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 Gulbudak
  • Vincent L. Cannataro
  • Necibe Tuncer
  • Maia Martcheva
Original Article

Abstract

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.

Keywords

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 

Notes

Acknowledgements

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.

References

  1. Anderson RM, May RM (1982) Coevolution of hosts and parasites. Parasitology 85:411–426CrossRefMATHGoogle Scholar
  2. Antia R, Levin BR, May RM (1994) Within-host population dynamics and the evolution and maintenance of microparasite virulence. Am Nat 457–472Google Scholar
  3. Antia R, Lipsitch M (1997) Mathematical models of parasite responses to host immune defences. Parasitology 115(07):155–167CrossRefGoogle Scholar
  4. Barreiro LB, Quintana-Murci L (2010) From evolutionary genetics to human immunology: how selection shapes host defence genes. Nat Rev Genet 11(1):17–30CrossRefGoogle Scholar
  5. Bird BH, Ksiazek TG, Nichol ST, Maclachlan NJ (2009) Rift Valley fever virus. J Am Vet Med Assoc 234:883–893CrossRefGoogle Scholar
  6. Bowers RG (2001) The basic depression ratio of the host: the evolution of host resistance to microparasites. Proc R Soc Lond B Biol Sci 268(1464):243–250CrossRefGoogle Scholar
  7. Bremermann HG, Thieme HR (1989) A competitive exclusion principle for pathogen virulence. J Math Biol 27:179–190MathSciNetCrossRefMATHGoogle Scholar
  8. Cai LM, Martcheva M, Li XZ (2013) Competitive exclusion in a vector–host epidemic model with distributed delay. J Biol Dyn 7:47–67MathSciNetCrossRefGoogle Scholar
  9. Ciota AT et al (2013) The evolution of virulence of West Nile virus in a mosquito vector: implications for arbovirus adaptation and evolution. BMC Evol Biol 13(1):1CrossRefGoogle Scholar
  10. Cressler CE et al (2016) The adaptive evolution of virulence: a review of theoretical predictions and empirical tests. Parasitology 143(07):915–930CrossRefGoogle Scholar
  11. Day T (2002) The evolution of virulence in vector-borne and directly transmitted parasites. Theor Popul Biol 62(2):199–213CrossRefMATHGoogle Scholar
  12. Day T, Proulx SR (2004) A general theory for the evolutionary dynamics of virulence. Am Nat 163(4):E40–E63CrossRefGoogle Scholar
  13. Dwyer G, Levin SA, Buttel L (1990) A simulation model of the population dynamics and evolution of myxomatosis. Ecol Monogr 60(4):423–447CrossRefGoogle Scholar
  14. Elliot SL, Adler FR, Sabelis MW (2003) How virulent should a parasite be to its vector? Ecology 84(10):2568–2574CrossRefGoogle Scholar
  15. Ewald PW (1983) Host-parasite relations, vectors, and the evolution of disease severity. Annu Rev Ecol Syst 14:465–485CrossRefGoogle Scholar
  16. Ewald PW (1994) Evolution of infectious disease. Oxford University Press on Demand, OxfordGoogle Scholar
  17. Feng Z, Velasco-Hernández JX (1997) Competitive exclusion in a vector–host model for the dengue fever. J Math Biol 35(5):523–544MathSciNetCrossRefMATHGoogle Scholar
  18. Fraser C et al (2014) Virulence and pathogenesis of HIV-1 infection: an evolutionary perspective. Science 343:1243727. doi: 10.1126/science.1243727 CrossRefGoogle Scholar
  19. Froissart R et al (2010) The virulence–transmission trade-off in vector-borne plant viruses: a review of (non-) existing studies. Philos Trans R Soc Lond B Biol Sci 365(1548):1907–1918CrossRefGoogle Scholar
  20. Ganusov VV, Bergstrom CT, Antia R (2002) Within-host population dynamics and the evolution of microparasites in a heterogeneous host population. Evolution 56(2):213–223CrossRefGoogle Scholar
  21. Ganusov VV, Antia R (2006) Imperfect vaccines and the evolution of pathogens causing acute infections in vertebrates. Evolution 60(5):957–969CrossRefGoogle Scholar
  22. Gilchrist MA, Sasaki A (2002) Modeling host-parasite coevolution: a nested approach based on mechanistic models. J Theor Biol 218:289–308MathSciNetCrossRefGoogle Scholar
  23. Gulbudak H, Martcheva M (2014) A structured avian influenza model with imperfect vaccination and vaccine-induced asymptomatic infection. Bull Math Biol 76(10):2389–2425MathSciNetCrossRefMATHGoogle Scholar
  24. Handel A, Rohani P (2015) Crossing the scale from within-host infection dynamics to transmission fitness: a discussion of current assumptions and knowledge. Philos Trans R Soc Lond B 370:20140302CrossRefGoogle Scholar
  25. Hellriegel B (2001) Immunoepidemiology bridging the gap between immunology and epidemiology. Trends Parasitol 17:102–106CrossRefGoogle Scholar
  26. Honjo T, Kinoshita K, Muramatsu M (2002) Molecular mechanism of class switch recombination: linkage with somatic hypermutation. Annu Rev Immunol 20:165–196CrossRefGoogle Scholar
  27. Kenney J, Brault A (2014) The role of environmental, virological and vector interactions in dictating biological transmission of arthropod-borne viruses by mosquitoes. Adv Virus Res 89:39–83CrossRefGoogle Scholar
  28. Lambrechts L, Scott TW (2009) Mode of transmission and the evolution of arbovirus virulence in mosquito vectors. Proc R Soc Lond B Biol Sci (rspb-2008)Google Scholar
  29. Lin C-J, Deger KA, Tien JH (2016) Modeling the trade-off between transmissibility and contact in infectious disease dynamics. Math Biosci 277:15–24MathSciNetCrossRefMATHGoogle Scholar
  30. Mackinnon MJ, Read A (1999) Selection for high and low virulence in the malaria parasite. Proc R Soc Lond B Biol Sci 266(1420):741–748CrossRefGoogle Scholar
  31. Magal P, McCluskey C (2013) Two-group infection age model including an application to nosocomial infection. SIAM J Appl Math 73(2):1058–1095MathSciNetCrossRefMATHGoogle Scholar
  32. Martcheva M, Tuncer N, Kim Y (2016) On the principle of host evolution in host–pathogen interactions. J Biol Dyn. doi: 10.1080/17513758.2016.1161089
  33. Morrill J, Knauert F, Ksiazek T (1989) Rift Valley fever infection of rhesus monkeys: implications for rapid diagnosis of human disease. Res Virol 140:139–146CrossRefGoogle Scholar
  34. Pepin M, Bouloy M, Bird BH, Kemp A, Paweska J (2010) Rift Valley fever virus (Bunyaviridae: Phlebovirus): an update on pathogenesis, molecular epidemiology, vectors, diagnostics and prevention. Vet Res 41:61CrossRefGoogle Scholar
  35. Pugliese A (2011) The role of host population heterogeneity in the evolution of virulence. J Biol Dyn 5(2):104–119MathSciNetCrossRefGoogle Scholar
  36. Tuncer N, Gulbudak H, Cannataro VL, Martcheva M (2016) Structural and practical identifiability issues of immuno-epidemiological vector–host models with application to Rift Valley Fever. Bull Math Biol 78(9):1796–1827MathSciNetCrossRefMATHGoogle Scholar
  37. Woolhouse MEJ, Webster JP, Domingo E, Charlesworth B, Levin BR (2002) Biological and biomedical implications of the co-evolution of pathogens and their hosts. Nat Genet 32:569–577CrossRefGoogle Scholar
  38. Yang JY, Li XZ, Martcheva M (2012) Global stability of a DS-DI epidemic model with age of infection. J Math Anal Appl 385:655–671MathSciNetCrossRefMATHGoogle Scholar
  39. Zhao X-Q (2013) Dynamical systems in population biology. Springer, BerlinGoogle Scholar

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

Personalised recommendations