Bulletin of Mathematical Biology

, Volume 79, Issue 2, pp 325–355 | Cite as

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System

  • Hayriye GulbudakEmail author
  • Vincent L. Cannataro
  • Necibe Tuncer
  • Maia Martcheva
Original Article


Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host’s immune system influences the pathogen’s transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence–transmission trade-offs and evolution in vector-borne pathogen–host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley fever and West Nile virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the \({\mathcal {R}}_0\) maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen \({\mathcal {R}}_0\), but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways.


Immuno-epidemiological modeling Rift Valley fever West Nile virus Vector-borne pathogen Differential equations Reproduction number Vector inoculum size Age-since-infection Within-host dynamics Coevolutionary attractor Trade-offs 

Mathematics Subject Classification

92D30 92D40 



The authors H. Gulbudak and V. Cannataro acknowledge partial support from IGERT Grant NSF DGE-0801544 in the Quantitative Spatial Ecology, Evolution and Environment Program at the University of Florida. Authors N. Tuncer and M. Martcheva would also like to acknowledge support from the National Science Foundation (NSF) under Grants DMS-1515661/DMS-1515442.


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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  1. 1.School of Biological Sciences and School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of BiologyUniversity of FloridaGainesvilleUSA
  3. 3.Department of Mathematical SciencesFlorida Atlantic UniversityBoca RatonUSA
  4. 4.Department of MathematicsUniversity of FloridaGainesvilleUSA

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