# American Institute of Mathematical Sciences

August  2017, 14(4): 1001-1017. doi: 10.3934/mbe.2017052

## Modeling environmental transmission of MAP infection in dairy cows

 1 Department of Mathematics, University of Peradeniya, Peradeniya, KY 20400, Sri Lanka 2 Department of Forestry, Wildlife and Fisheries, University of Tennessee, Knoxville, TN 37996, USA 3 Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA

* Corresponding author: Suzanne Lenhart

Received  March 20, 2016 Accepted  January 31, 2017 Published  February 2017

Fund Project: This work was partially supported by the National Institute for Mathematical Biological Synthesis, sponsored by the National Science Foundation Award NSF DBI-1300426.

Johne's disease is caused by Mycobacterium avium subspecies paratuberculosis(MAP). It is a chronic, progressive, and inflammatory disease which has a long incubation period. One main problem with the disease is the reduction of milk production in infected dairy cows. In our study we develop a system of ordinary differential equations to describe the dynamics of MAP infection in a dairy farm. This model includes the progression of the disease and the age structure of the cows. To investigate the effect of persistence of this bacteria on the farm on transmission in our model, we include environmental compartments, representing the pathogen input in an explicit way. The effect of indirect transmission from the bacteria in the environment and the culling of high-shedding adults can be seen in the numerical simulations. Since culling usually only happens once a year, we include a novel feature in the simulations with a discrete action of removing high-shedding adults once a year. We conclude that with culling of high shedders even at a high rate, the infection will persist in the modeled farm setting.

Citation: Kokum R. De Silva, Shigetoshi Eda, Suzanne Lenhart. Modeling environmental transmission of MAP infection in dairy cows. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1001-1017. doi: 10.3934/mbe.2017052
##### References:
 [1] D. J. Begg and R. J. Whittington, Experimental animal infection models for Johne's disease, an infectious enteropathy caused by Mycobacterium avium subsp. paratuberculosis, The Veterinary Journal, 176 (2008), 129-145.  doi: 10.1016/j.tvjl.2007.02.022. [2] R. Breban, Role of environmental persistence in pathogen transmission: A mathematical modeling approach, Journal of Mathematical Biology, 66 (2013), 535-546.  doi: 10.1007/s00285-012-0520-2. [3] K. L. Cook, J. S. Britt and C. H. Bolster, Survival of Mycobacterium avium subsp. paratuberculosis in biofilms on livestock watering trough materials, Veterinary Microbiology, 141 (2010), 103-109.  doi: 10.1016/j.vetmic.2009.08.013. [4] O. Diekmann, H. Heesterbeek and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynanics Princeton University Press, 2013. [5] O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, Journal of the Royal Society Interface, 7 (2010), 873-885.  doi: 10.1098/rsif.2009.0386. [6] E. Doré, J. Paré, G. Côté, S. Buczinski, O. Labrecque, J. P. Roy and G. Fecteau, Risk factors associated with transmission of Mycobacterium avium subsp. paratuberculosis to calves within dairy herd: A systematic review, Journal of Veterinary Internal Medicine, 26 (2012), 32-45.  doi: 10.1111/j.1939-1676.2011.00854.x. [7] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.  doi: 10.1016/S0025-5564(02)00108-6. [8] P. van den Driessche and J. Watmough, Further notes on the basic reproduction number, Mathematical Epidemiology, 1945 (2008), 159-178.  doi: 10.1007/978-3-540-78911-6_6. [9] L. A. Espejo, S. Godden, W. L. Hartmann and S. J. Wells, Reduction in incidence of Johne's disease associated with implementation of a disease control program in Minnesota demonstration herds, Journal of Dairy Science, 95 (2012), 4141-4152.  doi: 10.3168/jds.2011-4550. [10] A. B. Garcia and L. Shalloo, Invited review: The economic impact and control of paratuberculosis in cattle, Journal of Dairy Science, 98 (2015), 5019-5039.  doi: 10.3168/jds.2014-9241. [11] I. A. Gardner, S. S. Nielsen, R. J. Whittington, M. T. Collins, D. Bakker, B. Harris, S. Sreevatsan, J. E. Lombard, R. Sweeney, D. R. Smith, J. Gavalchin and S. Eda, Consensus-based reporting standards for diagnostic test accuracy studies for paratuberculosis in ruminants, Preventive Veterinary Medicine, 101 (2011), 18-34.  doi: 10.1016/j.prevetmed.2011.04.002. [12] G. F. Gerlach, Paratuberculosis: the pathogen and routes of infection, Dtsch Tierarztl Wochenschr, 109 (2002), 504-506. [13] R. W. Humphry, A. W. Stott, C. Adams and G. J. Gunn, A model of the relationship between the epidemiology of Johne's disease and the environment in suckler-beef herds, The Veterinary Journal, 172 (2006), 432-445.  doi: 10.1016/j.tvjl.2005.07.017. [14] Z. Lu, R. M. Mitchell, R. L. Smith, J. S. Van Kessel, P. P. Chapagain, Y. H. Schukken and Y. T. Gröhn, The importance of culling in Johne's disease control, Journal of Theoretical Biology, 254 (2008), 135-146.  doi: 10.1016/j.jtbi.2008.05.008. [15] C. Marcé, P. Ezanno, M. F. Weber, H. Seegers, D. U. Pfeiffer and C. Fourichon, Invited review: Modeling within-herd transmission of Mycobacterium avium subspecies paratuberculosis in dairy cattle: A review, Journal of Dairy Science, 93 (2010), 4455-4470.  doi: 10.3168/jds.2010-3139. [16] C. Marcé, P. Ezanno, H. Seegers, D. U. Pfeiffer and C. Fourichon, Predicting fadeout versus persistence of paratuberculosis in a dairy cattle herd for management and control purposes: a modelling study, Preventive Veterinary Medicine, 42 (2011), p36.  doi: 10.1186/1297-9716-42-36. [17] C. Marcé, P. Ezanno, H. Seegers, D. U. Pfeiffer and C. Fourichon, Within-herd contact structure and transmission of Mycobacterium avium subspecies paratuberculosis in a persistently infected dairy cattle herd, Preventive Veterinary Medicine, 100 (2011), 116-125.  doi: 10.1016/j.prevetmed.2011.02.004. [18] T. Massaro, S. Lenhart, M. Spence, C. Drakes, G. Yang, F. Agusto, R. Johnson, B. Whitlock, A. Wadhwa and S. Eda, Modeling for cost analysis of Johne's disease control based on EVELISA testing, Journal of Biological Systems, 21 (2013), 1340010.  doi: 10.1142/S021833901340010X. [19] R. M. Mitchell, G. F. Medley, M. T. Collins and Y. H. Schukken, A meta-analysis of the effect of dose and age at exposure on shedding of Mycobacterium avium subsp. paratuberculosis (MAP) in experimentally infected calves and cows, Epidemiology and Infection, 140 (2012), 231-246.  doi: 10.1017/S0950268811000689. [20] R. M. Mitchell, Y. Schukken, A. Koets, M. Weber, D. Bakker, J. Stabel, R. H. Whitlock and Y. Louzoun, Differences in intermittent and continuous fecal shedding patterns between natural and experimental Mycobacterium avium subsp. paratuberculosis infections in cattle, Veterinary Research, 46 (2015), p66.  doi: 10.1186/s13567-015-0188-x. [21] R. A. Mortier, H. W. Barkema, T. A. Wilson, T. T. Sajobi, R. Wolf and J. De Buck, Dose-dependent interferon-gamma release in dairy calves experimentally infected with Mycobacterium avium subsp. paratuberculosis, Veterinary Immunology and Immunopathology, 161 (2014), 205-210.  doi: 10.1016/j.vetimm.2014.08.007. [22] S. L. Ott, S. J. Wells and B. A. Wagner, Herd-level economic losses associated with Johne's disease on US dairy operations, Preventive Veterinary Medicine, 40 (1999), 179-192.  doi: 10.1016/S0167-5877(99)00037-9. [23] E. A. Raizman, J. Fetrow, S. J. Wells, S. M. Godden, M. J. Oakes and G. Vazquez, The association between Mycobacterium avium subsp. paratuberculosis fecal shedding or clinical \textrm{Johne's} disease and lactation performance on two Minnesota, USA dairy farms, Preventive veterinary medicine, 78 (2007), 179-195.  doi: 10.1016/j.prevetmed.2006.10.006. [24] J. Robins, S. Bogen, A. Francis, A. Westhoek, A. Kanarek, S. Lenhart and S. Eda, Agent-based model for Johne's disease dynamics in a dairy herd, Veterinary Research, 46 (2015), p68.  doi: 10.1186/s13567-015-0195-y. [25] H. J. W. van Roermund, D. Bakker, P. T. J. Willemsen and M. C. M. de Jong, Horizontal transmission of Mycobacterium avium subsp. paratuberculosis in cattle in an experimental setting: Calves can transmit the infection to other calves, Veterinary Microbiology, 122 (2007), 270-279.  doi: 10.1016/j.vetmic.2007.01.016. [26] A. M. Scanu, T. J. Bull, S. Cannas, J. D. Sanderson, L. A. Sechi, G. Dettori, S. Zanetti and J. H. Taylor, Mycobacterium avium subspecies paratuberculosis infection in cases of irritable bowel syndrome and comparison with Crohn's disease and Johne's disease: Common neural and immune pathogenicities, Journal of Clinical Microbiology, 45 (2007), 3883-3890.  doi: 10.1128/JCM.01371-07. [27] M. C. Scott, J. P. Bannantine, Y. Kaneko, A. J. Branscum, R. H. Whitlock, Y. Mori, C. A. Speer and S. Eda, Absorbed EVELISA: A diagnostic test with improved specificity for Johne's disease in cattle, Foodborne Pathogens and Disease, 7 (2010), 1291-1296.  doi: 10.1089/fpd.2010.0541. [28] S. Singh and K. Gopinath, Mycobacterium avium subspecies paratuberculosis and Crohn's regional ileitis: How strong is association?, Journal of Laboratory Physicians, 3 (2011), 69-74.  doi: 10.4103/0974-2727.86836. [29] R. L. Smith, Y. T. Gröhn, A. K. Pradhan, R. H. Whitlock, J. S. Van Kessel, J. M. Smith, D. R. Wolfgang and Y. H. Schukken, The effects of progressing and nonprogressing Mycobacterium avium subsp. paratuberculosis infection on milk production in dairy cows, Journal of Dairy Science, 99 (2016), 1383-1390.  doi: 10.3168/jds.2015-9822. [30] J. H. Taylor, Review Mycobacterium avium subspecies paratuberculosis, Crohn's disease and the doomsday scenario, Gut Pathogens, 1 (2009), p15.  doi: 10.1186/1757-4749-1-15. [31] R. H. Whitlock, R. W. Sweeney, T. L. Fyock and J. Smith, MAP supershedders: Another factor in the control of Johne's disease, In Proceedings of the 8th International Colloquium on Paratuberculosis}(2005). [32] R. J. Whittington, I. B. Marsh and L. A. Reddacliff, Survival of Mycobacterium avium subsp. paratuberculosis in dam water and sediment, Applied and Environmental Microbiology, 71 (2005), 5304-5308.  doi: 10.1128/AEM.71.9.5304-5308.2005. [33] R. J. Whittington and P. A. Windsor, In utero infection of cattle with Mycobacterium avium subsp. paratuberculosis: A critical review and meta-analysis, The Veterinary Journal, 179 (2009), 60-69.  doi: 10.1016/j.tvjl.2007.08.023. [34] M. Bani-Yaghoub, R. Gautam, Z. Shuai, P. van den Driessche and R. Ivanek, Reproduction numbers for infections with free-living pathogens growing in the environment, Journal of Biological Dynamics, 6 (2012), 923-940.  doi: 10.1080/17513758.2012.693206. [35] USDA. Johne's Disease on U. S. Dairies, 1991-2007, Fort Collins, CO, USA, NAHMS USDA-APHIS-VS-CEAH [36] Cow in and out game http://fergusonfoundation.org/lessons/cow_in_out/cowmoreinfo.shtml, Alice Ferguson Foundation, 2012.

show all references

##### References:
 [1] D. J. Begg and R. J. Whittington, Experimental animal infection models for Johne's disease, an infectious enteropathy caused by Mycobacterium avium subsp. paratuberculosis, The Veterinary Journal, 176 (2008), 129-145.  doi: 10.1016/j.tvjl.2007.02.022. [2] R. Breban, Role of environmental persistence in pathogen transmission: A mathematical modeling approach, Journal of Mathematical Biology, 66 (2013), 535-546.  doi: 10.1007/s00285-012-0520-2. [3] K. L. Cook, J. S. Britt and C. H. Bolster, Survival of Mycobacterium avium subsp. paratuberculosis in biofilms on livestock watering trough materials, Veterinary Microbiology, 141 (2010), 103-109.  doi: 10.1016/j.vetmic.2009.08.013. [4] O. Diekmann, H. Heesterbeek and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynanics Princeton University Press, 2013. [5] O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, Journal of the Royal Society Interface, 7 (2010), 873-885.  doi: 10.1098/rsif.2009.0386. [6] E. Doré, J. Paré, G. Côté, S. Buczinski, O. Labrecque, J. P. Roy and G. Fecteau, Risk factors associated with transmission of Mycobacterium avium subsp. paratuberculosis to calves within dairy herd: A systematic review, Journal of Veterinary Internal Medicine, 26 (2012), 32-45.  doi: 10.1111/j.1939-1676.2011.00854.x. [7] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.  doi: 10.1016/S0025-5564(02)00108-6. [8] P. van den Driessche and J. Watmough, Further notes on the basic reproduction number, Mathematical Epidemiology, 1945 (2008), 159-178.  doi: 10.1007/978-3-540-78911-6_6. [9] L. A. Espejo, S. Godden, W. L. Hartmann and S. J. Wells, Reduction in incidence of Johne's disease associated with implementation of a disease control program in Minnesota demonstration herds, Journal of Dairy Science, 95 (2012), 4141-4152.  doi: 10.3168/jds.2011-4550. [10] A. B. Garcia and L. Shalloo, Invited review: The economic impact and control of paratuberculosis in cattle, Journal of Dairy Science, 98 (2015), 5019-5039.  doi: 10.3168/jds.2014-9241. [11] I. A. Gardner, S. S. Nielsen, R. J. Whittington, M. T. Collins, D. Bakker, B. Harris, S. Sreevatsan, J. E. Lombard, R. Sweeney, D. R. Smith, J. Gavalchin and S. Eda, Consensus-based reporting standards for diagnostic test accuracy studies for paratuberculosis in ruminants, Preventive Veterinary Medicine, 101 (2011), 18-34.  doi: 10.1016/j.prevetmed.2011.04.002. [12] G. F. Gerlach, Paratuberculosis: the pathogen and routes of infection, Dtsch Tierarztl Wochenschr, 109 (2002), 504-506. [13] R. W. Humphry, A. W. Stott, C. Adams and G. J. Gunn, A model of the relationship between the epidemiology of Johne's disease and the environment in suckler-beef herds, The Veterinary Journal, 172 (2006), 432-445.  doi: 10.1016/j.tvjl.2005.07.017. [14] Z. Lu, R. M. Mitchell, R. L. Smith, J. S. Van Kessel, P. P. Chapagain, Y. H. Schukken and Y. T. Gröhn, The importance of culling in Johne's disease control, Journal of Theoretical Biology, 254 (2008), 135-146.  doi: 10.1016/j.jtbi.2008.05.008. [15] C. Marcé, P. Ezanno, M. F. Weber, H. Seegers, D. U. Pfeiffer and C. Fourichon, Invited review: Modeling within-herd transmission of Mycobacterium avium subspecies paratuberculosis in dairy cattle: A review, Journal of Dairy Science, 93 (2010), 4455-4470.  doi: 10.3168/jds.2010-3139. [16] C. Marcé, P. Ezanno, H. Seegers, D. U. Pfeiffer and C. Fourichon, Predicting fadeout versus persistence of paratuberculosis in a dairy cattle herd for management and control purposes: a modelling study, Preventive Veterinary Medicine, 42 (2011), p36.  doi: 10.1186/1297-9716-42-36. [17] C. Marcé, P. Ezanno, H. Seegers, D. U. Pfeiffer and C. Fourichon, Within-herd contact structure and transmission of Mycobacterium avium subspecies paratuberculosis in a persistently infected dairy cattle herd, Preventive Veterinary Medicine, 100 (2011), 116-125.  doi: 10.1016/j.prevetmed.2011.02.004. [18] T. Massaro, S. Lenhart, M. Spence, C. Drakes, G. Yang, F. Agusto, R. Johnson, B. Whitlock, A. Wadhwa and S. Eda, Modeling for cost analysis of Johne's disease control based on EVELISA testing, Journal of Biological Systems, 21 (2013), 1340010.  doi: 10.1142/S021833901340010X. [19] R. M. Mitchell, G. F. Medley, M. T. Collins and Y. H. Schukken, A meta-analysis of the effect of dose and age at exposure on shedding of Mycobacterium avium subsp. paratuberculosis (MAP) in experimentally infected calves and cows, Epidemiology and Infection, 140 (2012), 231-246.  doi: 10.1017/S0950268811000689. [20] R. M. Mitchell, Y. Schukken, A. Koets, M. Weber, D. Bakker, J. Stabel, R. H. Whitlock and Y. Louzoun, Differences in intermittent and continuous fecal shedding patterns between natural and experimental Mycobacterium avium subsp. paratuberculosis infections in cattle, Veterinary Research, 46 (2015), p66.  doi: 10.1186/s13567-015-0188-x. [21] R. A. Mortier, H. W. Barkema, T. A. Wilson, T. T. Sajobi, R. Wolf and J. De Buck, Dose-dependent interferon-gamma release in dairy calves experimentally infected with Mycobacterium avium subsp. paratuberculosis, Veterinary Immunology and Immunopathology, 161 (2014), 205-210.  doi: 10.1016/j.vetimm.2014.08.007. [22] S. L. Ott, S. J. Wells and B. A. Wagner, Herd-level economic losses associated with Johne's disease on US dairy operations, Preventive Veterinary Medicine, 40 (1999), 179-192.  doi: 10.1016/S0167-5877(99)00037-9. [23] E. A. Raizman, J. Fetrow, S. J. Wells, S. M. Godden, M. J. Oakes and G. Vazquez, The association between Mycobacterium avium subsp. paratuberculosis fecal shedding or clinical \textrm{Johne's} disease and lactation performance on two Minnesota, USA dairy farms, Preventive veterinary medicine, 78 (2007), 179-195.  doi: 10.1016/j.prevetmed.2006.10.006. [24] J. Robins, S. Bogen, A. Francis, A. Westhoek, A. Kanarek, S. Lenhart and S. Eda, Agent-based model for Johne's disease dynamics in a dairy herd, Veterinary Research, 46 (2015), p68.  doi: 10.1186/s13567-015-0195-y. [25] H. J. W. van Roermund, D. Bakker, P. T. J. Willemsen and M. C. M. de Jong, Horizontal transmission of Mycobacterium avium subsp. paratuberculosis in cattle in an experimental setting: Calves can transmit the infection to other calves, Veterinary Microbiology, 122 (2007), 270-279.  doi: 10.1016/j.vetmic.2007.01.016. [26] A. M. Scanu, T. J. Bull, S. Cannas, J. D. Sanderson, L. A. Sechi, G. Dettori, S. Zanetti and J. H. Taylor, Mycobacterium avium subspecies paratuberculosis infection in cases of irritable bowel syndrome and comparison with Crohn's disease and Johne's disease: Common neural and immune pathogenicities, Journal of Clinical Microbiology, 45 (2007), 3883-3890.  doi: 10.1128/JCM.01371-07. [27] M. C. Scott, J. P. Bannantine, Y. Kaneko, A. J. Branscum, R. H. Whitlock, Y. Mori, C. A. Speer and S. Eda, Absorbed EVELISA: A diagnostic test with improved specificity for Johne's disease in cattle, Foodborne Pathogens and Disease, 7 (2010), 1291-1296.  doi: 10.1089/fpd.2010.0541. [28] S. Singh and K. Gopinath, Mycobacterium avium subspecies paratuberculosis and Crohn's regional ileitis: How strong is association?, Journal of Laboratory Physicians, 3 (2011), 69-74.  doi: 10.4103/0974-2727.86836. [29] R. L. Smith, Y. T. Gröhn, A. K. Pradhan, R. H. Whitlock, J. S. Van Kessel, J. M. Smith, D. R. Wolfgang and Y. H. Schukken, The effects of progressing and nonprogressing Mycobacterium avium subsp. paratuberculosis infection on milk production in dairy cows, Journal of Dairy Science, 99 (2016), 1383-1390.  doi: 10.3168/jds.2015-9822. [30] J. H. Taylor, Review Mycobacterium avium subspecies paratuberculosis, Crohn's disease and the doomsday scenario, Gut Pathogens, 1 (2009), p15.  doi: 10.1186/1757-4749-1-15. [31] R. H. Whitlock, R. W. Sweeney, T. L. Fyock and J. Smith, MAP supershedders: Another factor in the control of Johne's disease, In Proceedings of the 8th International Colloquium on Paratuberculosis}(2005). [32] R. J. Whittington, I. B. Marsh and L. A. Reddacliff, Survival of Mycobacterium avium subsp. paratuberculosis in dam water and sediment, Applied and Environmental Microbiology, 71 (2005), 5304-5308.  doi: 10.1128/AEM.71.9.5304-5308.2005. [33] R. J. Whittington and P. A. Windsor, In utero infection of cattle with Mycobacterium avium subsp. paratuberculosis: A critical review and meta-analysis, The Veterinary Journal, 179 (2009), 60-69.  doi: 10.1016/j.tvjl.2007.08.023. [34] M. Bani-Yaghoub, R. Gautam, Z. Shuai, P. van den Driessche and R. Ivanek, Reproduction numbers for infections with free-living pathogens growing in the environment, Journal of Biological Dynamics, 6 (2012), 923-940.  doi: 10.1080/17513758.2012.693206. [35] USDA. Johne's Disease on U. S. Dairies, 1991-2007, Fort Collins, CO, USA, NAHMS USDA-APHIS-VS-CEAH [36] Cow in and out game http://fergusonfoundation.org/lessons/cow_in_out/cowmoreinfo.shtml, Alice Ferguson Foundation, 2012.
Flow diagram of the transitions in our model (Sc, Sh, Sa -Susceptible calves, heifers, adults, Ec, Eh, Ea -Exposed calves, heifers, adults, Lh, La -Low shedding heifers, adults, Ha -High shedding adults, B1 -Bacteria in the heifer environment, B2 -Bacteria in the adult environment)
Environmental transmission coefficient $f(B)$ with $K_1 = 1000$ and $K_2 = 100$
Dynamics of the animals in each compartment with no testing or culling and with annual testing and culling
Dynamics of the total animals in each disease class with no testing or culling and with annual testing and culling
Number of exposed cows from the bacteria in the environment 1 and 2 when $p = 0.3 , r_1 = 0.06$, and $r_2 = 0.06$ with no testing or culling and with annual testing and culling
Dynamics of the bacteria in the two environments with no testing or culling and with annual testing and culling
Number of exposed cows due to different infection routes without testing or culling and with annual testing and culling
Initial number of animals in each compartment
 Variable Defining the variable Initial value Sc Number of susceptible calves 130 Sh Number of susceptible heifers 520 Sa Number of susceptible adults 650 Ec Number of exposed calves 70 Eh Number of exposed heifers 248 Ea Number of exposed adults 250 Lh Number of low-shedding heifers 32 La Number of low-shedding adults 80 Ha Number of high-shedding adults 20 B1 Amount of bacteria (MAP) in the environment 1(Scaled in 108) 0.2 B2 Amount of bacteria (MAP) in the environment 2(Scaled in 108) 590
 Variable Defining the variable Initial value Sc Number of susceptible calves 130 Sh Number of susceptible heifers 520 Sa Number of susceptible adults 650 Ec Number of exposed calves 70 Eh Number of exposed heifers 248 Ea Number of exposed adults 250 Lh Number of low-shedding heifers 32 La Number of low-shedding adults 80 Ha Number of high-shedding adults 20 B1 Amount of bacteria (MAP) in the environment 1(Scaled in 108) 0.2 B2 Amount of bacteria (MAP) in the environment 2(Scaled in 108) 590
Parameters and their values
Initial prevalence of the disease in each age class
 Susceptible Exposed Low-shedding High-shedding Calves 65% 35% 0% 0% Heifers 65% 31% 4% 0% Adults 65% 25% 8% 2%
 Susceptible Exposed Low-shedding High-shedding Calves 65% 35% 0% 0% Heifers 65% 31% 4% 0% Adults 65% 25% 8% 2%
Comparison of the number of animals in each compartment at the end of 10 years without culling and with annual culling
 Compartment Without culling With annual testing & culling Sc 26 42 Ec 53 32 Sh 196 530 Eh 349 244 Lh 301 208 Sa 5 90 Ea 321 388 La 456 424 Ha 284 10
 Compartment Without culling With annual testing & culling Sc 26 42 Ec 53 32 Sh 196 530 Eh 349 244 Lh 301 208 Sa 5 90 Ea 321 388 La 456 424 Ha 284 10
Equilibrium values for the number of animals in each compartment at the end of 25 years without culling and the final values for the number of animals in each compartment at the end of 10 years with these equilibrium values as the initial values and annual culling
 Compartment Equilibrium values after 25 years without culling Final values with annual testing & culling Sc 25 40 Ec 54 33 Sh 184 498 Eh 349 252 Lh 311 230 Sa 4 67 Ea 308 370 La 455 439 Ha 296 11 B1 807×108 610×108 B2 3234523×108 786526×108
 Compartment Equilibrium values after 25 years without culling Final values with annual testing & culling Sc 25 40 Ec 54 33 Sh 184 498 Eh 349 252 Lh 311 230 Sa 4 67 Ea 308 370 La 455 439 Ha 296 11 B1 807×108 610×108 B2 3234523×108 786526×108
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