## Costs and Benefits

The variables cb1, cb2, cb3, and cb4 represent both the costs and benefits of each of the outcomes of the decision model. In our simple model, we consider only two costs and benefits: cost of a boil-water advisory and the benefit of averting illness. In general, the costs and benefits associated with outcomes in biosurveillance are some combination of financial costs (e.g., treatment), and effects on numbers of sick and dead individuals.

Efficacy of a Boil-Water Advisory. We assume that a boil-water advisory is heeded by every person in the half of the city where the water contamination is suspected; thus, there are no further infections and the total number of sick individuals equals the number of individuals infected up to the date of the advisory. We realize that not every individual in a community will heed a boil-water advisory. We make this assumption because there is little data about compliance with boil-water advisories. We could explore other efficacies in the sensitivity analyses phase, as discussed below.

Incubation Period of the Disease. Cases infected before the advisory may become symptomatic after the issuance of the boil-water advisory. The average incubation period of crypto-sporidiosis is often stated to be seven days. For the base case, we assume that the incubation period for all cases is exactly seven days.

Number of Sick Individuals. Figure 29.5 depicts a portion of the epidemic curve that we used in our model. It is a best-estimate curve that is derived from the surveillance data in Figure 29.1 and sales of diarrhea remedies during a known water-borne Cryptosporidium outbreak that occurred in North Battleford in 2001 (Stirling et al., 2001). We describe the methods for its estimation in Chapter 30.

The area under the epidemic curve up to a given date is the total number of individuals who became sick by that date. Based on our assumption of a constant incubation period of seven days, we computed the total number of infected individuals on the date of intervention by finding the cumulative number of symptomatic individuals seven days after the intervention.

Cost of a Boil-Water Advisory. We assume that the cost of a boil-water advisory is the cost of additional bottled water consumed. We note that the decision-makers in Glasgow did not consider this cost but rather the risk of increased scalding injuries. For the base case, we make an assumption that biases the decision against issuing a boil-water advisory without confirmatory testing. We assume the advisory motivates half the population of Chicago4 to consume one extra liter of bottled water at $1 per bottle per day. The population of Chicago

figure 29.5 The estimated epidemic curve by date of onset of symptoms. The alarm occurred on day 14. If a boil-water advisory is issued on that day, the total number of individuals who will develop symptomatic cryptosporidiosis is the area under the curve marked A. If the boil-water advisory is issued three days later after confirmation, the total number of individuals who will develop symptomatic crypto-sporidiosis is the sum of the areas under the curve marked A and B.

3 Note that the BARD and PANDA models are large networks of nodes similar to the chance nodes in Figure 29.3. These networks have a single node which represents the probability of outbreak given surveillance data. At a conceptual level, these detection systems can be linked directly to a decision tree via that node.

4 As we previously assumed, we model the situation in which there is a biosurveillance system that analyzes the sales data for the area served by one of the plants which provides the water for half of the city.

is 5.35 million, so the cost of a boil-water advisory for half of the city is $2.675 million per day.We believe this is a high estimate.

Benefit of Preventing Sickness. To quantify the benefit of a boil-water advisory, which depends both on the number of cases averted and the benefit per averted case, we use the average cost per case developed by Corso et al. (2003) for the Milwaukee 1993 Cryptosporidium outbreak of $239, adjusted from 1993 dollars to 2005 dollars. Our model ignores the possibility that immunocompromised individuals may die from Cryptosporidium infections.

cb1; cb2, cb3, and cb4. The variable cb4 describes the outcome in which the decision maker did not issue a boil-water advisory, and there was no Cryptosporidium found on testing. There are no sick individuals, and there is no cost incurred because no boil-water advisory was issued. Therefore, the cost and benefit for this outcome cb4 is zero.

The variable cb1 represents the outcome in which the decision maker issued a boil-water advisory and the Cryptosporidium outbreak occurred (true alarm). We assume that the problem in the water supply is resolved in five days; thus, the boil-water advisory will be in effect for five days at a cost of $2.675 million per day, for a total of $13.375 million. In Figure 29.5, the area under the epidemic curve marked A is the expected number of sick individuals for the outbreak in the case that the boil-water advisory is issued immediately. The expected number of sick individuals is equal to 235,110 individuals. The cost per sick individual is $3235 so the total cost of sickness is $75,940,780.49.6 Therefore, the value of cb1 is negative $89,315,780.49 ($13,375,000 + $75,940,780.49).

The variable cb2 describes the outcome in which the decision maker issued a boil-water advisory and the Cryptosporidium outbreak did not occur (false alarm). In this case there are no sick individuals; therefore, cb2 equals the total cost of the boil-water advisory. We assume the advisory is issued for three days (after this time, we know the results of testing the water). The cost of the boil-water advisory for a total of three days is $8.025 million ($2.675 million per day multiplied by three).

The variable cb3 represents the outcome in which the decision maker waited three days before issuing a boil-water advisory during an actual Cryptosporidium outbreak. The cost of the boil-water advisory is the same as cb1, $13.375 million. The total number of sick individuals will be the area A + B, or 316,034. The cost per sick individual is $323 so the total cost of sickness is $102,079,219.5. Therefore, the value of cb3 is negative $115,454,219.5 ($13,375,000 + $102,079,219.5).

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