacts and system service interruptions. Environ. Model. Softw.
**2014**, 51, 12–25. [Google Scholar] [CrossRef] - Zafari, M.; Tabesh, M.; Nazif, S. Minimizing the adverse effects of contaminant propagation in water distribution networks considering the pressure-driven analysis method. J. Water Resour. Plann. Manag.
**2017**, 143. [Google Scholar] [CrossRef] - Hatam, F.; Besner, M.-C.; Ebacher, G.; Prévost, M. Combining a multispecies water quality and pressure-driven hydraulic analysis to determine areas at risk during sustained pressure-deficient conditions in a distribution system. J. Water Resour. Plann. Manag.
**2018**, 144, 04018057. [Google Scholar] [CrossRef] - Lindley, T.R.; Buchberger, S.G. Assessing intrusion susceptibility in distribution systems. J. Am. Water Works Assoc.
**2002**, 94, 66–79. [Google Scholar] [CrossRef] - Craun, G.F.; Brunkard, J.M.; Yoder, J.S.; Roberts, V.A.; Carpenter, J.; Wade, T.; Calderon, R.L.; Roberts, J.M.; Beach, M.J.; Roy, S.L. Causes of outbreaks associated with drinking water in the United States from 1971 to 2006. Clin. Microbiol. Rev.
**2010**, 23, 507–528. [Google Scholar] [CrossRef] [PubMed] - Viñas, V.; Malm, A.; Pettersson, T.J.R. Overview of microbial risks in water distribution networks and their health consequences: quantification, modelling, trends, and future implications. Can. J. Civil Eng.
**2019**, 46, 149–159. [Google Scholar] [CrossRef] - Hamouda, M.A.; Jin, X.; Xu, H.; Chen, F. Quantitative microbial risk assessment and its applications in small water systems: A review. Sci. Total Environ.
**2018**, 645, 993–1002. [Google Scholar] [CrossRef] - Besner, M.-C.; Prévost, M.; Regli, S. Assessing the public health risk of microbial intrusion events in distribution systems: conceptual model, available data, and challenges. Water Res.
**2011**, 45, 961–979. [Google Scholar] [CrossRef] - Teunis, P.F.M.; Xu, M.; Fleming, K.K.; Yang, J.; Moe, C.L.; LeChevallier, M.W. Enteric virus infection risk from intrusion of sewage into a drinking water distribution network. Environ. Sci. Technol.
**2010**, 44, 8561–8566. [Google Scholar] [CrossRef] - Yang, J.; LeChevallier, M.W.; Teunis, P.F.M.; Xu, M. Managing risks from virus intrusion into water distribution systems due to pressure transients. J. Water Health
**2011**, 9, 291–305. [Google Scholar] [CrossRef] [PubMed] [Green Version] - LeChevallier, M.W.; Xu, M.; Yang, J.; Teunis, P.; Fleming, K.K. Managing Distribution System Low Transient Pressures for Water; Water Research Foundation and American Water Works Service Company, Inc.: Denver, CO, USA, 2011; p. 144. [Google Scholar]
- Besner, M.-C.; Messner, M.; Regli, S. Pathogen intrusion in distribution systems: model to assess the potential health risks. Proceedings of 12th Annual Conference on Water Distribution Systems Analysis (WDSA), Tucson, AZ, USA, 12–15 September 2010; pp. 484–493. [Google Scholar]
- Davis, M.J.; Janke, R. Development of a probabilistic timing model for the ingestion of tap water. J. Water Resour. Plann. Manag.
**2009**, 135, 397–405. [Google Scholar] [CrossRef] - Blokker, M.; Smeets, P.; Medema, G. Quantitative microbial risk assessment of repairs of the drinking water distribution system. Microb. Risk Anal.
**2018**, 8, 22–31. [Google Scholar] [CrossRef] - Blokker, M.; Smeets, P.; Medema, G. QMRA in the Drinking Water Distribution System. Procedia Eng.
**2014**, 89, 151–159. [Google Scholar] [CrossRef] [Green Version] - Schijven, J.; Forêt, J.M.; Chardon, J.; Teunis, P.; Bouwknegt, M.; Tangena, B. Evaluation of exposure scenarios on intentional microbiological contamination in a drinking water distribution network. Water Res.
**2016**, 96, 148–154. [Google Scholar] [CrossRef] [PubMed] - Islam, N.; Rodriguez, M.J.; Farahat, A.; Sadiq, R. Minimizing the impacts of contaminant intrusion in small water distribution networks through booster chlorination optimization. Stoch. Environ. Res. Risk Assess.
**2017**, 31, 1759–1775. [Google Scholar] [CrossRef] - Ebacher, G.; Besner, M.-C.; Clément, B.; Prévost, M. Sensitivity analysis of some critical factors affecting simulated intrusion volumes during a low pressure transient event in a full-scale water distribution system. Water Res.
**2012**, 46, 4017–4030. [Google Scholar] [CrossRef] [PubMed] - Gibson, J.; Karney, B.; Guo, Y. Predicting health risks from intrusion into drinking water pipes over time. J. Water Resour. Plann. Manag.
**2019**, 145, 04019001. [Google Scholar] [CrossRef] - Bentley Systems, Incorporated. WaterGEMS V8i Users Manual; Haestad Methods Solution Centre: Watertown, CT, USA, 2014. [Google Scholar]
- World Health Organization (WHO). Risk Assessment of Cryptosporidium in Drinking Water; WHO/HSE/WSH/09.04; Public Health and Environment, Water, Sanitation, Hygiene and Health; World Health Organization: Geneva, Switzerland, 2009; p. 134. [Google Scholar]
- Payment, P.; Plante, R.; Cejka, P. Removal of indicator bacteria, human enteric viruses, Giardia cysts, and Cryptosporidium oocysts at a large wastewater primary treatment facility. Can. J. Microbiol.
**2001**, 47, 188–193. [Google Scholar] [CrossRef] - Hatam, F.; Besner, M.-C.; Ebacher, G.; Prévost, M. Improvement of Accidental Intrusion Prediction Due to Sustained Low-Pressure Conditions: Implications for Chlorine and E. coli Monitoring in Distribution Systems. J. Water Resour. Plann. Manag. submitted.
- Van Zyl, J.E.; Clayton, C.R.I. The effect of pressure on leakage in water distribution systems. Inst. Civil Eng. Water Manag.
**2007**, 160, 109–114. [Google Scholar] [CrossRef] - Van Zyl, J.E.; Malde, R. Evaluating the pressure-leakage behaviour of leaks in water pipes. J. Water Suppl. Resear. Technol. Aqua
**2017**, 66, 287–299. [Google Scholar] [CrossRef] - Van Zyl, J.E.; Lambert, A.O.; Collins, R. Realistic modeling of leakage and intrusion flows through leak openings in pipes. J. Hydraul. Eng.
**2017**, 143. [Google Scholar] [CrossRef] - Besner, M.-C.; Ebacher, G.; Lavoie, J.; Prévost, M. Low and negative pressures in distribution systems: Do they actually result in intrusion? Proceedings of 9th Annual Water Distribution System Analysis Symposium, ASCE-EWRI World Environmental and Water Resources Congress, Tampa, FL, USA, 15–19 May 2007; p. 10. [Google Scholar]
- Ebacher, G.; Besner, M.-C.; Prevost, M. Submerged appurtenances and pipelines: An assessment of water levels and contaminant occurrence. J. Am. Water Works Assoc.
**2013**, 105, E684–E698. [Google Scholar] [CrossRef] - Besner, M.-C.; Broséus, R.; Lavoie, J.; Di Giovanni, G.; Payment, P.; Prévost, M. Pressure monitoring and characterization of external sources of contamination at the site of the Payment drinking water epidemiological studies. Environ. Sci. Technol.
**2010**, 44, 269–277. [Google Scholar] [CrossRef] [PubMed] - Yang, J.; Schneider, O.D.; Jjemba, P.K.; Lechevallier, M.W. Microbial risk modeling for main breaks. J. Am. Water Works Assoc.
**2015**, 107, E97–E108. [Google Scholar] [CrossRef] - Van Abel, N.; Blokker, E.J.; Smeets, P.W.; Meschke, J.S.; Medema, G.J. Sensitivity of quantitative microbial risk assessments to assumptions about exposure to multiple consumption events per day. J. Water Health
**2014**, 12, 727–735. [Google Scholar] [CrossRef] [PubMed] - Davis, M.J.; Janke, R. Importance of exposure model in estimating impacts when a water distribution system is contaminated. J. Water Resour. Plann. Manag.
**2008**, 134, 449–456. [Google Scholar] [CrossRef] - National Research Council of the National Academies. Drinking Water Distribution Systems: Assessing and Reducing Risks; The National Academies Press: Washington, DC, USA, 2006; p. 404. [Google Scholar]

**Figure 1.**Flowchart for QMRA of accidental intrusion during sustained PDCs; WL, water level; MO, microorganism.

**Figure 2.**Distribution of: (

**a**) nodal pressures for the whole network (30,077 nodes); and (

**b**) demand satisfaction ratios (DSRs) for nodes under pressure-deficient conditions (8578 nodes), excluding the nodes with zero demand.

**Figure 3.**Distribution of nodal intrusion flow rates through 93 leak openings under the simulated pressure-deficient conditions.

**Figure 4.**Number of infected people corresponding to median and maximum infection risks resulting from a 24-h depressurization; 200 Monte Carlo simulations (consumption events) for each Cryptosporidium concentration: 1, 6, 26, and 560 oocysts/L; number of infected people corresponds to the cumulative dose over four days of observation; F(x): probability that the median/maximum number of infected people will be less than or equal to x.

**Figure 5.**Impact of consumption volumes and number of glasses per day on the number of infected people corresponding to median infection risk over a four day-period; Cryptosporidium concentration = 560 oocysts/L; the x-axis scale is the same between the plots (150 people).

**Figure 6.**Comparing the probability distribution of the number of infected people over a four-day period for 200 Monte Carlo simulations for each duration of PDCs: 1, 10, and 24 h; Cryptosporidium concentration in sewage = 560 oocysts/L.

**Figure 7.**Spatial distribution of nodal risks for three durations of PDCs: 1, 10, and 24 h; Cryptosporidium concentration in sewage = 560 oocysts/L; nodes with an infection risk below 1 × 10

^{−3}are drawn in black; infection risks corresponding to consumption events with F(x) = 1 (Figure 6) are illustrated.

**Figure 8.**Number of infected people corresponding to median infection risk for Days 1–4 for the scenario of 1 h of PDCs with daily consumption patterns; C

_{out}= 560 oocysts/L; 200 Monte Carlo simulations (consumption events) every day.

**Figure 9.**Spatial distribution of nodal risk; Days 1–4 for the scenario of 1 h of PDCs with daily consumption patterns; C

_{out}= 560 oocysts/L; nodes with infection risk below 1 × 10

^{−3}are drawn in black; infection risks corresponding to consumption events with F(x) = 1 (Figure 8) are illustrated.

**Figure 10.**Probability distributions of the number of infected people during the first day of simulation when people with a DSR null and less than 5% do not drink water from tap; 200 Monte Carlo simulations for each scenario; C

_{out}= 560 oocysts/L with 1 h of PDCs with daily consumption patterns.

**Figure 11.**Number of infected people for different pressure (P) ranges (based on the pressure values under PDCs) on Days 1–4; Infection risks corresponding to the consumption event with F(x) = 1 (Figure 8) are illustrated. The event starts at 18:30 on Day 1 for a duration of 1 h. Daily patterns in the hydraulic model.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hatam, F.; Blokker, M.; Besner, M.-C.; Ebacher, G.; Prévost, M.
Using Nodal Infection Risks to Guide Interventions Following Accidental Intrusion due to Sustained Low Pressure Events in a Drinking Water Distribution System. *Water* **2019**, *11*, 1372.
https://doi.org/10.3390/w11071372

**AMA Style**

Hatam F, Blokker M, Besner M-C, Ebacher G, Prévost M.
Using Nodal Infection Risks to Guide Interventions Following Accidental Intrusion due to Sustained Low Pressure Events in a Drinking Water Distribution System. *Water*. 2019; 11(7):1372.
https://doi.org/10.3390/w11071372

**Chicago/Turabian Style**

Hatam, Fatemeh, Mirjam Blokker, Marie-Claude Besner, Gabrielle Ebacher, and Michèle Prévost.
2019. "Using Nodal Infection Risks to Guide Interventions Following Accidental Intrusion due to Sustained Low Pressure Events in a Drinking Water Distribution System" *Water* 11, no. 7: 1372.
https://doi.org/10.3390/w11071372