\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Modeling environmental transmission of MAP infection in dairy cows

  • * Corresponding author: Suzanne Lenhart

    * Corresponding author: Suzanne Lenhart
This work was partially supported by the National Institute for Mathematical Biological Synthesis, sponsored by the National Science Foundation Award NSF DBI-1300426.
Abstract / Introduction Full Text(HTML) Figure(7) / Table(5) Related Papers Cited by
  • 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.

    Mathematics Subject Classification: Primary: 92B05; Secondary: 34B15.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  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)

    Figure 2.  Environmental transmission coefficient $f(B)$ with $K_1 = 1000$ and $K_2 = 100$

    Figure 3.  Dynamics of the animals in each compartment with no testing or culling and with annual testing and culling

    Figure 4.  Dynamics of the total animals in each disease class with no testing or culling and with annual testing and culling

    Figure 5.  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

    Figure 6.  Dynamics of the bacteria in the two environments with no testing or culling and with annual testing and culling

    Figure 7.  Number of exposed cows due to different infection routes without testing or culling and with annual testing and culling

    Table 1.  Initial number of animals in each compartment

    VariableDefining the variableInitial value
    ScNumber of susceptible calves130
    ShNumber of susceptible heifers520
    SaNumber of susceptible adults650
    EcNumber of exposed calves70
    EhNumber of exposed heifers248
    EaNumber of exposed adults250
    LhNumber of low-shedding heifers32
    LaNumber of low-shedding adults80
    HaNumber of high-shedding adults20
    B1Amount of bacteria (MAP) in the environment 1(Scaled in 108)0.2
    B2Amount of bacteria (MAP) in the environment 2(Scaled in 108)590
     | Show Table
    DownLoad: CSV

    Table 2.  Parameters and their values

    ParameterDefining the parameterParameter value
    bBirth rate of calves from susceptible and exposed adults0.00127
    bLaBirth rate of calves from low-shedding adults0.00127
    bHaBirth rate of calves from high-shedding adults0.00127
    µScDeath rate of susceptible calves0.00028
    µEcDeath rate of exposed calves0.00028
    µShDeath rate of susceptible heifers0.000063
    µEhDeath rate of exposed heifers0.000063
    µLhDeath rate of low-shedding heifers0.000063
    µSaDeath rate of susceptible adults0.0012
    µEaDeath rate of exposed adults0.0012
    µLaDeath rate of low-shedding adults0.0012
    µHaDeath rate of high-shedding adults0.0012
    µB1Decay rate of bacteria in the heifer environment0.0027
    µB1Decay rate of bacteria in the adult environment0.0027
    δCulling rate of high-shedding adults0.9
    νLProbability of getting infected through vertical transmission from low-shedding adults0
    νHProbability of getting infected through vertical transmission from high-shedding adults0.22
    a1Transfer rate from calves to heifers due to age progression0.0168
    a2Transfer rate from heifers to adults due to age progression0.00151
    d1Transfer rate from exposed heifers to low-shedding heifers0.0014
    d2Transfer rate from exposed adults to low-shedding adults0.0014
    d3Transfer rate from low-shedding adults to high-shedding adults0.00078
    β1Transmission rate for susceptible calves due to the colostrum and milk from low-shedding adults0.000021
    β2Transmission rate for susceptible calves due to the colostrum and milk from high-shedding adults0.000028
    γ1Transmission rate for susceptible heifers due to direct contact with low-shedding heifers0.0000024
    γ2Transmission rate for susceptible adults due to direct contact with low-shedding adults0.0000012
    γ3Transmission rate for susceptible adults due to direct contact with high-shedding adults0.0000018
    pProbability of newborn susceptible calves getting infected by MAP in the adult environment0.3
    r1Probability of susceptible heifers getting infected by MAP in the heifer environment0.06
    r2Probability of susceptible adults getting infected by MAP in the adult environment0.06
    λ1Rate at which the bacteria is added to the heifer environment from the low-shedding heifers0.007
    λ2Rate at which the bacteria is added to the adult environment from the low-shedding adults0.007
    λ3Rate at which the bacteria is added to the adult environment from the high-shedding adults29.5
     | Show Table
    DownLoad: CSV

    Table 3.  Initial prevalence of the disease in each age class

    SusceptibleExposedLow-sheddingHigh-shedding
    Calves65%35%0%0%
    Heifers65%31%4%0%
    Adults65%25%8%2%
     | Show Table
    DownLoad: CSV

    Table 4.  Comparison of the number of animals in each compartment at the end of 10 years without culling and with annual culling

    CompartmentWithout cullingWith annual testing & culling
    Sc2642
    Ec5332
    Sh196530
    Eh349244
    Lh301208
    Sa590
    Ea321388
    La456424
    Ha28410
     | Show Table
    DownLoad: CSV

    Table 5.  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

    CompartmentEquilibrium values after 25 years without cullingFinal values with annual testing & culling
    Sc2540
    Ec5433
    Sh184498
    Eh349252
    Lh311230
    Sa467
    Ea308370
    La455439
    Ha29611
    B1807×108610×108
    B23234523×108786526×108
     | Show Table
    DownLoad: CSV
  • [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. CookJ. 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. DiekmannJ. 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. DoréJ. ParéG. CôtéS. BuczinskiO. LabrecqueJ. 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. EspejoS. GoddenW. 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. GardnerS. S. NielsenR. J. WhittingtonM. T. CollinsD. BakkerB. HarrisS. SreevatsanJ. E. LombardR. SweeneyD. R. SmithJ. 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. HumphryA. W. StottC. 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. LuR. M. MitchellR. L. SmithJ. S. Van KesselP. P. ChapagainY. 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. MarcéP. EzannoM. F. WeberH. SeegersD. 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. MarcéP. EzannoH. SeegersD. 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. MarcéP. EzannoH. SeegersD. 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. MassaroS. LenhartM. SpenceC. DrakesG. YangF. AgustoR. JohnsonB. WhitlockA. 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. MitchellG. F. MedleyM. 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. MitchellY. SchukkenA. KoetsM. WeberD. BakkerJ. StabelR. 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. MortierH. W. BarkemaT. A. WilsonT. T. SajobiR. 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. OttS. 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. RaizmanJ. FetrowS. J. WellsS. M. GoddenM. 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. RobinsS. BogenA. FrancisA. WesthoekA. KanarekS. 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 RoermundD. BakkerP. 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. ScanuT. J. BullS. CannasJ. D. SandersonL. A. SechiG. DettoriS. Zanetti and J. H. TaylorMycobacterium 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. ScottJ. P. BannantineY. KanekoA. J. BranscumR. H. WhitlockY. MoriC. 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. GopinathMycobacterium 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. SmithY. T. GröhnA. K. PradhanR. H. WhitlockJ. S. Van KesselJ. M. SmithD. 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. WhittingtonI. 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-YaghoubR. GautamZ. ShuaiP. 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.
  • 加载中

Figures(7)

Tables(5)

SHARE

Article Metrics

HTML views(1844) PDF downloads(65) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return