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Original Articles

Reproduction numbers for infections with free-living pathogens growing in the environment

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Pages 923-940 | Received 29 Jan 2012, Accepted 06 May 2012, Published online: 28 Jun 2012

References

  • Anderson , R. M. and May , R. M. 1991 . “ Infectious Diseases of Humans: Dynamics and Control ” . Oxford : Oxford University Press .
  • Ayliffe , G. A.J. , Babb , J. R. and Taylor , L. J. 1999 . Hospital-Acquired Infection: Principles and Prevention , 3 , Oxford : Butterworth-Heinemann .
  • Bani-Yaghoub , M. , Gautam , R. , Döpfer , D. , Kaspar , C. W. and Ivanek , R. 2012 . Effectiveness of environmental decontamination in control of infectious diseases . Epidemiol. Infect. , 140 : 542 – 553 .
  • Beretta , E. and Takeuchi , Y. 1995 . Global stability of an SIR epidemic model with time delays . J. Math. Biol. , 33 : 250 – 260 .
  • Bolton , D. J. , Byrne , C. M. , Sheridan , J. J. , McDowell , D. A. and Blair , I. S. 1999 . The survival characteristics of a non-toxigenic strain of Escherichia coli O157:H7 . J. Appl. Microbiol. , 86 : 407 – 411 .
  • Boone , S. A. and Gerba , C. P. 2007 . Significance of fomites in the spread of respiratory and enteric viral disease . Appl. Environ. Microbiol. , 73 : 1687 – 1696 .
  • Bourouiba , L. , Teslya , A. and Wu , J. 2011 . Highly pathogenic avian influenza outbreak mitigated by seasonal low pathogenic strains: Insights from dynamic modeling . J. Theor. Biol. , 271 : 181 – 201 .
  • Boyce , J. M. , Potter-Bynoe , G. , Chenevert , C. and King , T. 1997 . Environmental contamination due to methicillin-resistant Staphylococcus aureus: possible infection control implications . Infect. Control Hosp. Epidemiol. , 18 : 622 – 627 .
  • Brauer , F. , van den Driessche , P. and Wu , J. 2008 . “ Mathematical Epidemiology ” . In Lecture Notes in Mathematics 1945 , Edited by: Brauer , F. , van den Driessche , P. and Wu , J. Berlin : Springer .
  • Breban , R. , Drake , J. M. and Rohani , P. 2010 . A general multi-strain model with environmental transmission: Invasion conditions for the disease-free and endemic states . J. Theor. Biol. , 264 : 729 – 736 .
  • Butler , G. J. , Freedman , H. I. and Waltman , P. 1986 . Uniformly persistent systems . Proc. Amer. Math. Soc. , 96 : 425 – 430 .
  • Caraco , T. and Wang , I.-N. 2008 . Free-living pathogens: Life-history constraints and strain competition . J. Theor. Biol. , 250 : 569 – 579 .
  • Chapagain , P. P. , van Kessel , J. S. , Karns , J. S. , Wolfgang , D. R. , Hovingh , E. , Nelen , K. A. , Schukken , Y. H. and Gröhn , Y. T. 2007 . A mathematical model of the dynamics of Salmonella Cerro infection in a US dairy herd . Epidemiol. Infect. , 136 : 263 – 272 .
  • Codeço , C. T. 2001 . Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir . BMC Infect. Dis. , 1 : 1
  • Cozad , A. and Jones , R. D. 2003 . Disinfection and the prevention of infectious disease . Amer. J. Infect. Control , 31 : 243 – 254 .
  • Danforth , D. , Nicolle , L. E. , Hume , K. , Alfieri , N. and Sims , H. 1987 . Nosocomial infections on nursing units with floors cleaned with a disinfectant compared with detergent . J. Hosp. Infect. , 10 : 229 – 235 .
  • Daschner , F. and Schuster , A. 2004 . Disinfection and the prevention of infectious disease: No adverse effects? . Amer. J. Infect. Control , 32 : 224 – 225 .
  • Diekmann , O. and Heesterbeek , J. A.P. 2000 . “ Mathematical Epidemiology of Infectious Diseases ” . Chichester : John Wiley & Sons .
  • van den Driessche , P. and Watmough , J. 2002 . Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission . Math. Biosci. , 180 : 29 – 48 .
  • Freedman , H. I. , Ruan , S. and Tang , M. 1994 . Uniform persistence and flows near a closed positively invariant set . J. Dyn. Differ. Equat. , 6 : 583 – 600 .
  • Gao , S. , Liu , Y. , Luo , Y. and Xie , D. 2011 . Control problems of a mathematical model for schistosomiasis transmission dynamics . Nonlinear Dyn. , 63 : 503 – 512 .
  • Gardner , I. A. , Hird , D. W. , Utterback , W. W. , Danaye-Elmi , C. , Heron , B. R. , Christiansen , K. H. and Sischo , W. M. 1990 . Mortality, morbidity, case-fatality, and culling rates for California dairy cattle as evaluated by the National Animal Health Monitoring System, 1986–1987 . Prev. Vet. Med. , 8 : 157 – 170 .
  • Gautam , R. , Bani-Yaghoub , M. , Neill , W. H. , Döpfer , D. , Kaspar , C. W. and Ivanek , R. 2011 . Modeling impact of seasonal variation in ambient temperature on the transmission dynamics of a pathogen with a free-living stage: Simulation of Escherichia coli O157:H7 prevalence in a dairy herd . Prev. Vet. Med. , 102 : 10 – 21 .
  • Guo , H. , Li , M. Y. and Shuai , Z. 2006 . Global stability of the endemic equilibrium of multi-group SIR epidemic models . Can. Appl. Math. Q. , 14 : 259 – 284 .
  • Hartley , D. M. , Morris , J. G. Jr. and Smith , D. L. 2006 . Hyperinfectivity: A critical element in the ability of V. Cholerae to cause epidemics? . PLOS Med , 3 : 63 – 69 .
  • Heesterbeek , J. A.P. and Dietz , K. 1996 . The concept of R0 in epidemic theory . Stat. Neerl. , 50 : 89 – 110 .
  • Heesterbeek , J. A.P. and Roberts , M. G. 2007 . The type-reproduction number T in models for infectious disease control . Math. Biosci. , 206 : 3 – 10 .
  • Himathongkham , S. , Bahari , S. , Riemann , H. and Cliver , D. 1999 . Survival of Escherichia coli O157:H7 and Salmonella typhimurium in cow manure and cow slurry . FEMS Microbiol. Lett. , 178 : 251 – 257 .
  • Hota , B. 2004 . Contamination, disinfection, and cross-colonization: Are hospital surfaces reservoirs for nosocomial infection? . Clin. Infect. Dis. , 39 : 1182 – 1189 .
  • Hurford , A. , Cownden , D. and Day , T. 2010 . Next-generation tools for evolutionary invasion analyses . J. R. Soc. Interface , 7 : 561 – 571 .
  • Jensen , M. A. , Faruque , S. M. , Mekalanos , J. J. and Levin , B. R. 2006 . Modeling the role of bacteriophage in the control of cholera outbreaks . PNAS , 103 : 4652 – 4657 .
  • Joh , R. I. , Wang , H. , Weiss , H. and Weitz , J. S. 2009 . Dynamics of indirectly transmitted infectious diseases with immunological threshold . Bull. Math. Biol. , 71 : 845 – 862 .
  • Kabir , S. 2005 . Cholera vaccines: The current status and problems . Rev. Med. Microbiol. , 16 : 101 – 116 .
  • Lanzas , C. , Brien , S. , Ivanek , R. , Lo , Y. , Chapagain , P. P. , Ray , K. A. , Ayscue , P. , Warnick , L. D. and Gröhn , Y. T. 2008 . The effect of heterogeneous infectious period and contagiousness on the dynamics of Salmonella transmission in dairy cattle . Epidemiol. Infect. , 136 : 1496 – 1510 .
  • LaSalle , J. P. 1976 . “ The Stability of Dynamical Systems ” . In Regional Conference Series in Applied Mathematics , Philadelphia : SIAM .
  • LeJeune , J. T. , Besser , T. E. and Handcock , D. D. 2001 . Cattle water troughs as reservoirs of Escherichia coli O157 . Appl. Environ. Microbiol. , 67 : 3053 – 3057 .
  • Lélu , M. , Langlais , M. , Poulle , M.-L. and Gilot-Fromont , E. 2010 . Transmission dynamics of Toxoplasma gondii along an urban-rural gradient . Theor. Popul. Biol. , 78 : 139 – 147 .
  • Li , M. Y. , Graef , J. R. , Wang , L. and Karsai , J. 1999 . Global dynamics of a SEIR model with varying total population size . Math. Biosci. , 160 : 191 – 213 .
  • Maaløe , O. and Richmond , M. H. 1962 . The rate of growth of Salmonella typhimurium with proline or glutamate as sole C source . J. Gen. Microbiol , 27 : 269 – 284 .
  • Maki , D. G. , Alvarado , C. J. , Hassemer , C. A. and Zilz , M. A. 1982 . Relation of the inanimate hospital environment to endemic nosocomial infection . New Engl. J. Med. , 307 : 1562 – 1566 .
  • Mukandavire , Z. , Liao , S. , Wang , J. , Gaff , H. , Smith , D. L. and Morris , J. G. Jr. 2011 . Estimating the reproductive number for the 2008–2009 cholera outbreaks in Zimbabwe . PNAS , 108 : 8767 – 8772 .
  • Peleg , M. , Corradini , M. G. and Normand , M. D. 2007 . The logistic (Verhulst) model for sigmoid microbila growth curves revisited . Food Research Interna. , 40 : 808 – 818 .
  • Roberts , M. G. and Heesterbeek , J. A.P. 2003 . A new method for estimating the effort required to control an infectious disease . Proc. R. Soc. Lond. B , 270 : 1359 – 1364 .
  • Scott , E. and Bloomfield , S. F. 1990 . The survival and transfer of microbial contamination via cloths, hands and utensils . J. Appl. Bacteriol. , 68 : 271 – 278 .
  • Tien , J. H. and Earn , D. J.D. 2010 . Multiple transmission pathways and disease dynamics in a waterborne pathogen model . Bull. Math. Biol. , 72 : 1506 – 1533 .
  • Tien , J. H. , Poinar , H. N. , Fisman , D. N. and Earn , D. J.D. 2011 . Herald waves of Cholera in nineteenth century London . J. R. Soc. Interface , 8 : 756 – 760 .
  • Woodward , W. E. 1971 . Cholera reinfection in man . J. Infect. Dis. , 123 : 61 – 66 .
  • Xiao , Y. , Bowers , R. G. , Clancy , D. and French , N. P. 2005 . Understanding the dynamics of Salmonella infections in dairy herds: A modelling approach . J. Theor. Biol. , 233 : 159 – 175 .