Skip to main content
Log in

Role of environmental persistence in pathogen transmission: a mathematical modeling approach

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  • Anderson RM, Donnelly CA, Ferguson NM, Woolhouse ME, Watt CJ, Udy HJ, MaWhinney S, Dunstan SP, Southwood TR, Wilesmith JW, Ryan JB, Hoinville LJ, Hillerton JE, Austin AR, Wells GA (1996) Transmission dynamics and epidemiology of BSE in British cattle. Nature 382(6594): 779–788

    Article  Google Scholar 

  • Ballesteros S, Vergu E, Cazelles B (2009) Influenza A gradual and epochal evolution: insights from simple models. PLoS One 4(10): e7426

    Article  Google Scholar 

  • Berglund N, Gentz B (2006) Noise-induced phenomena in slow–fast dynamical systems: a sample-paths approach. Springer, Berlin

    MATH  Google Scholar 

  • Blanchong JA, Samuel MD, Goldberg DR, Shadduck DJ, Lehr MA (2006) Persistence of pasteurella multocida in wetlands following avian cholera outbreaks. J Wildl Dis 42(1): 33–39

    Google Scholar 

  • Breban R, Drake J, Rohani P (2010) A general multi-strain model with environmental transmission: invasion conditions for the disease-free and endemic states. J Theor Biol 264(3): 729–736

    Article  Google Scholar 

  • Breban R, Drake JM, Stallknecht DE, Rohani P (2009) The role of environmental transmission in recurrent avian influenza epidemics. PLoS Comput Biol 5(4): e1000346

    Article  Google Scholar 

  • Caley P, Philp DJ, McCracken K (2008) Quantifying social distancing arising from pandemic influenza. J R Soc Interface 5(23): 631–639

    Article  Google Scholar 

  • Chowell G, Nishiura H, Bettencourt LMA (2007) Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. J R Soc Interface 4(12): 155–166

    Article  Google Scholar 

  • Codeço C (2001) Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infect Dis 1(1): 1

    Article  Google Scholar 

  • Codeço C, Lele S, Pascual M, Bouma M, Ko A (2008) A stochastic model for ecological systems with strong nonlinear response to environmental drivers: application to two water-borne diseases. J R Soc Interface 5(19): 247–252

    Article  Google Scholar 

  • Dennis B (1989) Allee effects: population growth, critical density, and the chance of extinction. Nat Resour Model 3(4): 481–538

    MathSciNet  MATH  Google Scholar 

  • D’Souza DH, Sair A, Williams K, Papafragkou E, Jean J, Moore C, Jaykus L (2006) Persistence of caliciviruses on environmental surfaces and their transfer to food. Int J Food Microbiol 108(1): 84–91

    Article  Google Scholar 

  • Fenichel N (1979) Geometric singular perturbation theory for ordinary differential equations. J Differ Equ 31(1): 53–98

    Article  MathSciNet  MATH  Google Scholar 

  • Field H, Young P, Yob JM, Mills J, Hall L, Mackenzie J (2001) The natural history of Hendra and Nipah viruses. Microbes Infect 3(4): 307–314

    Article  Google Scholar 

  • Goldstein E, Dushoff J, Ma J, Plotkin JB, Earn DJD, Lipsitch M (2009) Reconstructing influenza incidence by deconvolution of daily mortality time series. Proc Natl Acad Sci USA 106(51): 21825–21829

    Article  Google Scholar 

  • Gralton J, Tovey E, McLaws ML, Rawlinson WD (2011) The role of particle size in aerosolised pathogen transmission: a review. J Infect 62(1): 1–13

    Article  Google Scholar 

  • Handel A, Longini IM, Antia R (2007) What is the best control strategy for multiple infectious disease outbreaks. Proc R Soc B 274(1611): 833–837

    Article  Google Scholar 

  • Henning J, Meers J, Davies PR, Morris RS (2005) Survival of rabbit haemorrhagic disease virus (RHDV) in the environment. Epidemiol Infect 133(4): 719–730

    Article  Google Scholar 

  • Jensen M, Faruque SM, Mekalanos JJ, Levin B (2006) Modeling the role of bacteriophage in the control of cholera outbreaks. Proc Natl Acad Sci USA 103(12): 4652

    Article  Google Scholar 

  • King AA, Ionides EL, Pascual M, Bouma MJ (2008) Inapparent infections and cholera dynamics. Nature 454(7206): 877–880

    Article  Google Scholar 

  • Li S, Eisenberg J, Spicknall I, Koopman J (2009) Dynamics and control of infections transmitted from person to person through the environment. Am J Epidemiol 170(2): 257–265

    Article  Google Scholar 

  • Miller MW, Hobbs NT, Tavener SJ (2006) Dynamics of prion disease transmission in mule deer. Ecol Appl 16(6): 2208–2214

    Article  Google Scholar 

  • Pascual M, Bouma M, Dobson A (2002) Cholera and climate: revisiting the quantitative evidence. Microbes Infect 4(2): 237–245

    Article  Google Scholar 

  • Pepper IL, Rusin P, Quintanar DR, Haney C, Josephson KL, Gerba CP (2004) Tracking the concentration of heterotrophic plate count bacteria from the source to the consumer’s tap. Int J Food Microbiol 92(3): 289–295

    Article  Google Scholar 

  • Reynolds KA, Watt PM, Boone SA, Gerba CP (2005) Occurrence of bacteria and biochemical markers on public surfaces. Int J Environ Heal R 15(3): 225–234

    Article  Google Scholar 

  • Roche B, Lebarbenchon C, Gauthier-Clerc M, Chang CM, Thomas F, Renaud F, van der Werf S, Guégan JF (2009) Water-borne transmission drives avian influenza dynamics in wild birds: the case of the 2005–2006 epidemics in the Camargue area. Infect Genet Evol 9(5): 800–805

    Article  Google Scholar 

  • Rohani P, Breban R, Stallknecht DE, Drake JM (2009) Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion. Proc Natl Acad Sci USA 106(25): 10365–10369

    Article  Google Scholar 

  • Roper MH, Vandelaer JH, Gasse FL (2007) Maternal and neonatal tetanus. Lancet 370(9603): 1947–1959

    Article  Google Scholar 

  • Rusin P, Orosz-Coughlin P, Gerba C (1998) Reduction of faecal coliform, coliform and heterotrophic plate count bacteria in the household kitchen and bathroom by disinfection with hypochlorite cleaners. J Appl Microbiol 85(5): 819–828

    Article  Google Scholar 

  • Sakamoto K (1990) Invariant manifolds in singular perturbation problems for ordinary differential equations. P Roy Soc Edinb A 116(1–2): 45–78

    Article  MathSciNet  MATH  Google Scholar 

  • Spicknall IH, Koopman JS, Nicas M, Pujol JM, Li S, Eisenberg JNS (2010) Informing optimal environmental influenza interventions: how the host, agent, and environment alter dominant routes of transmission. PLoS Comput Biol 6(10): e1000969

    Article  Google Scholar 

  • Vardavas R, Breban R, Blower S (2007) Can influenza epidemics be prevented by voluntary vaccination?. PLoS Comput Biol 3(5): e85

    Article  Google Scholar 

  • Webb CT, Brooks CP, Gage KL, Antolin MF (2006) Classic flea-borne transmission does not drive plague epizootics in prairie dogs. Proc Natl Acad Sci USA 103(16): 6236–6241

    Article  Google Scholar 

  • Xiao Y, Bowers RG, Clancy D, French NP (2007) Dynamics of infection with multiple transmission mechanisms in unmanaged/managed animal populations. Theor Popul Biol 71(4): 408–423

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Romulus Breban.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Breban, R. Role of environmental persistence in pathogen transmission: a mathematical modeling approach. J. Math. Biol. 66, 535–546 (2013). https://doi.org/10.1007/s00285-012-0520-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-012-0520-2

Keywords

Mathematics Subject Classification (2000)