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Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 234-264. doi: 10.3934/mbe.2019013
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Modeling nutrient and disease dynamics in a plant-pathogen system

  • 1.
    Department of Mathematics, Statistics, and Computer Science, St. Olaf College, Northfield, MN 55057, USA
  • 2.
    Agronomy Department, University of Florida, Gainesville, FL 32611, USA
  • 3.
    Department of Ecology, Evolution, and Behavior, University of Minnesota, St. Paul, MN 55108, USA
  • 4.
    School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
  • Received: 30 October 2018 Accepted: 30 October 2018 Published: 12 December 2018

  • Human activities alter elemental nutrient cycling, which can have profound impacts on agriculture, grasslands, lakes, and other systems. It is becoming increasingly clear that enhanced nitrogen and phosphorus levels can affect disease dynamics across a range of taxa. However, there are few mathematical models that explicitly incorporate nutrients into host-pathogen interactions. Using viral load and plant mass data from an experiment with cereal yellow dwarf virus and its host plant, Avena sativa, we propose and compare two models describing the overall infection dynamics. However, the first model considers nutrient-limited virus production while the other considers a nutrient-induced viral production delay. A virus reproduction number is derived for this nutrient model, which depends on environmental and physiological attributes. Results suggest that including nutrient mediated viral production mechanisms can give rise to robust models that can be used to untangle how nutrients impact pathogen dynamics.

    Citation: Bruce Pell, Amy E. Kendig, Elizabeth T. Borer, Yang Kuang. Modeling nutrient and disease dynamics in a plant-pathogen system[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 234-264. doi: 10.3934/mbe.2019013

    Related Papers:

  • Human activities alter elemental nutrient cycling, which can have profound impacts on agriculture, grasslands, lakes, and other systems. It is becoming increasingly clear that enhanced nitrogen and phosphorus levels can affect disease dynamics across a range of taxa. However, there are few mathematical models that explicitly incorporate nutrients into host-pathogen interactions. Using viral load and plant mass data from an experiment with cereal yellow dwarf virus and its host plant, Avena sativa, we propose and compare two models describing the overall infection dynamics. However, the first model considers nutrient-limited virus production while the other considers a nutrient-induced viral production delay. A virus reproduction number is derived for this nutrient model, which depends on environmental and physiological attributes. Results suggest that including nutrient mediated viral production mechanisms can give rise to robust models that can be used to untangle how nutrients impact pathogen dynamics.


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    [1] G. Ågren, Ideal nutrient productivities and nutrient proportions in plant growth, Plant Cell Environment, 11 (1988), 613–620.
    [2] M. Ali, S. Hameed, and M. Tahir, Luteovirus: insights into pathogenicity, Arc. Virol., 159 (2014), 2853–2860.
    [3] S. Alizon, M. van Baalen, A. E. J. Jokela, and E. M. A. Geber, Multiple infections, immune dynamics, and the evolution of virulence, Am. Nat., 172 (2008), E150–E168.
    [4] R. Antia, B. R. Levin, and R. M. May, Within-host population dynamics and the evolution and maintenance of microparasite virulence, Am. Nat., 144 (1994), 457–472.
    [5] N. Bacaër. The model of kermack and mckendrick for the plague epidemic in bombay and the type reproduction number with seasonality, J. Math. Biol., 64 (2012), 403–422.
    [6] M. Barfield, M. E. Orive, and R. D. Holt, The role of pathogen shedding in linking within-and between-host pathogen dynamics, Math. Biosci., 2015.
    [7] A. Béchette, T. Stojsavljevic, M. Tessmer, J. A. Berges, G. A. Pinter, and E. B. Young, Mathematical modeling of bacteria-virus interactions in lake michigan incorporating phosphorus content, J. Great Lake. Res., 39 (2013), 646–654.
    [8] E. Beretta and Y. Kuang, Modeling and analysis of a marine bacteriophage infection with latency period, Nonlinear Analys. Real World Appl., 2 (2001), 35–74.
    [9] E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Analys., 33 (2002), 1144–1165.
    [10] E. W. Birch, N. A. Ruggero, and M. W. Covert, Determining host metabolic limitations on viral replication via integrated modeling and experimental perturbation, 2012.
    [11] E. Borer, E. Seabloom, C. Mitchell, and A. Power, Local context drives infection of grasses by vector-borne generalist viruses, Ecol. Lett., 13 (2010), 810–818.
    [12] E. T. Borer, E. W. Seabloom, D. S. Gruner, W. S. Harpole, H. Hillebrand, E. M. Lind, P. B. Adler, J. Alberti, T. M. Anderson, J. D. Bakker, L. Biederman, D. Blumenthal, C. S. Brown, L. A. Brudvig, Y. M. Buckley, M. Cadotte, C. Chu, E. E. Cleland, M. J. Crawley, P. Daleo, E. I. Damschen, K. F. Davies, N. M. DeCrappeo, G. Du, J. Firn, Y. Hautier, R.W. Heckman, A. Hector, J. HilleRis- Lambers, O. Iribarne, J. A. Klein, J. M. H. Knops, K. J. La Pierre, A. D. B. Leakey, W. Li, A. S. MacDougall, R. L. McCulley, B. A. Melbourne, C. E. Mitchell, J. L. Moore, B. Mortensen, L. R. O'Halloran, J. L. Orrock, J. Pascual, S. M. Prober, D. A. Pyke, A. C. Risch, M. Schuetz, M. D. Smith, C. J. Stevens, L. L. Sullivan, R. J. Williams, P. D. Wragg, J. P. Wright, and L. H. Yang. Herbivores and nutrients control grassland plant diversity via light limitation, Nature, 508 (2014), 517.
    [13] E. T. Borer, E. W. Seabloom, C. E. Mitchell, and J. P. Cronin, Multiple nutrients and herbivores interact to govern diversity, productivity, composition, and infection in a successional grassland, Oikos, 123 (2014), 214–224.
    [14] G. Bratbak, A. Jacobsen, M. Heldal, K. Nagasaki, and F. Thingstad, Virus production in phaeocystis pouchetii and its relation to host cell growth and nutrition, Aquat. Microb. Ecol., 16 (1998),1–9.
    [15] L. Carrigan, H. Ohm, and J. Foster, Barley yellow dwarf virus translocation in wheat and oats, Crop Sci., 23 (1988), 611–612.
    [16] R. A. Chillakuru, D. D. Ryu, and T. Yilma, Propagation of recombinant vaccinia virus in hela cells: adsorption kinetics and replication in batch cultures, Biotechnol. Progress, 7 (1991), 85–92.
    [17] C. A. Clark, J. A. Davis, J. A. Abad, W. J. Cuellar, S. Fuentes, J. F. Kreuze, R. W. Gibson, S. B. Mukasa, A. K. Tugume, F. D. Tairo, AND J. P.T. Valkonen, Sweetpotato viruses: 15 years of progress on understanding and managing complex diseases, Plant Disease, 96 (2012), 168–185.
    [18] C. M. Clark and D. Tilman, Loss of plant species after chronic low-level nitrogen deposition to prairie grasslands, Nature, 451 (2008), 712.
    [19] J. L. Clasen and J. J. Elser, The effect of host Chlorella NC64A carbon:phosphorus ratio on the production of Paramecium bursaria Chlorella Virus-1, Freshwater Biol., 52 (2007), 112–122.
    [20] D. Coombs, M. A. Gilchrist, and C. L. Ball, Evaluating the importance of within- and betweenhost selection pressures on the evolution of chronic pathogens, Theoret. Popul. Biol., 72 (2007), 576–591.
    [21] D. Cordell, J.-O. Drangert, and S. White, The story of phosphorus: Global food security and food for thought, Global Environment. Change, 19 (2009), 292–305. Traditional Peoples and Climate Change.
    [22] T. Csorba, L. Kontra, and J. Burgyán, viral silencing suppressors: Tools forged to fine-tune hostpathogen coexistence, Virology, 479¢480 (2015), 85–103. 60th Anniversary Issue.
    [23] C. J. D'Arcy, P. A. Burnett, et al. Barley yellow dwarf: 40 years of progress. American Phytopathological Society (APS Press), 1995.
    [24] C. Dordas, Role of nutrients in controlling plant diseases in sustainable agriculture, Agron. Sustain. Develop., 428 (2008), 33–46.
    [25] M. Droop, Nutrient limitation in osmotrophic protista, Am. Zool., 13 (1973), 209–214.
    [26] M. Droop, Some thoughts on nutrient limitation in algae, J. Phycol., 9 (1973), 264–272.
    [27] M. Droop, The nutrient status of algal cells in continuous culture, J. Marine Biol. Asso. UK, 54 (1974), 825–855.
    [28] J. J. Elser, I. Loladze, A. L. Peace, and Y. Kuang, Lotka re-loaded: Modeling trophic interactions under stoichiometric constraints, Ecol. Modell., 245 (2012), 3–11.
    [29] G. G. Erion and W. E. Riedell, Barley yellow dwarf virus effects on cereal plant growth and transpiration, Crop Sci., 52 (2012), 2794–2799.
    [30] R. Everett, Applications of the Droop Cell Quota Model to Data Based Cancer Growth and Treatment Models, PhD thesis, Arizona State University, 2015.
    [31] R. Everett, J. Nagy, and Y. Kuang, Dynamics of a data based ovarian cancer growth and treatment model with time delay, J. Dynam. Different. Equat., (2015), 1–22.
    [32] R. Everett, A. Packer, and Y. Kuang, Can mathematical models predict the outcomes of prostate cancer patients undergoing intermittent androgen deprivation therapy? Biophys. Rev. Lett., 9 (2014), 173–191.
    [33] M. Eweida, P. Oxelfelt, and K. Tomenius, Concentration of virus and ultrastructural changes in oats at various stages of barley yellow dwarf virus infection, Ann. Appl. Biol., 112, 313–321.
    [34] K. Fuhrman, G. Pinter, and J. Berges, Dynamics of a virus–host model with an intrinsic quota, Math. Comput. Modell., 53 (2011), 716–730.
    [35] H. J. Gons, H. L. Hoogveld, S. G. Simis, and M. Tijdens, Dynamic modelling of viral impact on cyanobacterial populations in shallow lakes: implications of burst size, J. Marine Biol. Asso. UK, 86 (2006), 537–542.
    [36] S. A. Gourley, Y. Kuang, and J. D. Nagy, Dynamics of a delay differential equation model of hepatitis b virus infection, J. Biol. Dynam., 2 (2008), 140–153.
    [37] W. S. Harpole, L. L. Sullivan, E. M. Lind, J. Firn, P. B. Adler, E. T. Borer, J. Chase, P. A. Fay, Y. Hautier, H. Hillebrand, A. S. MacDougall, E. W. Seabloom, R. Williams, J. D. Bakker, M. W. Cadotte, E. J. Chaneton, C. Chu, E. E. Cleland, C. D¢¢Antonio, K. F. Davies, D. S. Gruner, N. Hagenah, K. Kirkman, J. M. H. Knops, K. J. La Pierre, R. L. McCulley, J. L. Moore, J. W. Morgan, S. M. Prober, A. C. Risch, M. Schuetz, C. J. Stevens, and P. D. Wragg, Addition of multiple limiting resources reduces grassland diversity, Nature, 537 (2016), 93.
    [38] W. R. Inc, Mathematica, Version 11.1. Champaign, IL, 2018.
    [39] J. D. Jones and J. L. Dangl, The plant immune system, Nature, 444 (2006), 323–329.
    [40] J. Karlsson, M. Anguelova, and M. Jirstrand, An efficient method for structural identifiability analysis of large dynamic systems, IFAC Proceed. Vol., 45 (2012), 941–946.
    [41] A. Kendig, E. Borer, E. Boak, T. Picard, and E. Seabloom, Plant virus coexistence occurs at multiple scales regardless of nutrient supply, Proceed. Royal Soc. B (submitted), 2018.
    [42] A. M. King, Virus taxonomy: classification and nomenclature of viruses: Ninth Report of the International Committee on Taxonomy of Viruses, volume 9. Elsevier, 2011.
    [43] Y. Kuang, Delay differential equations: with applications in population dynamics, volume 191. Academic Press, 1993.
    [44] Y. Kuang, J. Huisman and J. J. Elser, Stoichiometric plant-herbivore models and their interpretation, Math. Biosci. Engineer., 1 (2004), 215–222.
    [45] Y. Kuang, J. D. Nagy, and S. E. Eikenberry, Introduction to Mathematical Oncology. Chapman and Hall/CRC, 2016.
    [46] Y. Kuang, J. D. Nagy, and J. J. Elser, Biological stoichiometry of tumor dynamics: mathematical models and analysis, Discret. Cont. Dynam. Sys. Series B, 4 (2004), 221–240.
    [47] C. Lacroix, E.W. Seabloom, and E. T. Borer, Environmental nutrient supply alters prevalence and weakens competitive interactions among coinfecting viruses, New Phytol., 204 (2014), 424–433.
    [48] C. Lacroix, E. W. Seabloom, and E. T. Borer, Environmental nutrient supply directly alters plant traits but indirectly determines virus growth rate, Front. Microbiol., 8 (2017), 2116.
    [49] L. Mancio-Silva, K. Slavic, M. T. Grilo Ruivo, A. R. Grosso, K. K. Modrzynska, I. M. Vera, J. Sales-Dias, A. R. Gomes, C. R. MacPherson, P. Crozet, M. Adamo, E. Baena-Gonzalez, R. Tewari, M. Llinás, O. Billker, and M. M. Mota, Nutrient sensing modulates malaria parasite virulence, Nature, 547 (2017), 213–216.
    [50] E. Mitchell Charles, B. Reich Peter, T. David, and V. Groth James, Effects of elevated co2, nitrogen deposition, and decreased species diversity on foliar fungal plant disease, Global Change Biol., 9 (2018), 438–451.
    [51] G. Neofytou, Y. Kyrychko, and K. Blyuss, Mathematical model of plant-virus interactions mediated by rna interference, J. Theor. Biol., 403 (2016), 129–142.
    [52] G. Neofytou, Y. Kyrychko, and K. Blyuss, Time-delayed model of immune response in plants. J. Theoret. Biol., 389 (2016), 28–39.
    [53] H. Ogura, H. Sato, and M. Hatano, Relation of hvj (sendai virus) production to cell growth phase in persistently infected mouse 3t3 cells, Arc. Virol., 80 (1984), 47.
    [54] T. Pietschmann, V. Lohmann, G. Rutter, K. Kurpanek, and R. Bartenschlager, Characterization of cell lines carrying self-replicating hepatitis C virus RNAs, J. Virol., 75 (2001), 1252–1264.
    [55] T. Portz, Y. Kuang, and J. D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy, Aip. Adv., 2 (2012), 011002.
    [56] R. Poulin and S. Morand, The diversity of parasites. Quarter. Rev. Biol., 75 (2000), 277–293. PMID: 11008700.
    [57] R Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2013.
    [58] Z. Rapti and C. E. Cáceres, Effects of intrinsic and extrinsic host mortality on disease spread, Bull. Math. Biol., 78 (2016), 235–253.
    [59] A. Raue, J. Karlsson, M. P. Saccomani, M. Jirstrand, and J. Timmer, Comparison of approaches for parameter identifiability analysis of biological systems, Bioinformatics, 2014.
    [60] A. Raue, C. Kreutz, T. Maiwald, J. Bachmann, M. Schilling, U. Klingm¨uller, and J. Timmer, Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood, Bioinformatics, 25 (2009), 1923–1929.
    [61] P. H. Raven, R. F. Evert, and S. E. Eichhorn, Biology of plants, Macmillan, 2005.
    [62] M. P. Saccomani, S. Audoly, and L. D'Angiò, Parameter identifiability of nonlinear systems: the role of initial conditions, Automatica, 39 (2003), 619–632.
    [63] E. Seabloom, E. Borer, C. Mitchell, and P. Alison, Viral diversity and prevalence gradients in north american pacific coast grasslands, Ecology, 91 (2010), 721–732.
    [64] E. W. Seabloom, C. D. Benfield, E. T. Borer, A. G. Stanley, T. N. Kaye, and P. W. Dunwiddie, Provenance, life span, and phylogeny do not affect grass species' responses to nitrogen and phosphorus, Ecol. Appl. Publ. Ecol. Soc. Am., 2011.
    [65] E. W. Seabloom, E. T. Borer, C. Lacroix, C. E. Mitchell, and A. G. Power, Richness and composition of niche-assembled viral pathogen communities, PLOS ONE, 8 (2013), 1–9.
    [66] H. Smith, An introduction to delay differential equations with applications to the life sciences, volume 57. Springer Science & Business Media, 2010.
    [67] H. L. Smith and P. D. Leenheer, Virus dynamics: A global analysis, SIAM J. Appli. Math., 63 (2003), 1313–1327.
    [68] V. H. Smith, R. D. Holt, M. S. Smith, Y. Niu, and M. Barfield, Resources, mortality, and disease ecology: importance of positive feedbacks between host growth rate and pathogen dynamics, Israel J. Ecol. Evol., 61 (2015), 37–49.
    [69] K. Soetaert and T. Petzoldt, Inverse modelling, sensitivity and monte carlo analysis in R using package FME, J. Statist. Software, 33 (2010), 1–28.
    [70] W. Steffen, K. Richardson, J. Rockström, S. E. Cornell, I. Fetzer, E. M. Bennett, R. Biggs, S. R. Carpenter, W. de Vries, C. A. de Wit, C. Folke, D. Gerten, J. Heinke, G. M. Mace, L. M. Persson, V. Ramanathan, B. Reyers, and S. Sörlin, Planetary boundaries: Guiding human development on a changing planet, Science, 347 2015.
    [71] C. L. Stewart, J. D. Pyle, C. C. Jochum, K. P. Vogel, G. Y. Yuen, and K.-B. G. Scholthof, Multiyear pathogen survey of biofuel switchgrass breeding plots reveals high prevalence of infections by panicum mosaic virus and its satellite virus, Phytopathology, 105 (2015), 1146–1154.
    [72] N. Tromas, M. P. Zwart, G. Lafforgue, and S. F. Elena, Within-host spatiotemporal dynamics of plant virus infection at the cellular level, PLoS Genet., 10 (2014), e1004186.
    [73] P. M. Vitousek, J. D. Aber, R. W. Howarth, G. E. Likens, P. A. Matson, D. W. Schindler, W. H. Schlesinger, and D. G. Tilman, Human alteration of the global nitrogen cycle: sources and consequences, Ecol. Appl., 7 (1997), 737–750.
    [74] R. O. Wayne, Plant cell biology: from astronomy to zoology, Academic Press, 2009.
    [75] B. Whitaker, M. Rúa, and C. Mitchell, Viral pathogen production in a wild grass host driven by host growth and soil nitrogen, New Phytol., 207 (2015), 760–768.
    [76] J. Wu, R. Dhingra, M. Gambhir, and J. V. Remais, Sensitivity analysis of infectious disease models: methods, advances and their application, J. Royal Soc. Int., 10 (2013), 186.
    [77] L. You, P. F. Suthers, and J. Yin, Effects of escherichia coli physiology on growth of phage t7 in vivo and in silico, J. Bacteriol., 184 (2002), 1888–1894.
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