## 3 Results  
### Dose-Response Modeling  
For Adenovirus A-F, _Cryptosporidium_ and _Giardia_, the exponential dose-response model was used to determine the probability of infection from ingestion of various numbers of pathogens. The exponential model is  
\[\rm P(\textit{inf})=1-e^{-k*\rm N} \tag{3}\]  
where \(\rm P(\textit{inf})\) is the probability of infection resulting from daily ingestion of the number of pathogens (N) and \(K\) is the average dose, or number of organisms, that must be ingested to initiate an infection. The best-fit \(K\) values for Adenovirus, \(C\). _parvum_, and \(G\). _lamblia_ are 0.67 [23], 0.0042 [24], and 0.0198 [25], respectively.  
For _Salmonella_ spp., the Beta-Poisson model was used:  
\[\rm P(\textit{inf})=1\mathbb{Q}\ -[1+N\ ((2\cdot(1/\alpha)-1))/N_{50}]\mathbb{Q} \ ^{*}(-\alpha) \tag{4}\]  
where \(\rm P(\textit{inf})\) is the probability of infection resulting from the daily ingestion of the dose of pathogens (N); \(\alpha\) is the pathogen infectivity constant; and \(N_{50}\) is \(\rm LD_{50}\), the dose that is lethal to 50% of individuals, divided by \(\rm ID_{50}\), which is the median infective dose. The optimized parameters for non-typhoid _Salmonella_ are \(2.1\times 10^{-1}\) and \(4.98\times 10^{1}\) for \(\alpha\) and \(\rm N_{50}\), respectively [26].  
Estimates of daily risk can be extrapolated to the risk of infection over an extended period of time using the equation below [27]. This equation was used to calculate yearly risks of reclaimed water under the exposure scenario of 365 days of exposure to raw vegetables irrigated with Type 2 reclaimed water.  
\[\mathrm{P_{t}=1-(1-P_{d})^{t}} \tag{5}\]  
Here, \(\mathrm{P_{t}}\) is the probability of infection after \(t\) days, and \(\mathrm{P_{d}}\) is the probability of infection after one day of exposure.  
In order to further evaluate the risk of illness from exposure to pathogens in reclaimed waters used for agricultural purposes, it is necessary to calculate the disability adjusted life years (DALYs) as the health effect parameter associated with illness from the pathogens examined. The first step in this calculation is to estimate the risk of diarrheal illness per year (\(\mathrm{P_{ill}}\)) using the formula  
\[\mathrm{P_{ill}=P_{t}\times P_{ill}\mid_{inf}} \tag{6}\]  
where \(\mathrm{P_{t}}\) is the probability of infection after \(t\) days (in this case 356 days or 1 year), and \(\mathrm{P_{ill}\mid_{inf}}\) is the probability of illness given infection. This parameter is organism specific; the value for _Salmonella_ is 0.3, the values for _Cryptosporidium_ and _Giardia_ are 0.7, and the value for adenovirus is 0.5 [28]. DALYs per case is also organism specific, and the relevant values are 9.6 \(\times\) 10\({}^{-4}\) for _Salmonella_, 1.5 \(\times\) 10\({}^{-3}\) for _Cryptosporidium_ and _Giardia_, and 2 \(\times\) 10\({}^{-3}\) for adenovirus [6]. The health outcome target (\(HT\)), or DALYs per year, is calculated using the equation below:  
\[HT=\mathrm{Pill}\times db\times\mathrm{fs}\div\)100 (7)  
where \(\mathrm{f_{s}}\) is the fraction of the population susceptible to a given pathogen; for this analysis, 100% of the population is assumed to be susceptible to each pathogen.