PREVENTIVE VETERINARY

MEDICINE ELSEVIER Preventive Veterinary Medicine 33 (1998) 183-193

A 1i:near programming assessment of the profit from strategies to reduce the prevalence of

Staphylococcus aureus mastitis

Lydia Zepeda a*1, Kenneth L. Buelow b, Kenneth V. Nordlund b, Chester B. Thomas b, Michael T. Collins ‘, William J. Goodger b,* a Depa went of Consumer Science, 1300 Linden Drive, University of Wisconsin, Madison, WI 53706, USA

b Department of Medical Sciences, School of Veterinary Medicine, 2015 Linden Drive West,

University of Wisconsin, Madison, WI 53706, USA

’ D<?partment of Pathobiological Sciences, 2015 Linden Drive West, School of Veterinary Medicine,

University of Wisconsin, Madison, WI 53706, USA

Accepted 9 May 1991

Abstract

We used a linear programming model to estimate the financial returns to a Stuphylococcus aureus testing and control program over a l-year period for a lOO-cow herd, with a 8636-kg rolling-herd average. Six tests, which vary in sensitivity from 0.80 to 0.98 and specificity of 0.99,

were examined in simulated herds with 10, 20 and 30% prevalence of S. aureus infection. Sensitivity of these results to a range of assumptions regarding rolling-herd average, milk price, somatic cell-count premium, and cost and cure rate of dry treatment were examined to determine the profits from the program. The profits of a control program are most dependent upon prevalence, cell-count premium, and cost of dry treatment. In our simulation for a lOO-cow herd, a testing and control program appears to cost less than US$lO per cow per year, and pays for itself within 1 yr, except under the lowest prevalence and most-adverse conditions (low yield, high cost of dry treatment, or low SCC premium). 0 1998 Elsevier Science B.V.

Keywords: Staphylococcus aureus; Modelling; Mastitis; Control; Strategies; Economics

-_ * Corresponding author. Tel.: + 1 608 263 7896; fax: + 1 608 265 8020; e-mail:

wgoodger@facstaff.wisc.edu.

’ Present address: Food and Agriculture Organization, ESAE, C-309, Viale delle Terme di Caracalla, 00153

Roma, Italy.

0167-5877/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved.

PI1 SOlC7-5877(97)00054-8

184 L. Zepeda et al. / Preventive Veterinary Medicine 33 (1998) 183-193

1. Introduction

New diagnostic testing methods and modifications of old methods continue to be promoted to identify cows with Staphylococcus aureus intramammary infection (IMI). Recent papers have developed a model which has improved the sensitivity of such tests and has calculated test sensitivity and specificity for various sampling strategies (Buelow et al., 1996a,b). Recommendations for reducing prevalence of S. aureus IMI are commonly based on using diagnostic testing methods to complement various control

strategies. However, economic analyses generally assume a 100% accurate test was used. This recent research gives us an opportunity to consider test accuracy for different sampling strategies when profits are estimated for a S. uu~eus control program.

Linear programming (LP) is an analytic technique that is easy to use and readily available. It allows strategies to be evaluated based on the objective of the decision

maker (in this case, the contribution to profits). In addition to determining the optimal strategy, it yields the opportunity cost of adopting suboptimal strategies. Moreover, the

shadow price (or, ‘imputed cost’) of constraints used in the LP model are generated. A shadow price indicates how much profits would change if a constraint is relaxed by one unit. Shadow prices are used to determine the value of testing and test accuracy.

The objectives of this study were to: (1) develop an LP model to maximize the net profits of a testing and control strategy to reduce prevalence of S. aureus IMI; (2) use the LP model to evaluate short-run costs and potential profits using baseline test and control-strategy data; and (3) perform sensitivity analyses on test accuracy.

2. Materials and methods

Linear programming is a method of selecting from several alternative decisions. The general goal of an LP problem is to optimize an objective of the decision maker-either minimizing costs or maximizing profits-subject to technical constraints on the system. Mathematically, one solves a system of equations for optimal values of unknown variables which, when combined, define the alternative decisions. An algorithm (such as the Simplex method) is used to determine the optimal, feasible strategy (Paris, 1991, p. 95-121). For example, LP is used for balancing feed rations for cows by determining the least-cost combination of feeds that meet all nutritional requirements and physio- logical constraints.

Linear programming (LP) does require one to impose a number of assumptions in modeling decisions: linearity, additivity, divisibility, certainty, and nonnegativity. Lin- earity implies that the relationship between the variables are linear. Over small ranges in the variables, a linear relationship may be a good approximation; nonlinear program- ming can be used when the linearity assumption cannot be justified. Additivity implies that the relationship between inputs and outputs is a fixed proportion, in that all inputs

L. Zepeda et al./ Preuentiue Veterinary Medicine 33 (1998) 183-193 185

are complements to each other. At a point in time, or over a small range in production,

this may also be a reasonable assumption. Divisibility implies that all variables or decisions are infinitely divisible. Even if the

variables are not divisible (for example, ‘cows’) if the numbers analyzed are large, the assumption may yield a good approximation of the optimal decision. Integer program- ming can be used for problems with a small number of discrete choices (Paris, 1991, p.

25). The certainty assumption implies that one knows the prices and technical relation-

ships of the variables with certainty. Stochastic programming may be used if one is uncertain about the objective function coefficients. Another method of dealing with

uncertain coefficients is to do sensitivity analysis: one can vary the values of the coefficients to see if and how the optimal strategy changes. Nonnegativity is a trivial assumption; it implies that activities or decisions must be zero or positive.

Another aspect of linear programming is that it implies a single time period. Dynamic programming can be used if the process is continuous and occurs over time. Multiperiod linear programming can be used to model discrete time periods.

Quattro ProTM 3.0 was used to run the LP model. The goal of the LP model is to

maximize returns or profits of a S. aureu~ testing-and-control program versus no program over a 1-yr period. A I-yr period was selected to represent the financial planning horizon of milk producers. There are three baseline results, one each for 10, 20,

and 30% baseline prevalence. These three levels were chosen for examination as a result of our extensive experience in herd mastitis investigations involving S. az4reu.r mastitis. These levels represent the results of whole-herd individual-cow culture results using the sampling strategies examined in Buelow et al. (1996a,b). Thus, we felt that these levels of S. ctureus would represent what would be encountered in clinical practice at higher levels of S. aureus (approximately 30%) moderate levels of S. aureus (approximately 20%), and milder levels of S. aureus (approximately 10%). Assumptions for the

baseline models are the following. (1) Herd size is 100 cows. (2) IRolling-herd average is the Wisconsin AgSource 1995 Holstein average rounded

up to 8636 kg, (AgSource, 1995, unpub. notes) Sensitivity analysis represents low and

high yield herds in Wisconsin: 6363 kg. and 10909 kg.

(3) S. aureus IMI reduces milk yield by 230 kg (Firat, 1993; Erb, 1985; Lucey and

Rowlands, 1984). (4) All replacement animals produce the same level of milk as the non-S. aureus cow

mean milk yield. (5) The SCC of non-S. aureus cows is 200000 cells/ml, and that of cows with S.

aureus IMI is 900000 (Buelow, Unpub. thesis, 1993). (6) Milk price is US$26.40/100 kg. Sensitivity analysis is done using low and high

milk prices: US$22.00 and US$30.80/100 kg. (7) SCC premium is 20 cents per 100 X lo3 (or a fraction thereof) decrease in SCC

per hundred weight of milk produced. Sensitivity analysis is done using low and high premiums of 10 cents and 30 cents per 100 X lo3 decrease.

186 L. Zepeda et al./ Preventive Veterinary Medicine 33 (1998) 183-193

(8) Tests are administered by a technician at US$lO/h. (9) There are 6 possible tests (Buelow et al., 1996a,b):

Test US$ cost Sensitivity

RQSPC 20.83 0.97

RQSCS 40.83 0.98

RCSPC 5.50 0.90

RCSCS 10.50 0.95 QSCO 20.42 0.87

csc 5.25 0.80

Specificity

0.995

0.995 0.995

0.995 0.995 0.990

where the tests are defined as follows: (a) repeated quarter samples pooled and cultured (RQSPC)-quarter milk samples taken from each quarter of each cow on day 0, and repeated once from each quarter at the sampling intervals of 0.5, 1, 2, 3, 4, or 5 days, then pooled and cultured as one sample; (b) repeated quarter samples cultured separately

(RQSCS)-quarter milk samples taken from each quarter of each cow on day 0, and repeated once from each quarter at the sampling intervals of 0.5, 1, 2, 3, 4, or 5 days and cultured separately; (c) repeated 4-quarter composite sample pooled and cultured

(RCSPC)-equal-volume aliquots of milk taken from each quarter sample and pooled to produce a composite sample on day 0, pooled and cultured jointly with a second composite sample created at the sampling intervals 0.5, 1, 2, 3, 4, or 5 days; (d) repeated 4-quarter composite sample cultured separately (RCSCS)-equal volume aliquots of milk taken from each quarter sample and pooled to produce a composite sample on day 0 (a second composite sample was created and cultured separately using samples collected at the sampling intervals 0.5, 1, 2, 3, 4, or 5 days); (e) quarter sample cultured once (QSCO)-a sample of milk taken from each quarter of each cow and cultured once; (f) four-quarter composite sample cultured (CSC)-equal volume aliquots of milk taken from

each quarter sample and pooled to produce a composite sample for each cow that was cultured once.

(10) All cows are tested at the beginning and the end of the year. (11) After the first test, one can choose (or not) to segregate all positive cows at a

cost of US$20 per cow per year. (12) 50% of all S. aureus cows develop clinical mastitis that can be treated at a cost

of US$lOO per cow. (13) After a second test at the end of the year, the options are either to cull a positive

cow (net cost US$650) or to dry-treat her. The option of culling is above the number normally culled for S. uureus. All cows that test negative are treated with a standard dry-treatment antibiotic tube in each quarter at dry off. All cows identified as positive (infected) are dry-treated either with a dry-treatment antibiotic tube specific for S. aureus (25% cure rate), or a special dry-treatment antibiotic tube plus intramuscular injections of antibiotic (50% cure rate), or special dry-treatment antibiotic tube plus intramuscular injections of antibiotic plus one week of lactation therapy with a special lactation treatment antibiotic tube specific for S. aureus (75% cure rate). The baseline

L. Zepeda et al./Preventiue Veterinary Medicine 33 (1998) 183-193 187

Table 1

Predicted incidence and transmission rates for S. aweus and predicted cull rates needed to maintain S. aureus

in steady-state in a lOO-cow dairy herda

Prevalence (%) Incidence Transmission rates Steady state cull rate

(% per year)

Per 100 cow-months New infections per infected

cow per year

Segregated Not segregated Segregated Not segregated

10 1.75 2.53 1.89 2.73 27.3

20 2.70 4.25 1.29 2.04 40.8

30 3.64 5.98 1.02 1.67 50.2

“See Set tion 2 assumptions 14 and 15 for an explanation of how these predictions are estimated.

cure raite for dry treating is 50% and costs US$lOO. Sensitivity analysis is done for a 25% cure rate, US$25 cost and a 75% cure rate, US$lSO cost. ’

(14) Using the nine observations on incidence and prevalence from Fox and Hancock (1989), the following regression model (with standard errors) was estimated to predict incidence given segregation:

incidence = 0Y0!t5 + 0i3!4:” prevalence - f’lWT;( prevalence X segregation)

R2 = 0.66, F = 5.8(significant at 10%).

Incidence is the number of newly-infected cows per 100 cow-months; prevalence is the percent of cows with the infection at a point in time; and segregation is equal to 1 if

the infected cows were segregated, 0 if the infected cows were not segregated. The coeffici’ent on the interactive segregation term represents a shift in the marginal impact

of prevalence on incidence (the slope) due to segregation. Models with only a fixed effect or with both fixed and marginal effects did not perform as well in terms of overall fit and coefficient significance (data not shown).

Transmission rates are calculated using this model:

predicted incidence X 12 months X proportion of uninfected cows

% prevalence

where the predicted incidence, transmission rates, and resulting cull rates using this

model are listed in Table 1. (15) The S. aureus normal cull rate is the number of cows normally culled in the

testing <and program year with S. aureus IMI required to maintain prevalence at its initial level, given that there is no testing and control program in place for S. aureus

mastitis. It is assumed that the minimum number of cows culled equals the S. aureus

normal cull rate for a particular prevalence to maintain prevalence at a steady state. For

’ The treatment alternatives were examined by running three separate models with each alternative. They

could not be examined simultaneously in a single model since it is a l-year model and no benefits from

treatment would accrue because treatment occurs at the end of the year; hence, if the three alternative

treatments were simultaneously available, the solution would always be to choose the cheapest (US$25, 25%

cure rate) test.

188 L. Zepeda et al./Preuentiue Veterinary Medicine 33 (1998) 183-193

example, at 10% prevalence, the nonsegregated transmission rate is 2.73, meaning that in a herd of 100 cows, 10 cows are infected, and during the course of the year they infect 27.3 other cows. Therefore, the normal S. aureus cull rate for a herd of 100 cows with a 10% prevalence is 27.3 cows. That is, 27.3 cows with S. aureus need to be culled to maintain prevalence at 10% when there is no testing and control program.

These same cull rates are applied to a herd with a testing and control program, but the number of S. aureus cows declines because segregation lowers the transmission rate, and the more specific dry treatment has a better cure rate. For example, in a herd of 100

cows with a testing and control program and a 10% prevalence of S. aureus, the 10 infected cows are segregated. Then, given a 1.89 transmission rate they will infect 18.9 other cows by the end of the year. Approximately 4 additional infections will occur,

since the tests at the beginning and end of the year are not 100% accurate. The total number of infected cows (33) less the normal S. aureus cull rate of approximately 27 cows results in 6 positive cows to be dry-treated and with a 50% cure rate results in a true herd prevalence of 3% at the end of one year of the testing and control program, given that the tests are not 100% accurate, and the treatment are not 100% effective. Thus, at 10% prevalence, the testing-and-control program results in a reduction of seven S. aureus cows when compared to no testing-and-control program.

2.1. Linear programming model

The objective set for the linear programming model was to maximize the net benefits of a control program. The benefits include the change in milk yield, XC premium

revenue, and reduction in clinical mastitis cases. Costs include the costs of testing at the beginning and end of the year, segregating positive cows, culling S. aureus identified cows above the number normally culled, and dry-treating S. aureus identified cows. The constraints to the LP model are as follows.

(1) All cows are tested at the beginning of the year. (2) True-positives (TP) = prevalence * sensitivity. (3) True-negatives (TN) = (1 - prevalence) * specificity. (4) False-negatives (FN) = prevalence * (1 - sensitivity). (5) False-positives (FP) = (1 - prevalence) * (1 - specificity). (6) Segregated S. aureus + non-segregated S. aureus = positives. (7) New infections with program = [transmission rate if cows are not

segregated * ( - FP + FN + non-segregated S. aureus cows>] + [transmission rate if cows are segregated *(segregated S. aureus)].

(8) S. aureus cows after one year with program = S. aureus cows at beginning + new infections with program.

(9) Test all cows at the end of the year. (10) Non-S. aureus cows after one year with program = 100-S. aureus cows after one

year with program. (11) New infections with no program = transmission rate for prevalence * S. aureus

cows at beginning of year. (12) S. aureus cows with no program = S. aureus cows at the beginning of the

year + new infections with no program. (13) Non-S. aureus cows with no program = 100 - S. aureus cows with no program.

L. Zepeda et al./ Preventive Veterinary Medicine 33 (1998) 183-193 189

(14) Change in SCC at end of the year = SCC if no program - SCC if with program.

(15) Change in the cases of clinical mastitis with the testing-and-control program = 0.5 *(S. aureus cows with no program - S. aureus cows with a testing-and-control

program). Constraints 16-21 are accounting identities to ensure that after the second test, the

number of cows tested using each test equals the sum of those classified as TP, FP, TN,

and FN according to each test type.

(16) 2nd test: RQSPC = TPRQspc + FPRQspC + FNRqsPC (17) 2nd test: RQSCS = TPRqscs + FPaqscs + TNaos,-s + FNRQscs (18) 2nd test: RCSPC = TP,,,,, + FP,,,,, + TN,,,,, + FN,,,,, (19) 2nd test: RCSCS = TP,,,,, + FP,,,,, + TN,,,,, + FN,,,,, (20) 2nd test: QSCO = TPosco + TPo,,, + TNQsco + FNQsco (21) 2nd test: CSC = TPc,, + FPc,, + TN,,, + FN,,, Constraints 22-25 are accounting identities to determine the total number of TP, FP,

TN, and FN after the second test across all test types (i = RQSPC, RQSCS, RCSPC,

RCSCS, QSCO, CSC). (22) True positive S. aureus cows at end of year = TP, (23) False positive S. aureus cows at end of year = FP,

(24) True negatives at end of year = TN, (25) False negatives at end of year = FN, (26) All positive cows must either be culled or dry treated. (27) Ending S. aureus cows = FN + 0.5 *dry-treated cows. (28) Ending non-S. aureus cows = 100 - ending S. aureus cows.

3. Results

3. I. Baseline

The returns to testing and control increase with increasing baseline prevalence.

Results in Table 2 represent the minimum benefits of a testing and control program, since benefits in subsequent years from a lower SCC, higher milk yield, and fewer mastitis cases are not included. In all cases, the testing and control program reduces the prevalence of S. aureus. Given the possible combinations of testing and control, only two strategies emerge as dominant among both the baseline assumptions and the sensitivity analysis. Strategy 1 involves using the RCSPC test on all cows at the beginning of the year, then segregating all positive cows, then testing all cows with the CSC test at the end of the year, then (after normal culling) dry-treating all the remaining positive cows. Strategy 2 is identical to Strategy 1, except that the initial test is RCSCS.

The more expensive, more sensitive RCSCS is profitable when the prevalence is high (20% or 30%). The tests themselves represent the bulk of the cost of the program, then dry treatment; segregation is a small cost. The bulk of the profits from the program come from the increase in the SCC premium resulting from the lower SCC; the reduction in the cases of clinical mastitis is the next most important source of profits, while the increase in milk yield is a minor contribution to profits.

190 L. Zepeda et al./Preventive Veterinary Medicine 33 (1998) 183-193

Table 2

Baseline results from linear programming model for most profitable .S. aureus testing and control strategy for

a lOO-cow dairy herd after one year

Prevalence

10% 20% 30%

Profits (US$)

Test at beginning of year

Number of cows segregated at beginning of year

Test used at end of year

Number of cows dry treated

Number of year-end number S. aureus cows

Rolling-herd average milk yield

Beginning (kg/cow)

Year-end (kg/cow)

SCC beginning of year

SCC year-end

Reduction in new infections

Reduction in cases of clinical mastitis

Cost of tests (USS)

Cost of segregation (US$)

Cost of dry treatment (US$)

Increased SCC premium payment (US$)

RCSPC”

10

CSC’

5.9

3.3

8636 8636 8636

8651 8673 8689

268 322 337017 406085

222 267 227 866 247 974

4.4 12.1 16.4

2.2 6.1 8.2

1075 1575 1575

200 400 600

586 766 1369

584 1613 2198

- 152 -27

RCSCSb RCSCSb

20 30

CSC’ CSC’

7.7 13.7

4.1 7.0

aRepeated 4-quarter composite sample pooled and cultured.

bRepeated 4-quarter composite sample cultured separately.

CFour-quarter composite sample cultured.

Along with the combination of actions which maximize profits, the solution to a LP model yields shadow prices. The shadow prices in this case (Table 3) reveal the

marginal impacts of testing, segregation, and test accuracy on profits. That is, the shadow price for testing measures the value testing an additional cow has on generating

profits. The value of testing rises with prevalence. However, the value of segregation decreases with prevalence.

The returns to test accuracy also decline with prevalence. The returns to test accuracy can be viewed as avoidance of unnecessary costs. The shadow price for a false positive measures the cost of a cow that is incorrectly identified as an S. aureus cow. The

Table 3

Baseline shadow prices calculated within the linear programming model: the imputed value or marginal

contribution to profits of S. aweus testing, segregation and test accuracy in a IOO-cow dairy herd

Prevalence

10% 20% 30%

Value of testing a cow (US$) 79 105 124

Value of segregating an infected cow (US@ 605 420 337

Cost of a true-positive cows (US$) 605 420 337

Cost of a false-positive cow (US$) 1450 1052 855

Cost of a false-negative cow (US$) 845 632 518

L. Zepeda et al./ Preventive Veterinary Medicine 33 (1998) 183-193 191

Table 4

Sensitivit,y analysis generated from the linear programming model: the difference in profits from the baseline

under each scenario in a lOO-cow dairy herd

Prevalence

10% (US$) 20% (US$) 30% WS$)

Profits generated in baseline modela - 920 - 152 -27b

Difference from baseline Milk Price: US$22.00/100 kg -22 -61 -83

US$30.80/100 kg 23 61 83

Dry treatment: US$25/25% 439 589 1027

US$150/75% - 293 -383 -685

RHA: 6363 kg/cow - 155 -425 -575

10,909 kg/cow 156 425 574

SCC premium: 10 cents - 292 -806 - 1099

30 cents - 307 806 0

aBaseline assumptions are US$26.40/100 kg milk, RHA 8636 kg, SCC premium of 20 cents, and dry

treatment that costs US$lOO and has a 50% cure rate; other scenarios change only one assumption at a time.

bSolutions in bold are Strategy 2 (repeated 4-quarter composite sample cultured separately at beginning of

year), all others are Strategy 1 (repeated 4-quarter composite sample pooled and cultured at beginning of year).

shadow price for a false negative measures the cost of an S. aureus cow that is not

identified. The shadow price for a true positive measures the cost of an S. aureus cow

that is correctly identified. Since the cost per cow of falsely identified S. uureus is inversely related to prevalence, owners of lower prevalence herds have greater incen-

tives to utilize a more accurate test. Note also that a false positive is much more costly than a false negative; it has nearly twice the impact on profits as a true positive.

3.2. Sensitivity analyses

Milk. price has little impact on the results of the model (Table 41, because milk yield is only a small part of the returns from the testing-and-control program. Changing dry

treatment to the low-cost, low cure-rate regimen increases profits and prevalence, while the high-cost, high cure-rate dry treatment decreases profits and prevalence. The higher

the prevalence, the bigger the impact of dry treatment on profits. Varying the RHA to

6363 and 10,909 kg has little impact at 10, 20, and 30% prevalence. In contrast, SCC premium has a large effect on profits, and its impact increases with prevalence.

4. Discussion

A linear programming model was used to calculate the returns to an S. aureus

testing-and-control program after one year. Since it can be expected that additional profits will be generated in subsequent years from the lower prevalence of S. aureus

resulting from the testing and control program, these results are conservative estimates. Future research might include a multiyear model that recognizes subsequent benefits.

192 L. Zepeda et al./Preuentive Veterinary Medicine 33 (1998) 183-193

One consequence of the single-year model is that Test 6 is always chosen at the end of the year because it is the cheapest test (the benefits to this second test (e.g., lower SCC) would not occur until year 2 so are not available in year 1 to offset costs in year 1).

Although the RCSCS test costs nearly twice as much as the RCSPC test, it increases

sensitivity by only 5%. It is only the best strategy when the cost of S. aureu~ is high. That is, the added sensitivity of using the RCSCS test is profitable only for high prevalence, and when the premium for a low SCC is high.

The RQSPC, RQSCS, and QSCO tests are never selected because they are too expensive relative to the added benefits of higher sensitivity. Composite samples are cheaper, less labor-intensive, and more likely to be implemented in the field. Clearly, the

returns of quarter samples do not justify their use; the added cost of somewhat higher sensitivity does not pay. However, the shadow prices indicate that specificity can have an important effect on the profit of a S. aureus control program (Table 3). A false-positive cow is nearly twice as costly as a true-positive. This suggests that tests to

identify S. aureu~ IMIs should have a high and consistent specificity. The repetition of tests after one year is the key to the testing-and-control strategy

because without a second test, it is not possible to identify the appropriate cows for

culling and treatment. A second test is needed to identify any new infections. Even with segregation, some transmission can occur (depending on the false-negative rate of the

test used). Without the second test, one would not be able to identify new infections and make appropriate decisions about culling versus treatment (the 2 control options at the end of the year). At each prevalence level examined by the LP model, more rigorous dry-cow therapy is part of the optimal strategy (versus routine dry-cow treatment) to control S. aureus IMI because of the higher cure rate resulting in a further reduction in prevalence. However, incorrect culling decisions can be very costly as shown by the fact that the LP program always selected dry-treatment and never selected culling (culling above the number normally culled for S. aureus) as an option for a profit-maximizing

solution. A testing-and-control program can be profitable within one year and also prevent unnecessary costs associated with incorrect culling versus treatment decisions.

The decrease in SCC from the testing-and-control program is the major factor influencing profits with respect to the testing-and-control program. S. aureus causes chronic mastitis and high SCCs. SCC premium is the largest source of profit from the program and is the clearest out-of-pocket cost to a dairy farmer because it is a line item in the milk check from the processing plant.

At each prevalence examined by the LP model, segregation (versus not segregating) is part of the optimal strategy to control S. aureus mastitis because of the reduced transmission rate resulting in a reduced prevalence rate. Segregation can be quite practical in a parlor herd that can be milked by cow group or string and the S. aureus can be milked last or in a stanchion or tie-stall barn where cows can be milked last with a dedicated milking unit. Segregation does not preclude standard post-dipping practices and milking cows with gloves to reduce the spread of S. aureus from false-negative cows. This result is in agreement with a recent study involving 76 herds which concluded that segregation of cows known to be positive for S. aureus reduced prevalence from 29.5 to 16.3% in segregated herds versus 22.5 to 20.2% in nonsegre- gated herds within 6 to 24 months (Wilson et al., 1995).

L. Zepeda et al. /Preventive Veterinary Medicine 33 (19981 183-193 193

We are assuming that with no testing-and-control program, the herd would be no

worse off than it is currently with respect to herd prevalence; this is because S. aureus

cows would be culled as they become chronic and are no longer profitable to have in the herd. Culling in the context of this paper is used as a method to simplify a complex shift of cow inventories at the beginning of the year and at the end of the year of the

testing-and-control program. This is done by maintaining steady-state prevalence in the herds without a testing-and-control program and establishing a point from which to assess the benefit of segregating and/or rigorously treating cows in the testing-and-con- trol program herds. This would not be a realistic culling strategy for a dairy farm operator; we have assumed (for simplicity) cause-specific culling, whereas several criteria are reviewed when one culls a S. aureus cow; thus, it is a complex decision. S. aweus cows may be culled for low production, a market with high cull prices, high

number of heifers available on-farm, and poor reproductive efficiency. In conclusion, the benefits of a control program are most dependent upon prevalence,

SCC premium, and dry-treatment cost. Milk yield and milk price have minimal impact on net returns. For our simulation lOO-cow herd, a testing-and-control program appears to cost less than US$lO per cow or even pays for itself within one year under all

circumstances considered, except under the lowest prevalence with the most adverse conditions (low yield, high cost of treatment, or low SCC premium). The next step in this research would be to validate the results of this model in a field study using actual

farm data.

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