Skip to main content

Advertisement

SpringerLink
Log in

Models of Bovine Babesiosis Including Juvenile Cattle

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Bovine Babesiosis in cattle is caused by the transmission of protozoa of Babesia spp. by ticks as vectors. Juvenile cattle (\(<\)9 months of age) have resistance to Bovine Babesiosis, rarely show symptoms, and acquire immunity upon recovery. Susceptibility to the disease varies between breeds of cattle. Models of the dynamics of Bovine Babesiosis transmitted by the cattle tick that include these factors are formulated as systems of ordinary differential equations. Basic reproduction numbers are calculated, and it is proved that if these numbers are below the threshold value of one, then Bovine Babesiosis dies out. However, above the threshold number of one, the disease may approach an endemic state. In this case, control measures are suggested by determining target reproduction numbers. The percentage of a particular population (for example, the adult bovine population) needed to be controlled to eradicate the disease is evaluated numerically using Columbia data from the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abbas RZ, Zaman MA, Colwell DD, Gilleard J, Iqbal Z (2014) Acaricide resistance in cattle ticks and approaches to its management: the state of play. Vet Parasitol 203:6–20

    Article  Google Scholar 

  • Aranda DF, Trejos DY, Valverde JC, Villanueva RJ (2012) A mathematical model for Babesiosis disease in bovine and tick populations. Math Methods Appl Sci 35:249–256. See also: D. F. Aranda Lozano (2011) Modeling of parasitic disease with vector of transmission: toxoplasmosis and babesiosis bovine, PhD thesis, Universidad Politecnica de Valencia, Departmento de Matematica Aplicada

  • Berman A, Plemmons RJ (1994) Nonnegative matrices in the mathematical sciences. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Bock RE, de Vos AJ, Kingston TG, McLellan DJ (1997) Effect of breed of cattle on innate resistance to infection with Babesia bovis, B. bigemina and Anaplasma marginale. Aust Vet J 75:337–340

    Article  Google Scholar 

  • Bock RE, Jackson L, de Vos AJ (1999a) Effect of breed of cattle on transmission rate and innate resistance to infection with Babesia bovis and B. bigemina transmitted by Boophilus microplus. Aust Vet J 77:461–464

    Article  Google Scholar 

  • Bock RE, Kingston TG, Standfast NF, de Vos AJ (1999b) Effect of cattle breed on innate resistance to inoculations of Babesia bigemina. Aust Vet J 77:465–466

    Article  Google Scholar 

  • Bock RE, Jackson L, de Vos A, Jorgensen W (2004) Babesiosis of cattle. Parasitology 129:247–269

    Article  Google Scholar 

  • Caswell H (2001) Matrix population models construction, analysis and interpretation, 2nd edn. Sinauer Associates, Sunderland

    Google Scholar 

  • Charrel RN, Attoui H, Butenko AM, Clegg JC, Deubel V, Frolova TV, Gould EA, Gritsun TS, Heinz FX, Labuda N, Laskevich VA, Loktev V, Lundkvist A, Lvov DV, Mandl CW, Niedrig M, Papa A, Petrov VS, Plyusnin A, Randolph S, Suss J, Zlobin VI, De Lamballerie X (2004) Tick-borne diseases of human interest in Europe. Clin Microbiol Infect 10:1040–1055

    Article  Google Scholar 

  • Chitnis N, Hyman JM, Cushing JM (2008) Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol 70:1272–1296

    Article  MathSciNet  MATH  Google Scholar 

  • de Vos AJ, Bock RE (2000) Vaccination against bovine babesiosis. Ann N Y Acad Sci 916:540–545

    Article  Google Scholar 

  • de Waal DT, Combrink MP (2006) Live vaccines against bovine babesiosis. Vet Parasitol 138:88–96

    Article  Google Scholar 

  • Diekmann O, Heesterbeek JAP (2000) Mathematical epidemiology of infectious diseases. Wiley, West Sussex

    Google Scholar 

  • Freedman HI, Ruan S, Tang M (1994) Uniform persistence and flows near a closed positively invariant set. J Dyn Differ Equ 6:583–600

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman A, Yakubu A (2014) A Bovine Babesiosis model with dispersion. Bull Math Biol 76:98–135

    Article  MathSciNet  MATH  Google Scholar 

  • Gaff HD, Gross LJ (2007) Modeling tick-borne disease: a metapopulation model. Bull Math Biol 69:265–288

    Article  MathSciNet  MATH  Google Scholar 

  • Guerrero FD, Bendele KG, Davey RB, George JE (2007) Detection of Babesia bigemina infection in strains of Rhipicephalus (Boophilus) microplus collected from outbreaks in South Texas. Vet Parasitol 145:156–163

    Article  Google Scholar 

  • Guo H, Li MY, Shuai Z (2006) Global stability of the endemic equilibrium of multigroup SIR epidemic models. Can Appl Math Q 14:259–284

    MathSciNet  MATH  Google Scholar 

  • Hall WTK, Tammemagi L, Johnston LAY (1968) Bovine Babesiosis: the immunity of calves to Babesia bigemina infection. Aust Vet J 44:259–264

    Article  Google Scholar 

  • Heesterbeek JAP, Roberts MG (2007) The type-reproduction number T in models for infectious disease control. Math Biosci 206:3–10

    Article  MathSciNet  MATH  Google Scholar 

  • Hilpertshauser H, Deplazes P, Schnyder M, Gern L, Mathis A (2006) Babesia spp. identified by PCR in ticks collected from domestic and wild ruminants in southern Switzerland. Appl Environ Microbiol 72:6503–6507

    Article  Google Scholar 

  • Hoch T, Goebel J, Agoulon A, Malandrin L (2012) Modelling Bovine Babesiosis: a tool to stimulate scenarios for pathogen spread and to test control measures for the disease. Prev Vet Med 106:136–142

    Article  Google Scholar 

  • Holman PJ, Carroll JE, Pugh R, Davis DS (2011) Molecular detection of Babesia bovis and Babesia bigemina in white-tailed deer (Odocoileus virginianus) from Tom Green County in central Texas. Vet Parasitol 177:298–304

    Article  Google Scholar 

  • Jonsson NN, Bock R, Jorgensen WK (2008) Productivity and health effects of anaplasmosis and babesiosis on Babesia indicus cattle and their crosses, and the effects of differing intensity of tick control in Australia. Vet Parasitol 155:1–9

    Article  Google Scholar 

  • LaSalle JP (1976) The stability of dynamical systems, regional conference series in applied mathematics. SIAM, Philadelphia

    Google Scholar 

  • Li MY, Greaf JR, Wang L, Karsai J (1999) Global dynamics of a SEIR model with varying total population size. Math Biosci 160:191–213

    Article  MathSciNet  MATH  Google Scholar 

  • Manore CA, Hickmann KS, Xu S, Wearing HJ, Hyman JM (2014) Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus. J Theor Biol 356:174–191

    Article  MathSciNet  Google Scholar 

  • Piper EK, Jackson LA, Bagnall NH, Kongsuwan KK, Lew AE, Jonsson NN (2008) Gene expression in the skin of Bos taurus and Bos indicus cattle infested with the cattle tick, Rhipicephalus (Boophilus) microplus. Vet Immunol Immunopathol 126:110–119

    Article  Google Scholar 

  • Randolf SE (2004) Tick ecology: processes and patterns behind the epidemiological risk posed by ixodid ticks as vectors. Parasitology 129:37–65

    Article  Google Scholar 

  • Ramos CM, Cooper SM, Holman PJ (2010) Molecular and serologic evidence for Babesia bovis-like parasites in white-tailed deer (Odocoileus virginianus) in south Texas. Vet Parasitol 172:214–220

    Article  Google Scholar 

  • Roberts MG, Heesterbeek JAP (2003) A new method for estimating the effort required to control an infectious disease. Proc R Soc Lond B 270:1359–1364

    Article  Google Scholar 

  • Schnittger L, Rodriguez AE, Florin-Christensen M, Morrison DA (2012) Babesia: a world emerging. Infect Genet Evol 12:1788–1809

    Article  Google Scholar 

  • Shuai Z, Heesterbeek JAP, van den Driessche P (2013) Extending the type reproduction number to infectious disease control targeting contacts between types. J Math Biol 67:1067–1082. Also see the erratum at http://math.cos.ucf.edu/~zshuai/paper/target_erratum.pdf

  • Shuai Z, van den Driessche P (2013) Global stability of infectious disease models using Lyapunov functions. SIAM J Appl Math 74:1513–1532

    Article  Google Scholar 

  • Smith HL, Waltman P (1995) The theory of the chemostat, dynamics of microbial competition, Cambridge studies in math biology. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Spickler A, Roth J, Galyon J, Lofstedt J (2010) Emerging and exotic diseases of animals. CFSPH Iowa State University, Ames

    Google Scholar 

  • Uilenberg G (1995) International collaborative research: significance of tick-borne hemoparasitic diseases to world animal health. Vet Parasitol 57:19–41

    Article  Google Scholar 

  • van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29–48

    Article  MathSciNet  MATH  Google Scholar 

  • Yeruham I, Avidar Y, Aroch I, Hadani A (2003) Intra-uterine infection with Babesia bovis in a 2-day-old calf. J Vet Med 50:60–62

    Article  Google Scholar 

  • Zintl A, Gray JS, Skerrett HE, Mulcahy G (2005) Possible mechanisms underlying age-related resistance to Bovine Babesiosis. Parasite Immunol 27:115–120

    Article  Google Scholar 

Download references

Acknowledgments

This research was partially supported by NSERC, through a USRA (C.M.S.-R.) and a Discovery Grant (P.vdD.), and by the University of Central Florida through a start-up fund (Z.S.). Z.S. and P.vdD. thank A. Yakubu for sharing with them a preprint of Friedman and Yakubu (2014) and the thesis by D. F. Aranda. The authors thank two anonymous reviewers for helpful comments.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada

    C. M. Saad-Roy & P. van den Driessche

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Zhisheng Shuai

Authors
  1. C. M. Saad-Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhisheng Shuai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. van den Driessche
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. M. Saad-Roy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saad-Roy, C.M., Shuai, Z. & van den Driessche, P. Models of Bovine Babesiosis Including Juvenile Cattle. Bull Math Biol 77, 514–547 (2015). https://doi.org/10.1007/s11538-015-0068-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-015-0068-6

Keywords

Mathematics Subject Classification

Search

Navigation