Bulletin of Mathematical Biology

, Volume 81, Issue 6, pp 2011–2028 | Cite as

Modeling Approach Influences Dynamics of a Vector-Borne Pathogen System

  • Allison K. ShawEmail author
  • Morganne Igoe
  • Alison G. Power
  • Nilsa A. Bosque-Pérez
  • Angela Peace


The choice of a modeling approach is a critical decision in the modeling process, as it determines the complexity of the model and the phenomena that the model captures. In this paper, we developed an individual-based model (IBM) and compared it to a previously published ordinary differential equation (ODE) model, both developed to describe the same biological system although with slightly different emphases given the underlying assumptions and processes of each modeling approach. We used both models to examine the effect of insect vector life history and behavior traits on the spread of a vector-borne plant virus, and determine how choice of approach affects the results and their biological interpretation. A non-random distribution of insect vectors across plant hosts emerged in the IBM version of the model and was not captured by the ODE. This distribution led simultaneously to a slower-growing vector population and a faster spread of the pathogen among hosts. The IBM model also enabled us to test the effect of potential control measures to slow down virus transmission. We found that removing virus-infected hosts was a more effective strategy for controlling infection than removing vector-infested hosts. Our findings highlight the need to carefully consider possible modeling approaches before constructing a model.


Barley yellow dwarf virus Individual-based model Mean field Ordinary differential equation Vector-borne plant pathogen 



We thank members of the Shaw lab and two anonymous reviewers for helpful advice and insight. We acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper (

Supplementary material

11538_2019_595_MOESM1_ESM.pdf (109 kb)
Supplementary material 1 (pdf 110 KB)


  1. Ajayi BO, Dewar AM (1983) The effect of barley yellow dwarf virus on field populations of the cereal aphids, Sitobion avenae and Metopolophium dirhodum. Ann Appl Biol 103(1):1–11Google Scholar
  2. Bazghandi A (2012) Techniques, advantages and problems of agent based modeling for traffic simulation. Int J Comput Sci 9(1):115–119Google Scholar
  3. Bolnick DI, Amarasekare P, Arajo MS, Bürger R, Levine JM, Novak M, Rudolf VH, Schreiber SJ, Urban MC, Vasseur DA (2011) Why intraspecific trait variation matters in community ecology. Trends Ecol Evolut 26(4):183–192CrossRefGoogle Scholar
  4. Champagnat N, Méléard S (2007) Invasion and adaptive evolution for individual-based spatially structured populations. J Math Biol 55(2):147–188MathSciNetCrossRefzbMATHGoogle Scholar
  5. DeAngelis DL, Mooij W (2005) Individual-based modeling of ecological and evolutionary processes. Ann Rev Ecol Evolut Syst 36:147–168CrossRefGoogle Scholar
  6. Dixon AFG, Glen DM (1971) Morph determination in the bird cherry-oat aphid, Rhopalosiphum padi L. Ann Appl Biol 68(1):11–21Google Scholar
  7. Durrett R, Levin SA (1994) The importance of being discrete (and spatial). Theor Popul Biol 46:363–363Google Scholar
  8. Figueredo GP, Siebers PO, Aickelin U (2013) Investigating mathematical models of immuno-interactions with early-stage cancer under an agent-based modelling perspective. BMC Bioinform 14:S6CrossRefGoogle Scholar
  9. Hosseini PR (2003) How localized consumption stabilizes predator-prey systems with finite frequency of mixing. Am Nat 161(4):567–585CrossRefGoogle Scholar
  10. Ingwell LL, Eigenbrode SD, Bosque-Pérez NA (2012) Plant viruses alter insect behavior to enhance their spread. Sci Rep 2:578CrossRefGoogle Scholar
  11. Irwin ME, Thresh JM (1990) Epidemiology of barley yellow dwarf: a study in ecological complexity. Ann Rev Phytopathol 28:393–424CrossRefGoogle Scholar
  12. Jeger MJ, Chan MS (1995) Theoretical aspects of epidemics: uses of analytical models to make strategic management decisions. Can J Plant Pathol 17(2):109–114CrossRefGoogle Scholar
  13. Jensen JLWV (1906) Sur les fonctions convexes et les ingalits entre les valeurs moyennes. Acta Math 30(1):175–193MathSciNetCrossRefzbMATHGoogle Scholar
  14. Jiménez-Martnez ES, Bosque-Pérez NA (2004) Variation in Barley yellow dwarf virus transmission efficiency by Rhopalosiphum padi (Homoptera: Aphididae) after acquisition from transgenic and nontransformed wheat genotypes. J Econ Entomol 97(6):1790–1796Google Scholar
  15. Jiménez-Martnez ES, Bosque-Pérez NA, Berger PH, Zemetra RS (2004) Life history of the bird cherry-oat aphid, Rhopalosiphum padi (Homoptera: Aphididae), on transgenic and untransformed wheat challenged with Barley yellow dwarf virus. J Econ Entomol 97(2):203–212Google Scholar
  16. Keeling MJ, Grenfell BT (2000) Individual-based perspectives on \(R_0\). J Theor Biol 203(1):51–61CrossRefGoogle Scholar
  17. Keitt TH (1997) Stability and complexity on a lattice: coexistence of species in an individual-based food web model. Ecol Model 102(2–3):243–258CrossRefGoogle Scholar
  18. Kiureghian AD, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Struct Saf 31(2):105–112CrossRefGoogle Scholar
  19. Levins R (1966) The strategy of model building in population biology. Am Sci 54(4):421–431Google Scholar
  20. Magal P, Ruan S (2014) Susceptible-infectious-recovered models revisited: from the individual level to the population level. Math Biosci 250:26–40MathSciNetCrossRefzbMATHGoogle Scholar
  21. Marino S, Hogue IB, Ray CJ, Kirschner DE (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254(1):178–196MathSciNetCrossRefzbMATHGoogle Scholar
  22. Railsback S, Grimm V (2012) Agent-based and individual-based modeling: a practical introduction. Princeton University Press, Princeton, NJzbMATHGoogle Scholar
  23. Scholl HJ (2001) Agent-based and system dynamics modeling: a call for cross study and joint research. In: Proceedings of the 34th annual Hawaii international conference on system sciences, 2001. IEEE, pp 1–8Google Scholar
  24. Shaw AK, Peace A, Power AG, Bosque-Prez NA (2017) Vector population growth and condition-dependent movement drive the spread of plant pathogens. Ecology 98:2145–2157CrossRefGoogle Scholar
  25. Shaw AK, Peace A, Power AG, Bosque-Prez NA (2018) Errata. Vector population growth and condition-dependent movement drive the spread of plant pathogens. Ecology 99:2904CrossRefGoogle Scholar
  26. Thresh JM (1988) Eradication as a virus disease control measure. In: Clifford BC, Lester E (eds) Control of plant diseases: costs and benefits. Blackwell Scientific Publications, Oxford, pp 155–194Google Scholar
  27. Ward SA, Leather SL, Pickup J, Harrington R (1998) Mortality during dispersal and the cost of host-specificity in parasites: How many aphids find hosts? J Anim Ecol 67:763–773CrossRefGoogle Scholar
  28. Young WR, Roberts AJ, Stuhne G (2001) Reproductive pair correlations and the clustering of organisms. Nature 412(6844):328–331CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of Ecology, Evolution, and BehaviorUniversity of MinnesotaSt. PaulUSA
  2. 2.Department of MathematicsUniversity of MinnesotaMinneapolisUSA
  3. 3.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  4. 4.Department of Ecology and Evolutionary BiologyCornell UniversityIthacaUSA
  5. 5.Department of Entomology, Plant Pathology and NematologyUniversity of IdahoMoscowUSA
  6. 6.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA

Personalised recommendations