We used the iCull PTB simulation model, which is a bio-economic model that simulates a dairy farm using single-day time steps [15]. The model simulates a farm with 200 dairy cows, corresponding to a medium-sized Danish dairy herd. The model is a mechanistic, stochastic simulation model that simulated the individual cows in great detail, e.g. with individual lactation curves and SCC curves based on data. The iCull PTB model runs in daily time steps. Animals enter the herd as calves, are reared as heifers and later milked as cows. The farmer takes weekly decisions on which cows to cull if there are more than 200 cows present in the herd, thus keeping the number of cows stable [15]. In this study, we simulated that the farmer purchased one, five or ten pregnant heifers per year. We simulated both a situation where the farmer had a single supplier of animals, and a situation where the farmer bought from multiple suppliers (see description below). Within the model, cows feed, lactate and are inseminated and dried off as in a real herd. In the model, two thirds of culled animals are culled involuntarily due to diseases (such as lameness and mastitis) or acute injuries. This means that the farmer can make decisions for one third of the culled animals, thus resembling a real farm.

The model simulated spread of MAP between animals through the environment: bacteria are shed by infected animals every day. Accumulated bacteria followed a survival curve estimated from data. The probability of infection from the environment is based on the amount of bacteria present in the farm section where each animal is located. Additionally, animals can be infected in utero, through colostrum and waste milk [15]. If no new animals are infected from the environment or other transmission routes, disease fadeout occurs. We here defined fadeout as a permanent situation where no new animals were infected during the simulations. However, MAP bacteria can still be present in the environment for some time without infecting new animals.

The purchases were evenly spread over the year. We simulated purchases of pregnant heifers from other farms, which is a common practice in Denmark and other countries such as France [16]. Purchased pregnant heifers were introduced into the heifer section of the housing. The number of days remaining before calving was randomly drawn from a uniform distribution between 42 and 280 days after insemination. In this study, we assume that the risk of infection from an animal bought from a supplier herd is the same as the prevalence in the supplier herd, resembling that the pregnant heifer came from another farm. In Denmark, it is common for farmers to trade animals directly or through a cattle market. The probability of infection in the purchased animals was modeled according to each scenario (see below). All other properties of the purchased heifers were generated from the same distributions used in the model by [15]. In this study, we simulated for 10 years and repeated the stochastic simulations 500 times, which was previously found to be appropriate for convergence [15]. In this study, no control actions against the spread of MAP were simulated.

### Open herd scenarios

We simulated a herd with a stable herd size of 200 cows and a steady prevalence of either 0% or 5.6%. A 10-year period was chosen for this study, though it should be noted that an increase in infection prevalence or an introduction of MAP would have consequences spanning more than 10 years if no control or eradication measures were implemented. All purchased animals were pregnant heifers, as this is common practice in Denmark.

The model simulates a reduced milk production in the subclinical phase [15]. If there are infected animals in the herd, they are culled when they are detected, preventing the farmer from automatically culling the lowest producing animals. Thus the model captures that low producing cows are kept in the herd for longer time than normal. The economic calculations did not include salary for personnel or expenses such as machines and housing. Neither did we include changes in the feed conversion ratio of infected animals or potential consequences for trade. The model simulates other expenses like insemination (16.1 EUR), feed (0.133 EUR per feed unit) and the destruction of dead animals (64.8 EUR) [15]. The price of a pregnant heifer was set to EUR 1275 [17]. Each milk-ELISA cost 5.3 EUR [15].

In the simulations, the farmer could buy cattle from random herds with unknown probability of infection, or from herds certified with a low, medium or high probability of infection. We used the true within-herd prevalence in Danish herds based on [15] as the probability that a purchased animal from a given farm was infected. Therefore, in the scenarios where random suppliers were used, the probability of infection in the purchased animals was sampled from the empirical distribution of true prevalence found in 102 tested Danish herds. We also simulated three risk levels when purchasing animals: low risk, medium risk and high risk. Low risk animals had 0% to 5% probability of being infected at purchase. Medium risk animals had 5% to 15% probability of being infected, and high risk animals had 15% to 45% probability of being infected at purchase. These intervals were chosen based on the empirical distribution of within-herd prevalence in Denmark [15]. For each purchase, the probability of infection from the herd of origin was drawn from a uniform distribution between the numbers given for the risk levels described above. Whether the purchased animal was infected or not was then decided using a binomial distribution based on this probability. This resembles that a farmer purchase from a farm with a given risk level where the animal has a probability of being infected. We simulated both scenarios where the farmer purchased from a single supplier and from multiple suppliers. If multiple suppliers were used, the probability of infection in each purchased cow was redrawn from the respective distribution (described above) for every purchase.

The number of cattle purchased annually is likely to have an impact on the prevalence and thus on the economic output. We therefore simulated scenarios where farmers purchased one, five or ten animals per year. We also evaluated the impact of using single or multiple suppliers. For this purpose, we used a dataset with the number of suppliers for 19,056 Danish dairy herds registered between 01 March 2014 and 28 February 2015. Of these herds, 19,015 used fewer than 50 suppliers in that year (Fig. 1). In the scenario where multiple suppliers were used, we sampled from the empirical distribution of the number of suppliers for each farm. However, we limited the number to a maximum of 50 suppliers since we presumed that farms with more than 50 suppliers were not dairy farms. In practice, however, the maximum number of possible suppliers was ten because in this study the farmer bought either one, five or ten animals per year.

We simulated all combinations of scenarios with random, low, medium or high-risk purchases of one, five or ten heifers per year from single and multiple suppliers. All simulations included a burn-in period of 3 years and thereafter we simulated for 10 years.

### Infection fadeout

Infection fadeout is when the farm becomes free of MAP infections. It is important to estimate the probability of infection fadeout in order to make informed decisions on factors such as the implementation of disease control actions. In order to estimate the probability of infection fadeout in a herd, we simulated an initially disease-free herd under different scenarios where MAP infection was introduced. We first wanted to estimate the probability of infection fadeout in a farm without MAP, where the farmer bought one to ten infected animals in the first year only. These simulations were run for 10 years in order to estimate the probability of infection fadeout over time. The probability of infection fadeout was calculated from 500 simulations.

We then wanted to estimate the probability of disease fadeout when the farmer of an initially MAP-free herd consistently bought one to ten animals per year. This was achieved by running simulations where the farmer bought a fixed number of animals per year with a 100% probability of infection. We then calculated what percentage of the 500 simulations resulted in a fadeout of disease after 1 to 10 simulated years.

### Model updates

We used the iCull PTB model version 9.1 in this study [15]. This model included monthly milk testing in order to observe the milk yield for each cow, which was updated from an earlier version that used quarterly testing. The observed milk production is affected by the infection status [18] and as a result, the farmer would be more likely to cull infected cows with a lower milk yield. Therefore, we readjusted the force of infection and the infection probability from colostrum and waste milk in the model (using the procedure as described in [15]), in order to obtain a steady prevalence in the herd. Therefore, a fundamental presumption is that the prevalence in the simulated herd is steady without any control actions.

We also updated the model with a standard lactation fitted to every cow so that the farmer could compare the observed milk yield with the expected milk yield. This allowed for a better estimate of the milk yield level, thus helping the farmer to prioritize cows with lower production for culling.