As mentioned before, we assumed that the main route of MAP transmission in the calf population is the through the general environment. Although there are some studies that consider MAP transmission from transient shedders to susceptible calves, we assumed that the number of calf-to-calf transmission in pen 1 is negligible. Furthermore, since the calf population is separated from the heifer and adult populations, the adult-to-calf transmission rates are considered zero. As suggested in [15, 38, 43], we assumed that a portion between zero to 15% of newborn calves become infected in the fresh/hospital, maternity and calving pens . To calculate βG in the calf population we used the values given in columns 2 and 3 of Table 1 in [37] for βG in heifer population was estimated based on the total number of heifers that tested positive for MAP by fecal culture . The upper range was calculated by dividing the number of test positive heifers, 3 to 24 months of age by the total number tested [~32/1266 = 0.0256]. The estimate was assumed to be the highest annual percentage of infected heifers since it spanned a range of 12 to 21 months of follow up and for βG in the adult population we used the range considered in [8]. The infectious cattle transmission rate βI in the heifer population is adopted from [8]. However, βI in the adult population is calculated from the values provided in columns 3 and 4 of Table 2 in [30]. The value of βC in the calf and heifer population is considered zero due to the fact that the super-shedders are only considered in the adult population. The ranges of stage durations 1/σL, 1/σI and 1/σC are mainly adopted from the previous studies.
The average shedding rate of infectious cattle in the heifer and adult population is obtained from our clinical study and the work by Bolton et al.. Duration of pathogen survival is considered the same for all pens. We therefore considered a range of 0.8 to 1.5 year as suggested by Magonbedze et al.. Pathogen transmission rate from pen environments to the general environment may vary based on the age group due to the amount of manure produced by each age group. We assumed larger values for adult populations compared to heifer and calf populations. The animal removal rates vary from farm to farm, rolling tables but it is known that the rates are higher in the calf and heifer populations. We adopted the same range of values used in [36]. Historical computerized dairy farm records with information on cattle IDs in each of the farms’ pens were obtained with the herd veterinarians’ and farm owners’ permission and no animals were enrolled for the purpose of the current study.Dairy herd movement records exported from each study herd included cow identification numbers, date of record and pen location in Table A , for a snapshot of the dairy farm data from 2011 to 2015. Some dairies had intervals of missing data for one or more pens, the latter could be due to the dairy management not utilizing such a pen or pens, or simply due to missing backups at regular intervals. The missing data was removed from the study. As summarized in Table 4, the cattle movement data of four dairy farms were used in this study. Farm 1 contributed records from 01/07/11 through 04/10/15 with data missing during the change of its breed make up between 02/01/12 through 12/31/13 interval resulting in herds 1 and 1 of Holsteins and Holstein Jersey mix breeds, respectively.
Particularly, we divided the data of Farm1 into two parts and excluded the interval with missing data. Farm 2 had pen residence records from 01/07/11 through 05/26/15. At the pen level, both Farm 1 and Farm 2 had data on cows residing in pens 1 through 13, but not pen 14 due to the transitory nature of cows moved into the maternity pen at calving only. Farm 3 contributed data from 06/15/13 through 05/13/15 on cow movements between pens 2, 3, 4, 7, . . ., 13 with no data recorded from pens 1, 5, and 14. Farm 4 records were the most completely recorded data for the herd of 4,604 cows. The data was complete for the period from 01/18/11 through 06/02/15 and it includes cow movement data for pens 1 through 14. Farms 1 and 2 have substantially higher numbers of cows than the other farms. Using Matlab optimization toolbox the CM model was fitted to the movement data of each farm. The model fitting resulted the estimated rates of moving cows between pens on 4 dairy farms. These di,j rates are presented in Table B . Tables D and E summarize the number of observations and the number of between-pen movements for all farms, respectively .In summary, serum ELISA test and cull is the most effective single control measure in reducing MAP infection. By far the best outcome is obtained by combining three control measures of test and cull, cleaning, and isolating calves and heifers from the herd. The risk of MAP occurrence was calculated by dividing the number of iterations with R0 greater than one by total number of iterations that R0 has been calculated. When we compare the no control option versus all combined control strategies, the risk of MAP occurrence in dairy cattle drops from 82% to 42% and the mean R0 value drops from 3.92 to 0.89. Although this demonstrates a very effective approach to JD management on a dairy farm, it reveals that the MAP occurrence risk is not eliminated even though that all control measures are simultaneously applied. Despite 42% risk of MAP occurrence, simulations of a MAP infected herd showed that employing all control measures reduced mean prevalence of MAP below 0.02% in calves and heifers, and mean prevalence in adult cows of 1.05% over ten years. Hence complete eradication of MAP was not possible, despite the fact that the prevalence and incidence of MAP were extremely low in the window of ten years. Table 5 summarizes results of the NC model simulations assuming that each control measure separately applied to a dairy farm. S1 Fig depicts the distributions of R0 values. In each panel, the curve represents the fitted generalized extreme value distribution. See Table F for the estimated sigma and mean values. In the absence of any control measures, identified as Control 0 in Table 5, the mean R0 value was 3.92 and with a long tail in the frequency plot such that it exceeded R0 = 20. The numerical simulations indicated that none of the controls were individually effective and hence they each failed to reduce the mean R0 values to below 1. In this regard, the top three measures were controls 4b, 3 and 4a with the mean R0 values of 1.31, 1.51, and 2.11, respectively. Table 6 summarizes statistics of R0 values for MAP transmission under all possible binary combinations of the control measures. Also, S2 and S3 Figs shows the related R0 distributions. Although the mean R0 values was reduced from 3.92 to 3.85 but the combination of controls 1 and 2 were not successful in reducing the risk of infection and hence MAP transmission. Control measure 4a, cannabis grower supplies weekly test and cull of cows at dry-off , and 4b, annual test and cull of adult cows made up the most effective binary combination control measure, while a combination of Control 3 with Control 4a or 4b was the second most effective combination control measure. Nevertheless, none of these binary combinations reduced the mean R0 value below one.
However, as shown in Table 6 the risk significantly dropped in the cases in which test and cull was combined with a control measure other than controls 1 or 2 . In the best case scenario, the risk of MAP occurrence decreased from 81% to 47% . Also, in all cases the mean R0 value was greater than 1, which indicates that JD will gradually spread in the herd. Although risk of MAP infection decreased with triple and all control measures, the risk was not eliminated and remained non-zero. In particular, as shown in Table 7, the risk of MAP infection decreased from 81% to 42% and the mean R0 value decreased from 3.92 to 0.89. From the most effective to the least, the combined measures with mean R0 values less than 1 are controls All, , , and , with mean R0 values of 0.898, 0.94, 0.95, and 0.97, respectively . Hence, on average, a farm that employs all control measures, or a combination of the three control measures should remain or gradually become disease free. However, there is still more than 40% risk of MAP infection remaining in the herd. In a similar manner, prevalence and incidence of MAP infection were estimated based on simulations for applying single control measures. Fig 6 represents the asymptotic behavior of MAP infection prevalence and incidence in a dairy farm. Namely, the curves were obtained by taking the mean values of 50,000 NC model simulations for a long period of time . For each simulation, a super shedder and an infected cow are initially introduced to the herd. It can be seen that control 4b was the most successful method in the population of adult cows. Control 3 could effectively slow down the increase of incidence and prevalence in calf and heifer populations. It should also be noted that control 5, which was designed for delaying the exposure of calves and heifers to infected cows, was the most effective method in the calf and heifer population to keep both prevalence and incidence low. This is despite the fact that control 5 had a poor efficacy of 81% risk of MAP occurrence . Details of the asymptotic values associated with the single measures can be found in Table F . Further simulations indicated that a combination of test and cull with control 1 did not reduce the incidence and prevalence in the calf and heifer populations due to the fact that test and cull is rarely applied to calf and heifer pens. We also calculated the range of the mean prevalence and incidence estimates in a practical time period using 50,000 NC model simulations. These values are presented in Table 8, where control 5 is still the best control measure in the population of calves and heifers. In the population of adult cows there was no single control measure, which was superior to all other measures. Hence, we investigated the prevalence and the incidence for the cases that more than one measure was employed. Namely, the results of combined control measures are presented in Table 9 showing that the mean prevalence and incidence estimates were substantially less in the calf and heifer populations. Moreover, the binary controls 3 and 4 are ineffective in calf and heifer populations, but they are effective in adult populations. NC model simulations for calves and heifer populations with the combination of double control measures 1 & 5, 2 & 5, 3 & 5, 5 & 4a, 5 & 4b , result in prevalence estimates below 0.01% , which is an important result that a disease-free herd can remain disease free, under two assumptions. First, extremely low number of infectious cow or supper shedder are accidently introduced to the herd. Second, a combination of the above-mentioned control measures is strictly implemented. A common control measure among these effective combinations is control measure 5 under which calves are born and raised in uninfected herds delaying to exposure to infected cattle. Despite being a different scenario, such Estimates may serve as a conservative scenario resulting in a prevalence of 0.008% estimated in the heifer population, making it the most effective measure in this age group. The next most effective control measure in calves and heifers were combinations with controls 2 resulting in a prevalence of 0.07% . All of these combinations included control 2 where exposure of calves to MAP infection is avoided starting at birth by relocated them off-site before being returned to their source herd as springers. Although the offsite nursery prevents contact between the calves and adult cattle, the environment in the off-site nursery pens may be contaminated by lagoon water in case of recycling flush water; and therefore, a mean of 0.07% prevalence is expected. Nevertheless, the simulations suggested that control 2 was the second best measure to reduce the JD prevalence in the calf and heifer populations.