Analyze Diet
Scientific reports2019; 9(1); 3227; doi: 10.1038/s41598-019-40151-2

Comparing the effects of non-homogenous mixing patterns on epidemiological outcomes in equine populations: A mathematical modelling study.

Abstract: Disease transmission models often assume homogenous mixing. This assumption, however, has the potential to misrepresent the disease dynamics for populations in which contact patterns are non-random. A disease transmission model with an SEIR structure was used to compare the effect of weighted and unweighted empirical equine contact networks to weighted and unweighted theoretical networks generated using random mixing. Equine influenza was used as a case study. Incidence curves generated with the unweighted empirical networks were similar in epidemic duration (5-8 days) and peak incidence (30.8-46.4%). In contrast, the weighted empirical networks resulted in a more pronounced difference between the networks in terms of the epidemic duration (8-15 days) and the peak incidence (5-25%). The incidence curves for the empirical networks were bimodal, while the incidence curves for the theoretical networks were unimodal. The incorporation of vaccination and isolation in the model caused a decrease in the cumulative incidence for each network, however, this effect was only seen at high levels of vaccination and isolation for the complete network. This study highlights the importance of using empirical networks to describe contact patterns within populations that are unlikely to exhibit random mixing such as equine populations.
Publication Date: 2019-03-01 PubMed ID: 30824806PubMed Central: PMC6397169DOI: 10.1038/s41598-019-40151-2Google Scholar: Lookup
The Equine Research Bank provides access to a large database of publicly available scientific literature. Inclusion in the Research Bank does not imply endorsement of study methods or findings by Mad Barn.
  • Comparative Study
  • Journal Article
  • Research Support
  • Non-U.S. Gov't

Summary

This research summary has been generated with artificial intelligence and may contain errors and omissions. Refer to the original study to confirm details provided. Submit correction.

This scientific research focuses on disease transmission in horse populations and uses mathematical modeling to compare the effects of different types of mixing patterns (random and non-random) on disease outcomes. It specifically studies the spread of equine influenza under different contact assumptions and the impact of prevention measures like vaccination and isolation.

Research Objective and Background

  • The study aims to assess the effect of homogeneous and non-homogeneous (or random and non-random) mixing patterns on disease transmission in equine populations using a disease transmission model with an SEIR (Susceptible, Exposed, Infectious, and Recovered) structure.
  • Often, disease transmission models assume homogenous or random mixing patterns. However, this may misrepresent the actual disease dynamics in real-world scenarios where the contact patterns are non-random.

Methodology and Case Study

  • The researchers used both empirical (real-world data) and theoretical (artificially generated) equine contact networks, with weighted (more realistic, considering the differences in contact frequencies) and unweighted (all contacts equally likely) forms, to study their influence on outbreak scenarios.
  • Equine influenza, a common disease in horse populations, was used as a case study.

Results and Findings

  • The outcomes of unweighted empirical networks i.e., based on real-world data but where every contact has an equal chance of disease transmission, were found to be similar in terms of the duration of the epidemic (5-8 days) and peak incidence (30.8-46.4%).
  • However, when considering the weighted (frequency-based contact) empirical networks, a more pronounced difference was observed with a wider epidemic duration (8-15 days) and varied peak incidence (5-25%).
  • The incidence curves for empirical networks showed a bimodal distribution, whereas theoretical networks generated unimodal curves, implying different patterns of disease spread between real-world and imagined scenarios.
  • The incorporation of control measures like vaccination and isolation in the model led to a decrease in the cumulative incidence for each network. However, this reduction was only observed at high levels of implementation, especially in the complete network scenario indicating the need for thorough preventive actions.

Conclusion

  • The research re-emphasizes the importance of using empirical networks or real-world data to portray contact patterns in populations, especially where random mixing is unlikely as in the case of equine communities. It encourages the use of more complex models that take into account the true nature of population interactions for better disease control and management.

Cite This Article

APA
Milwid RM, O'Sullivan TL, Poljak Z, Laskowski M, Greer AL. (2019). Comparing the effects of non-homogenous mixing patterns on epidemiological outcomes in equine populations: A mathematical modelling study. Sci Rep, 9(1), 3227. https://doi.org/10.1038/s41598-019-40151-2

Publication

ISSN: 2045-2322
NlmUniqueID: 101563288
Country: England
Language: English
Volume: 9
Issue: 1
Pages: 3227
PII: 3227

Researcher Affiliations

Milwid, Rachael M
  • Department of Population Medicine, University of Guelph, Guelph, ON, Canada.
O'Sullivan, Terri L
  • Department of Population Medicine, University of Guelph, Guelph, ON, Canada.
Poljak, Zvonimir
  • Department of Population Medicine, University of Guelph, Guelph, ON, Canada.
Laskowski, Marek
  • Department of Population Medicine, University of Guelph, Guelph, ON, Canada.
  • Department of Mathematics and Statistics, York University, Toronto, ON, Canada.
Greer, Amy L
  • Department of Population Medicine, University of Guelph, Guelph, ON, Canada. agreer@uoguelph.ca.

MeSH Terms

  • Animals
  • Contact Tracing / methods
  • Contact Tracing / veterinary
  • Epidemics / prevention & control
  • Horse Diseases / prevention & control
  • Horse Diseases / transmission
  • Horse Diseases / virology
  • Horses
  • Humans
  • Incidence
  • Influenza, Human / epidemiology
  • Influenza, Human / transmission
  • Influenza, Human / virology
  • Models, Theoretical
  • Neural Networks, Computer
  • Ontario
  • Orthomyxoviridae / physiology
  • Orthomyxoviridae Infections / epidemiology
  • Orthomyxoviridae Infections / transmission
  • Orthomyxoviridae Infections / virology
  • Time Factors
  • Vaccination / methods
  • Vaccination / veterinary

Conflict of Interest Statement

The authors declare no competing interests.

References

This article includes 53 references
  1. Lofgren ET, Halloran ME, Rivers CM, Drake JM, Porco TC, Lewis B, Yang W, Vespignani A, Shaman J, Eisenberg JN, Eisenberg MC, Marathe M, Scarpino SV, Alexander KA, Meza R, Ferrari MJ, Hyman JM, Meyers LA, Eubank S. Opinion: Mathematical models: a key tool for outbreak response.. Proc Natl Acad Sci U S A 2014 Dec 23;111(51):18095-6.
    doi: 10.1073/pnas.1421551111pmc: PMC4280577pubmed: 25502594google scholar: lookup
  2. Craft ME. Infectious disease transmission and contact networks in wildlife and livestock.. Philos Trans R Soc Lond B Biol Sci 2015 May 26;370(1669).
    doi: 10.1098/rstb.2014.0107pmc: PMC4410373pubmed: 25870393google scholar: lookup
  3. Perisic A, Bauch CT. Social contact networks and disease eradicability under voluntary vaccination.. PLoS Comput Biol 2009 Feb;5(2):e1000280.
  4. Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A. Dynamical patterns of epidemic outbreaks in complex heterogeneous networks.. J Theor Biol 2005 Jul 21;235(2):275-88.
    doi: 10.1016/j.jtbi.2005.01.011pubmed: 15862595google scholar: lookup
  5. Pellis L, Ball F, Bansal S, Eames K, House T, Isham V, Trapman P. Eight challenges for network epidemic models.. Epidemics 2015 Mar;10:58-62.
    doi: 10.1016/j.epidem.2014.07.003pubmed: 25843385google scholar: lookup
  6. Krivitsky PN, Morris M. INFERENCE FOR SOCIAL NETWORK MODELS FROM EGOCENTRICALLY SAMPLED DATA, WITH APPLICATION TO UNDERSTANDING PERSISTENT RACIAL DISPARITIES IN HIV PREVALENCE IN THE US.. Ann Appl Stat 2017 Mar;11(1):427-455.
    doi: 10.1214/16-AOAS1010pmc: PMC5737754pubmed: 29276550google scholar: lookup
  7. Keeling MJ, Eames KT. Networks and epidemic models.. J R Soc Interface 2005 Sep 22;2(4):295-307.
    doi: 10.1098/rsif.2005.0051pmc: PMC1578276pubmed: 16849187google scholar: lookup
  8. Kiss IZ, Green DM, Kao RR. The network of sheep movements within Great Britain: Network properties and their implications for infectious disease spread.. J R Soc Interface 2006 Oct 22;3(10):669-77.
    doi: 10.1098/rsif.2006.0129pmc: PMC1664651pubmed: 16971335google scholar: lookup
  9. Martínez-López B, Perez AM, Sánchez-Vizcaíno JM. Social network analysis. Review of general concepts and use in preventive veterinary medicine.. Transbound Emerg Dis 2009 May;56(4):109-20.
  10. Barabási AL, Bonabeau E. Scale-free networks.. Sci Am 2003 May;288(5):60-9.
  11. Bansal S, Grenfell BT, Meyers LA. When individual behaviour matters: homogeneous and network models in epidemiology.. J R Soc Interface 2007 Oct 22;4(16):879-91.
    doi: 10.1098/rsif.2007.1100pmc: PMC2394553pubmed: 17640863google scholar: lookup
  12. Keeling M. The implications of network structure for epidemic dynamics.. Theor Popul Biol 2005 Feb;67(1):1-8.
    doi: 10.1016/j.tpb.2004.08.002pubmed: 15649519google scholar: lookup
  13. Lloyd AL, Valeika S, Cintr A. Infection Dynamics on Small-World Networks. Math. Stud. Hum. Dis. Dyn. Emerg. Paradig. challanges 209–234 (2006).
  14. May RM, Lloyd AL. Infection dynamics on scale-free networks.. Phys Rev E Stat Nonlin Soft Matter Phys 2001 Dec;64(6 Pt 2):066112.
    doi: 10.1103/PhysRevE.64.066112pubmed: 11736241google scholar: lookup
  15. Bioglio L, Génois M, Vestergaard CL, Poletto C, Barrat A, Colizza V. Recalibrating disease parameters for increasing realism in modeling epidemics in closed settings.. BMC Infect Dis 2016 Nov 14;16(1):676.
    doi: 10.1186/s12879-016-2003-3pmc: PMC5109722pubmed: 27842507google scholar: lookup
  16. Gemmetto V, Barrat A, Cattuto C. Mitigation of infectious disease at school: targeted class closure vs school closure.. BMC Infect Dis 2014 Dec 31;14:695.
    doi: 10.1186/s12879-014-0695-9pmc: PMC4297433pubmed: 25595123google scholar: lookup
  17. Stehlé J, Voirin N, Barrat A, Cattuto C, Colizza V, Isella L, Régis C, Pinton JF, Khanafer N, Van den Broeck W, Vanhems P. Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees.. BMC Med 2011 Jul 19;9:87.
    doi: 10.1186/1741-7015-9-87pmc: PMC3162551pubmed: 21771290google scholar: lookup
  18. Stehlé J, Voirin N, Barrat A, Cattuto C, Isella L, Pinton JF, Quaggiotto M, Van den Broeck W, Régis C, Lina B, Vanhems P. High-resolution measurements of face-to-face contact patterns in a primary school.. PLoS One 2011;6(8):e23176.
  19. VanderWaal K, Perez A, Torremorrell M, Morrison RM, Craft M. Role of animal movement and indirect contact among farms in transmission of porcine epidemic diarrhea virus.. Epidemics 2018 Sep;24:67-75.
  20. Chen S, White BJ, Sanderson MW, Amrine DE, Ilany A, Lanzas C. Highly dynamic animal contact network and implications on disease transmission.. Sci Rep 2014 Mar 26;4:4472.
    doi: 10.1038/srep04472pmc: PMC3966050pubmed: 24667241google scholar: lookup
  21. Webb CR. Investigating the potential spread of infectious diseases of sheep via agricultural shows in Great Britain.. Epidemiol Infect 2006 Feb;134(1):31-40.
    doi: 10.1017/S095026880500467Xpmc: PMC2870361pubmed: 16409648google scholar: lookup
  22. Myers C, Wilson WD. Equine influenza virus. Clin. Tech. Equine Pract. 2006;5:187–196.
  23. van Maanen C, Cullinane A. Equine influenza virus infections: an update.. Vet Q 2002 Jun;24(2):79-94.
    doi: 10.1080/01652176.2002.9695127pubmed: 12095083google scholar: lookup
  24. Constable PD, Hinchcliff KW, Done SH, Gruenberg W. Veterinary medicine. (W. B. Saunders), 10.1016/B978-0-7020-5246-0.00027-9 (2017).
  25. Cullinane A, Elton D, Mumford J. Equine influenza - surveillance and control.. Influenza Other Respir Viruses 2010 Nov;4(6):339-44.
  26. OIE World Organisation for Animal Health. Equine influenza: general disease information sheets. Available at: http://www.oie.int (2018).
  27. Wright B, Kenney D. Influenza in horses. (2011). Available at, http://www.omafra.gov.on.ca/. (Accessed: 13th March 2018).
  28. Equine Guelph. Equine biosecurity risk calculator. Available at, http://www.equineguelph.ca/Tools/biosecurity_calculator.php. (2018).
  29. Glass K, Wood JL, Mumford JA, Jesset D, Grenfell BT. Modelling equine influenza 1: a stochastic model of within-yard epidemics.. Epidemiol Infect 2002 Jun;128(3):491-502.
    doi: 10.1017/S0950268802006829pmc: PMC2869847pubmed: 12113495google scholar: lookup
  30. Park AW, Wood JL, Daly JM, Newton JR, Glass K, Henley W, Mumford JA, Grenfell BT. The effects of strain heterology on the epidemiology of equine influenza in a vaccinated population.. Proc Biol Sci 2004 Aug 7;271(1548):1547-55.
    doi: 10.1098/rspb.2004.2766pmc: PMC1691760pubmed: 15306299google scholar: lookup
  31. de la Rua-Domenech R, Reid SW, González-Zariquiey AE, Wood JL, Gettinby G. Modelling the spread of a viral infection in equine populations managed in Thoroughbred racehorse training yards.. Prev Vet Med 1999 Oct 19;47(1-2):61-77.
    doi: 10.1016/S0167-5877(00)00161-6pubmed: 11018735google scholar: lookup
  32. Park AW, Wood JL, Newton JR, Daly J, Mumford JA, Grenfell BT. Optimising vaccination strategies in equine influenza.. Vaccine 2003 Jun 20;21(21-22):2862-70.
    doi: 10.1016/S0264-410X(03)00156-7pubmed: 12798628google scholar: lookup
  33. Baguelin M, Newton JR, Demiris N, Daly J, Mumford JA, Wood JL. Control of equine influenza: scenario testing using a realistic metapopulation model of spread.. J R Soc Interface 2010 Jan 6;7(42):67-79.
    doi: 10.1098/rsif.2009.0030pmc: PMC2839373pubmed: 19364721google scholar: lookup
  34. Garner MG, Cowled B, East IJ, Moloney BJ, Kung NY. Evaluating the effectiveness of early vaccination in the control and eradication of equine influenza--a modelling approach.. Prev Vet Med 2011 Apr 1;99(1):15-27.
  35. Heesterbeek H. The law of mass-action in epidemiology: a historical perspectiveitle. Ecol. Paradig. lost routes theory Chang. 81–104 (2005).
  36. McCallum H, Barlow N, Hone J. How should pathogen transmission be modelled?. Trends Ecol Evol 2001 Jun 1;16(6):295-300.
    doi: 10.1016/S0169-5347(01)02144-9pubmed: 11369107google scholar: lookup
  37. Allen LJ, Brauer F, Van den Driessche P, Wu J. Mathematical epidemiology. (Springer 2008).
  38. Newman ME. Spread of epidemic disease on networks.. Phys Rev E Stat Nonlin Soft Matter Phys 2002 Jul;66(1 Pt 2):016128.
    doi: 10.1103/PhysRevE.66.016128pubmed: 12241447google scholar: lookup
  39. May RM. Network structure and the biology of populations.. Trends Ecol Evol 2006 Jul;21(7):394-9.
    doi: 10.1016/j.tree.2006.03.013pubmed: 16815438google scholar: lookup
  40. Scott J. Social network analysis. (SAGE Publications Limited 2017).
  41. Gumel AB. Causes of backward bifurcations in some epidemiological models. J. Math. Anal. Appl. 2012;395:355–365.
  42. Brauer F. Backward bifurcations in simple vaccination models. J. Math. Anal. Appl. 2004;298:418–431.
  43. Heffernan JM, Smith RJ, Wahl LM. Perspectives on the basic reproductive ratio.. J R Soc Interface 2005 Sep 22;2(4):281-93.
    doi: 10.1098/rsif.2005.0042pmc: PMC1578275pubmed: 16849186google scholar: lookup
  44. Arino J, McCluskey CC, van den Driessche P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM J. Appl. Math. 2003;64:260–276.
    doi: 10.1137/S0036139902413829google scholar: lookup
  45. R Core Team. R: A language and environment for statistical computing. (2016).
  46. Milwid RM, O'Sullivan TL, Poljak Z, Laskowski M, Greer AL. Comparison of the dynamic networks of four equine boarding and training facilities.. Prev Vet Med 2019 Jan 1;162:84-94.
  47. Handcock MS, Hunter DR, Butts CT, Goodreau SM, Morris M. statnet: Software tools for the Statistical Modeling of Network Data. (2003).
  48. Butts CT, Leslie-Cook A, Krivitsky PN, Bender-deMoll S. networkDynamic: Dynamic extensions for network objects. (2016).
  49. Jenness SM, Goodreau SM, Morris M. EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.. J Stat Softw 2018 Apr;84.
    pmc: PMC5931789pubmed: 29731699doi: 10.18637/jss.v084.i08google scholar: lookup
  50. Majecka K, Klawe A. Influence of Paddock Size on Social Relationships in Domestic Horses.. J Appl Anim Welf Sci 2018 Jan-Mar;21(1):8-16.
    doi: 10.1080/10888705.2017.1360773pubmed: 28820613google scholar: lookup
  51. Daly JM, Newton JR, Wood JL, Park AW. What can mathematical models bring to the control of equine influenza?. Equine Vet J 2013 Nov;45(6):784-8.
    doi: 10.1111/evj.12104pmc: PMC3935405pubmed: 23679041google scholar: lookup
  52. Daly JM, Murcia PR. Strategic implementation of vaccines for control of equine influenza.. Equine Vet J 2018 Mar;50(2):153-154.
    doi: 10.1111/evj.12794pubmed: 29392805google scholar: lookup
  53. Lewis NS, Daly JM, Russell CA, Horton DL, Skepner E, Bryant NA, Burke DF, Rash AS, Wood JL, Chambers TM, Fouchier RA, Mumford JA, Elton DM, Smith DJ. Antigenic and genetic evolution of equine influenza A (H3N8) virus from 1968 to 2007.. J Virol 2011 Dec;85(23):12742-9.
    pmc: PMC3209411pubmed: 21937642doi: 10.1128/jvi.05319-11google scholar: lookup

Citations

This article has been cited 2 times.
  1. Gonzalez-Obando J, Forero JE, Zuluaga-Cabrera AM, Ruiz-Saenz J. Equine Influenza Virus: An Old Known Enemy in the Americas.. Vaccines (Basel) 2022 Oct 14;10(10).
    doi: 10.3390/vaccines10101718pubmed: 36298583google scholar: lookup
  2. Fielding HR, Silk MJ, McKinley TJ, Delahay RJ, Wilson-Aggarwal JK, Gauvin L, Ozella L, Cattuto C, McDonald RA. Spatial and temporal variation in proximity networks of commercial dairy cattle in Great Britain.. Prev Vet Med 2021 Sep;194:105443.