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Bulletin of Mathematical Biology

, Volume 78, Issue 2, pp 235–253 | Cite as

Effects of Intrinsic and Extrinsic Host Mortality on Disease Spread

  • Z. RaptiEmail author
  • C. E. Cáceres
Original Article

Abstract

The virulent effects of a pathogen on host fecundity and mortality (both intrinsic and extrinsic mortality due to predation) often increase with the age of infection. Age of infection often is also correlated with parasite fitness, in terms of the number of both infective propagules produced and the between-host transmission rate. We introduce a four-population partial differential equations (PDE) model to investigate the invasibility and prevalence of an obligately killing fungal parasite in a zooplankton host as they are embedded in an ecological network of predators and resources. Our results provide key insights into the role of ecological interactions that vary with the age of infection. First, selective predation, which is known both theoretically and empirically to reduce disease prevalence, does not always limit disease spread. This condition dependency relies on the timing and intensity of selective predation and how that interacts with the direct effects of the parasite on host mortality. Second, low host resources and intense predation can prevent disease spread, but once conditions allow the invasion of the parasite, the qualitative dynamics of the system do not depend on the intensity of the selective predation. Third, a comparison of the PDE model with a model based on ordinary differential equations (ODE model) reveals a parametrization for the ODE version that yields an endemic steady state and basic reproductive ratio that are identical to those in the PDE model. Our results highlight the complexity of resource–host–parasite–predator interactions and suggest the need for additional data–theory coupling exploring how community ecology influences the spread of infectious diseases.

Keywords

Daphnia Epidemic model Partial differential equations Age of infection Predators Virulence 

Mathematics Subject Classification

35Q92 92D30 92D40 

Notes

Acknowledgments

We gratefully acknowledge support from the Illinois Campus Research Board through Grant 14038 and the National Science Foundation through Grants DUE-1129198, DEB-1120804 and DEB-1354407. We also thank an anonymous referee for his thoughtful comments and suggestions.

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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.School of Integrative BiologyUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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