Theoretical Ecology

, Volume 7, Issue 2, pp 163–179 | Cite as

Infectious disease in consumer populations: dynamic consequences of resource-mediated transmission and infectiousness

  • Paul J. HurtadoEmail author
  • Spencer R. Hall
  • Stephen P. Ellner


Nonhost species can strongly affect the timing and progression of epidemics. One central interaction—between hosts, their resources, and parasites—remains surprisingly underdeveloped from a theoretical perspective. Furthermore, key epidemiological traits that govern disease spread are known to depend on resource density. We tackle both issues here using models that fuse consumer–resource and epidemiological theory. Motivated by recent studies of a phytoplankton–zooplankton–fungus system, we derive and analyze a family of dynamic models for parasite spread among consumers in which transmission depends on consumer (host) and resource densities. These models yield four key insights. First, host–resource cycling can lower mean host density and inhibit parasite invasion. Second, host–resource cycling can create Allee effects (bistability) if parasites increase mean host density by reducing the amplitude of host–resource cycles. Third, parasites can stabilize host–resource cycles; however, host–resource cycling can also cause disease cycling. Fourth, resource dependence of epidemiological traits helps to govern the relative dominance of these different behaviors. However, these resource dependencies largely have quantitative rather than qualitative effects on these three-species dynamics. Given the extent of these results, host–resource–parasite interactions should become more fundamental components of the burgeoning theory for the community ecology of infectious diseases.


Host–parasite Predator–prey Transmission rate Oscillations Hydra effect Daphnia 



This article is based on the work in the lead author’s doctoral dissertation (Hurtado 2012) submitted in partial fulfillment of the requirements for a PhD in Applied Mathematics at Cornell University. Paul J. Hurtado thanks the Mathematical Biosciences Institute at The Ohio State University (NSF DMS 06-35561, 09-31642) for hosting him during the writing of this manuscript. Spencer R. Hall was supported by NSF grants DEB 06-13510 and DEB 06-14316. Stephen P. Ellner was supported by grant 220020137 from the James S. McDonnell Foundation and US National Science Foundation grant DEB 08-13743.

Supplementary material

12080_2013_208_MOESM1_ESM.pdf (611 kb)
(PDF 610 KB)


  1. Abrams PA (2009) When does greater mortality increase population size? The long history and diverse mechanisms underlying the hydra effect. Ecol Lett 12: 462–474PubMedCrossRefGoogle Scholar
  2. Anderson RM, May RM (1981) The population dynamics of microparasites and their invertebrate hosts. Phil Trans Roy Soc Lond B Biol Sci 291: 451–524CrossRefGoogle Scholar
  3. Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, OxfordGoogle Scholar
  4. Armstrong RA, McGehee R (1980) Competitive exclusion. Am Nat 115: 151–170CrossRefGoogle Scholar
  5. Bedhomme S, Agnew P, Sidobre C, Michalakis Y (2004) Virulence reaction norms across a food gradient. Proc Roy Soc Lond B Biol Sci 271: 739–744CrossRefGoogle Scholar
  6. Bittner K, Rothhaupt K-O, Ebert D (2002) Ecological Interactions of the microparasite Caullerya mesnili and its host Daphnia galeata. Limnol Oceanogr 47: 300–305CrossRefGoogle Scholar
  7. Cáceres CE, Knight CJ, Hall SR (2009) Predatorspreaders: predation can enhance parasite success in a planktonic hostparasite system. Ecology 90: 2850–2858sPubMedCrossRefGoogle Scholar
  8. Cintrón-Arias A, Castillo-Chávez C, Bettencourt LMA, Lloyd AL, Banks H (2009) The estimation of the effective reproductive number from disease outbreak data. Math Biosci Eng 6: 261–282PubMedCrossRefGoogle Scholar
  9. D’Amico V, Elkinton JS, Dwyer G, Willis RB, Montgomery ME (1998) Foliage damage does not affect within-season transmission of an insect virus. Ecology 79: 1104–1110CrossRefGoogle Scholar
  10. de Roode JC, Yates AJ, Altizer S (2008) Virulence-transmission trade-offs and population divergence in virulence in a naturally occurring butterfly parasite. Proc Natl Acad Sci 105: 7489–7494PubMedCentralPubMedCrossRefGoogle Scholar
  11. Duffy M, Hall S (2008) Selective predation and rapid evolution can jointly dampen effects of virulent parasites on Daphnia populations. Am Nat 171: 499–510PubMedCrossRefGoogle Scholar
  12. Duffy MA, Hall SR, Tessier AJ, Huebner M (2005) Selective predators and their parasitized prey: are epidemics in zooplankton under top-down control?Limnol Oceanogr 50: 412–420CrossRefGoogle Scholar
  13. Duffy MA, Housley JM, Penczykowski RM, Cáceres CE, Hall SR (2011) Unhealthy herds: indirect effects of predators enhance two drivers of disease spread. Funct Ecol 25: 945–953CrossRefGoogle Scholar
  14. Dwyer G, Dushoff J, Yee SH (2004) The combined effects of pathogens and predators on insect outbreaks. Nature 430: 341–345PubMedCrossRefGoogle Scholar
  15. Dwyer G, Firestone J, Stevens TE (2005) Should models of disease dynamics in herbivorous insects include the effects of variability in host-plant foliage quality?Am Nat 165: 16–31PubMedCrossRefGoogle Scholar
  16. Ebert D (2005) Ecology, epidemiology, and evolution of parasitism in Daphnia. National Library of Medicine (US), National Center for Biotechnology Information, Bethesda, MD. Accessed 8 Feb 2008
  17. Ebert D, Weisser WW (1997) Optimal killing for obligate killers: the evolution of life histories and virulence of semelparous parasites. Proc Roy Soc Lond B Biol Sci 264: 985–991CrossRefGoogle Scholar
  18. Ebert D, Carius HJ, Little T, Decaestecker E (2004) The evolution of virulence when parasites cause host castration and gigantism. Am Nat 164: S19–S32PubMedCrossRefGoogle Scholar
  19. Ebert D, Zschokke-Rohringer CD, Carius HJ (2000) Dose effects and density-dependent regulation of two microparasites of Daphnia magna. Oecologia 122: 200–209CrossRefGoogle Scholar
  20. Greenman J, Hudson P (1997) Infected coexistence instability with and without density-dependent regulation. J Theor Biol 185: 345–356CrossRefGoogle Scholar
  21. Grover JP (1997) Resource competition. In: Population and community biology, vol 19. Chapman & Hall, LondonGoogle Scholar
  22. Gubbins SC, Gilligan A, Kleczkowski A (2000) Population dynamics of plantparasite interactions: thresholds for invasion. J Theor Biol 57: 219–233CrossRefGoogle Scholar
  23. Guckenheimer J, Myers M (1996) Computing Hopf bifurcations. II: three examples from neurophysiology. SIAM J Sci Comput 17: 1275–1301CrossRefGoogle Scholar
  24. Guckenheimer J, Myers M, Sturmfels B (1997) Computing Hopf bifurcations I. SIAM J Numer Anal 34: 1–21CrossRefGoogle Scholar
  25. Hall S, Duffy M, Cáceres C (2005) Selective predation and productivity jointly drive complex behavior in host-parasite systems. Am Nat 165: 70–81PubMedCrossRefGoogle Scholar
  26. Hall SR, Tessier AJ, Duffy MA, Huebner M, Cáceres CE (2006) Warmer does not have to mean sicker: temperature and predators can jointly drive timing of epidemics. Ecology 87: 1684–1695PubMedCrossRefGoogle Scholar
  27. Hall SR, Sivars-Becker L, Becker C, Duffy MA, Tessier AJ, Cáceres CE (2007) Eating yourself sick: transmission of disease as a function of foraging ecology. Ecol Lett 10: 207–218PubMedCrossRefGoogle Scholar
  28. Hall S, Simonis J, Nisbet R, Tessier A, Cáceres C (2009a) Resource ecology of virulence in a planktonic host-parasite system: an explanation using dynamic energy budgets. Am Nat 174: 149–162CrossRefGoogle Scholar
  29. Hall SR, Becker CR, Simonis JL, Duffy MA, Tessier AJ, Cáceres CE (2009b) Friendly competition: evidence for a dilution effect among competitors in a planktonic host-parasite system. Ecol 90: 791–801CrossRefGoogle Scholar
  30. Hall SR, Knight CJ, Becker CR, Duffy MA, Tessier AJ, Cáceres CE (2009c) Quality matters: resource quality for hosts and the timing of epidemics. Ecol Lett 12: 118–128CrossRefGoogle Scholar
  31. Hall SR, Smyth R, Becker CR, Duffy MA, Knight CJ, MacIntyre S, Tessier AJ, Cáceres CE (2010) Why are Daphnia in some lakes sicker? Disease ecology, habitat structure, and the plankton. BioScience 60: 363–375CrossRefGoogle Scholar
  32. Hatcher MJ, Dick JTA, Dunn AM (2006) How parasites affect interactions between competitors and predators. Ecol Lett 9: 1253–1271PubMedCrossRefGoogle Scholar
  33. Hethcote H (1973) Asymptotic behavior in a deterministic epidemic model. Bull Math Biol 35: 607–614PubMedCrossRefGoogle Scholar
  34. Hethcote H, Levin S (1989) Periodicity in epidemiological models. In: Gross L, Hallam T, Levin S (eds) Applied mathematical ecology, vol 18. Springer, New York, pp 193–211CrossRefGoogle Scholar
  35. Hethcote HW, Stech HW, Driessche PVD (1981) Nonlinear oscillations in epidemic models. SIAM J Appl Math 40: 1–9CrossRefGoogle Scholar
  36. Hilker FM, Schmitz K (2008) Disease-induced stabilization of predator-prey oscillations. J Theor Biol 255: 299–306PubMedCrossRefGoogle Scholar
  37. Hilker FM, Langlais M, Malchow H (2009) The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations. Am Nat 173: 72–88PubMedCrossRefGoogle Scholar
  38. Holmes EE (1997) Basic epidemiological concepts in a spatial context. In: Tilman D, Kareiva PM (eds) Spatial ecology: the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, pp 111–136Google Scholar
  39. Holt RD, Roy M (2007) Predation can increase the prevalence of infectious disease. Am Nat 169: 690–699PubMedCrossRefGoogle Scholar
  40. Holt RD, Dobson AP, Begon M, Bowers RG, Schauber EM (2003) Parasite establishment in host communities. Ecol Lett 6: 837–842CrossRefGoogle Scholar
  41. Hunter MD, Schultz JC (1993) Induced plant defenses breached? Phytochemical induction protects an herbivore from disease. Oecologia 94: 195–203. doi:10.1007/BF00.341317CrossRefGoogle Scholar
  42. Hurtado PJ (2012) Infectious disease ecology: immune-pathogen dynamics, and how trophic interactions drive prey-predator-disease dynamics. PhD thesis. Cornell UniversityGoogle Scholar
  43. Jensen CX, Ginzburg LR (2005) Paradoxes or theoretical failures? The jury is still out. Ecol Model 188: 3–14CrossRefGoogle Scholar
  44. Johnson PTJ, Chase JM, Dosch KL, Hartson RB, Gross JA, Larson DJ, Sutherland DR, Carpenter SR (2007) Aquatic eutrophication promotes pathogenic infection in amphibians. Proc Natl Acad Sci 104: 15781–15786PubMedCentralPubMedCrossRefGoogle Scholar
  45. Keating S, Schultz J, Yendol W (1990) The effect of diet on gypsy moth (Lymantria dispar) larval midgut pH, and its relationship with larval susceptibility to a baculovirus. J Invertebr Pathol 56: 317–326CrossRefGoogle Scholar
  46. Keeling MJ, Rohani P (2008) Modeling infectious diseases in humans and animals. Princeton University Press, PrincetonGoogle Scholar
  47. Keesing F, Holt RD, Ostfeld RS (2006) Effects of species diversity on disease risk. Ecol Lett 9: 485–498PubMedCrossRefGoogle Scholar
  48. Kirk KL (1998) Enrichment can stabilize population dynamics: autotoxins and density dependence. Ecology 79: 2456–2462CrossRefGoogle Scholar
  49. Liu W-m, Levin SA, Iwasa Y (1986) Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J Math Biol 23: 187–204PubMedCrossRefGoogle Scholar
  50. London WP, Yorke JA (1973) Recurrent outbreaks of measles, chickenpox and mumps. Am J Epidemiol 98: 453–468PubMedGoogle Scholar
  51. Matsuda H, Abrams PA (2004) Effects of predator-prey interactions and adaptive change on sustainable yield. Can J Fish Aquat Sci 61: 175–184CrossRefGoogle Scholar
  52. McCauley E, Murdoch WW (1990) Predatorprey dynamics in environments rich and poor in nutrients. Nature 343: 455–457CrossRefGoogle Scholar
  53. McCauley E, Nisbet RM, Murdoch WW, de Roos AM, Gurney WSC (1999) Large-amplitude cycles of Daphnia and its algal prey in enriched environments. Nature 402: 653–656CrossRefGoogle Scholar
  54. Murdoch WW, Briggs CJ, Nisbet RM (2003) Consumer-resource dynamics. Monographs in population biology, vol 36. Princeton University Press, PrincetonGoogle Scholar
  55. Norman R, Bowers R, Begon M, Hudson P (1999) Persistence of tick-borne virus in the presence of multiple host species: tick reservoirs and parasite mediated competition. J Theor Biol 200: 111–118PubMedCrossRefGoogle Scholar
  56. Ostfeld RS, Holt RD (2004) Are predators good for your health? Evaluating evidence for top-down regulation of zoonotic disease reservoirs. Front Ecol Environ 2: 13–20CrossRefGoogle Scholar
  57. Ostfeld RS, Keesing F (2000) The function of biodiversity in the ecology of vector-borne zoonotic diseases. Can J Zool 78: 2061–2078CrossRefGoogle Scholar
  58. Packer C, Holt RD, Hudson PJ, Lafferty KD, Dobson AP (2003) Keeping the herds healthy and alert: implications of predator control for infectious disease. Ecol Lett 6: 797–802CrossRefGoogle Scholar
  59. Porter KG, Gerritsen J, Orcutt J, John D (1982) The effect of food concentration on swimming patterns, feeding behavior, ingestion, assimilation, and respiration by Daphnia. Limnol Oceanogr 27: 935–949CrossRefGoogle Scholar
  60. Pulkkinen K, Ebert D (2004) Host starvation decreases parasite load and mean host size in experimental populations. Ecology 85: 823–833CrossRefGoogle Scholar
  61. Regoes RR, Ebert D, Bonhoeffer S (2002) Dosedependent infection rates of parasites produce the Allee effect in epidemiology. Proc Roy Soc Lond B Biol Sci 269: 271–279CrossRefGoogle Scholar
  62. Rosenzweig ML (1971) Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171: 385–387PubMedCrossRefGoogle Scholar
  63. Ryder JJ, Hathway J , Knell RJ (2007) Constraints on parasite fecundity and transmission in an insect-STD system. Oikos 116: 578–584CrossRefGoogle Scholar
  64. Scheffer M, Rinaldi S, Kuznetsov YA, van Nes EH (1997) Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system. Oikos 80: 519–532CrossRefGoogle Scholar
  65. Scheffer M, Rinaldi S, Kuznetsov YA (2000) Effects of fish on plankton dynamics: a theoretical analysis. Can J Fish Aquat Sci 57: 1208–1219CrossRefGoogle Scholar
  66. Sieber M, Hilker F (2011) The hydra effect in predatorprey models. J Math Biol Online: 1–20Google Scholar
  67. Sorokin C, Krauss RW (1958) The Effects of light intensity on the growth rates of green algae. Plant Physiol 33: 109–113PubMedCentralPubMedCrossRefGoogle Scholar
  68. Tessier AJ, Woodruff P (2002) Cryptic trophic cascade along a gradient of lake size. Ecol 83: 1263–1270CrossRefGoogle Scholar
  69. Tseng M (2004) Sexspecific response of a mosquito to parasites and crowding. Proc Roy Soc Lond B Biol Sci 271: S186–S188CrossRefGoogle Scholar
  70. Tseng M (2006) Interactions between the parasite’s previous and current environment mediate the outcome of parasite infection. Am Nat 168: 565–571PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Paul J. Hurtado
    • 1
    Email author
  • Spencer R. Hall
    • 2
  • Stephen P. Ellner
    • 3
  1. 1.Center for Applied MathematicsCornell UniversityNYUSA
  2. 2.Department of BiologyIndiana UniversityINUSA
  3. 3.Center for Applied Mathematics, Department of Ecology and Evolutionary BiologyCornell UniversityIthacaUSA

Personalised recommendations