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Mathematical Analysis of the Impact of Social Structure on Ectoparasite Load in Allogrooming Populations

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Understanding Complex Biological Systems with Mathematics

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 14))

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Abstract

In many social species, there exist a few highly connected individuals living among a larger majority of poorly connected individuals. Previous studies have shown that, although this social network structure may facilitate some aspects of group-living (e.g., collective decision-making), these highly connected individuals can act as super-spreaders of circulating infectious pathogens. We build on this literature to instead consider the impact of this type of network structure on the circulation of ectoparasitic infections in a population. We consider two ODE models that each approximate a simplified network model; one with uniform social contacts, and one with a few highly connected individuals. We find that, rather than increasing risk, the inclusion of highly connected individuals increases the probability that a population will be able to eradicate ectoparasitic infection through social grooming.

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References

  1. L.J. Allen, Some discrete-time SI, SIR, and SIS epidemic models. Math. Biosci. 124, 83–105 (1994)

    Article  Google Scholar 

  2. L.J. Allen, A.M. Burgin, Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math. Biosci. 163(1), 1–33 (2000)

    Article  MathSciNet  Google Scholar 

  3. G. An, Agent-based computer simulation and SIRS: building a bridge between basic science and clinical trials. Shock 16(4), 266–273 (2001)

    Article  Google Scholar 

  4. R.M. Anderson, R.M. May, Population biology of infectious diseases Part I. Nature 280, 361–367 (1979)

    Article  Google Scholar 

  5. A.-L. Barabasi, Scale-free networks: a decade and beyond. Science 325(5939), 412–413 (2009)

    Article  MathSciNet  Google Scholar 

  6. A.-L. Barabási, E. Bonabeau, Scale-free networks. Sci. Am. 288(5), 60–69 (2003)

    Article  Google Scholar 

  7. C. Dhanaraj, A. Parkhe, Orchestrating innovation networks. Acad. Manag. Rev. 31(3), 659–669 (2006)

    Article  Google Scholar 

  8. S. Drozdz, Physical approach to complex systems. Phys. Rep. Rev. Sect. Phys. Lett. 515(3–4), 115–226 (2012)

    MathSciNet  Google Scholar 

  9. W. Duan, Z. Fan, P. Zhang, G. Guo, X. Qiu, Mathematical and computational approaches to epidemic modeling: a comprehensive review. Front. Comput. Sci. 9(5), 806–826 (2015)

    Article  Google Scholar 

  10. K. Eames, S. Bansal, S. Frost, S. Riley, Six challenges in measuring contact networks for use in modelling. Epidemics 10, 72–77 (2015)

    Article  Google Scholar 

  11. N. Fefferman, K. Ng, How disease models in static networks can fail to approximate disease in dynamic networks. Phys. Rev. E 76, 031919 (2007)

    Article  MathSciNet  Google Scholar 

  12. N.H. Fefferman, K.L. Ng, The role of individual choice in the evolution of social complexity. Ann. Zool. Fenn. 44, 58–69 (2007). JSTOR

    Google Scholar 

  13. R.H. Griffin, C.I. Nunn, Community structure and the spread of infectious disease in primate social networks. Evol. Ecol. 26, 779–800 (2012)

    Article  Google Scholar 

  14. K. Hock, N.H. Fefferman, Social organization patterns can lower disease risk without associated disease avoidance or immunity. Ecol. Complex. 12, 34–42 (2012)

    Article  Google Scholar 

  15. W. Huang, C. Li, Epidemic spreading in scale-free networks with community structure. J. Stat. Mech: Theory Exp. 2007(01), P01014 (2007)

    Article  Google Scholar 

  16. P. Jordano, J. Bascompte, J. Olesen, Invariant properties in coevolutionary networks of plant-animal interactions. Ecol. Lett. 6(1), 69–81 (2003)

    Article  Google Scholar 

  17. W. Karesh, R. Cook, E. Bennett, J. Newcomb, Wildlife trace and global disease emergence. Emerg. Infect. Dis. 11(7), 1000–1002 (2005)

    Article  Google Scholar 

  18. M. Keeling, The effects of local spatial structure on epidemiological invasions. Proc. Biol. Sci. 266, 859–867 (1999)

    Article  Google Scholar 

  19. W. Kermack, A. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. A 700–721 (1927). https://doi.org/10.1098/rspa.1927.0118

    Article  Google Scholar 

  20. S. Lion, S. Gandon, Evolution of spatially structured host-parasite interactions. J. Evol. Biol. 28, 10–28 (2015)

    Article  Google Scholar 

  21. A. Mactintosh, C. Jacobs, A. Nad Garcia, K. Shimizu, K. Mouri, M. Huffman, A. Hernandez, Monkeys in the middle: parasite transmission through the social network of a wild primate. PLoSOne 7, e51144 (2012)

    Article  Google Scholar 

  22. M. Newman, The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)

    Article  MathSciNet  Google Scholar 

  23. R. Pastor-Santoras, A. Vespignani, Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86(14), 3200–3203 (2001)

    Article  Google Scholar 

  24. M. Peltomäki, V. Vuorinen, M. Alava, M. Rost, Host-parasite models on graphs. Phys. Rev. E 72(4), 046134 (2005)

    Google Scholar 

  25. S. Riley, K. Eames, V. Isham, D. Mollison, P. Trapman, Five challenges for spatial epidemic models. Epidemics 10, 68–71 (2015)

    Article  Google Scholar 

  26. R.B. Rosengaus, A.B. Maxmen, L.E. Coates, J.F. Traniello, Disease resistance: a benefit of sociality in the dampwood termite Zootermopsis angusticollis (Isoptera: Termopsidae). Behav. Ecol. Sociobiol. 44(2), 125–134 (1998)

    Article  Google Scholar 

  27. P. Sah, J. Mann, S. Bansal, Disease implications of animal social network structure: a synthesis across social systems. Cold Spring Harbor Laboratory, February 2017. https://doi.org/10.1111/1365-2656.12786

    Article  Google Scholar 

  28. D. Salkeld, M. Salathé, P. Stapp, J. Johes, Plague outbreaks in prairie dog populations explained by percolation threshold of alternate host abundance. Proc. Natl. Acad. Sci. U.S.A. 107, 14247–14250 (2010)

    Article  Google Scholar 

  29. C. Sauter, R. Morris, Dominance hierarchies in cattle and red deer (Cerus elaphus): their possible relationship to the transmission of bovine tuberculosis. N. Z. Vet. J. 43, 301–305 (1995)

    Article  Google Scholar 

  30. P. Schmid-Hempel, Parasites and their social hosts. Trends Parasitol. 33(6), 453–462 (2017)

    Article  Google Scholar 

  31. S.D. Webb, M.J. Keeling, M. Boots, Host-parasite interactions between the local and the mean-field: how and when does spatial population structure matter? J. Theor. Biol. 249, 140–152 (2007)

    Article  MathSciNet  Google Scholar 

  32. R. West, J. Thompson, Models for the simple epidemic. Math. Biosci. 141(1), 29–39 (1997)

    Article  Google Scholar 

  33. T. Wey, D.T. Blumstein, W. Shen, F. Jordán, Social network analysis of animal behaviour: a promising tool for the study of sociality. Anim. Behav. 75(2), 333–344 (2008)

    Article  Google Scholar 

  34. S.H. Whilte, A.M. del Rey, G.R. Sanchez, Modeling epidemics using cellular automata. Appl. Math. Comput. 186(1), 193–202 (2007)

    MathSciNet  MATH  Google Scholar 

  35. L.A. White, J.D. Forester, M.E. Craft, Dynamic, spatial models of parasite transmission in wildlife: their structure, applications and remaining challenges. J. Anim. Ecol. 87, 1–22 (2017)

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of Utah, Salt Lake City, UT, USA

    Heather Z. Brooks

  2. University of California, Santa Barbara, Santa Barbara, CA, USA

    Maryann E. Hohn

  3. University of San Diego, San Diego, CA, USA

    Candice R. Price

  4. Mathematics Department, Pomona College, Claremont, CA, USA

    Ami E. Radunskaya

  5. University of California Merced, Merced, CA, USA

    Suzanne S. Sindi

  6. United States Military Academy, West Point, NY, USA

    Nakeya D. Williams

  7. Morehouse College, Atlanta, GA, USA

    Shelby N. Wilson

  8. University of Tennessee, Knoxville, TN, USA

    Nina H. Fefferman

Authors
  1. Heather Z. Brooks
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  2. Maryann E. Hohn
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  3. Candice R. Price
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  4. Ami E. Radunskaya
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  5. Suzanne S. Sindi
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  6. Nakeya D. Williams
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  7. Shelby N. Wilson
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  8. Nina H. Fefferman
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Editor information

Editors and Affiliations

  1. Mathematics Department, Pomona College, Claremont, CA, USA

    Ami Radunskaya

  2. Department of Mathematics, Virginia Commonwealth University, Richmond, VA, USA

    Rebecca Segal

  3. Mathematics Department, Pomona College, Claremont, CA, USA

    Blerta Shtylla

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© 2018 The Author(s) and the Association for Women in Mathematics

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Brooks, H.Z. et al. (2018). Mathematical Analysis of the Impact of Social Structure on Ectoparasite Load in Allogrooming Populations. In: Radunskaya, A., Segal, R., Shtylla, B. (eds) Understanding Complex Biological Systems with Mathematics. Association for Women in Mathematics Series, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-98083-6_3

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