A dynamical systems model for poly-cyclic foliar forest pathogens

A simple systems model is proposed to understand and quantify the onset and epidemiology of red needle cast in radiata pine. This disease is impacting much of the New Zealand forestry estate being driven through the production of self-replicating spores which are dispersed with water. The model is at present deterministic, not spatially or age-structured, nor dependent on environmental or seasonal effects. This model shows the clear existence of calculable thresholds for disease proliferation and elimination, showing it has captured the essential components of the biological mechanisms. It is to be used to identify thresholds for infection to spread or retract. Further it will provide a base model from which we can fit and then predict experimental outcomes. References C Lee Campbell, Laurence V Madden, et al. Introduction to plant disease epidemiology. John Wiley and Sons., 1990. Margaret Anne Dick, Nari Michelle Williams, Martin Karl-Friedrich Bader, Judy Frances Gardner, and Lindsay Stuart Bulman. Pathogenicity of phytophthora pluvialis to pinus radiata and its relation with red needle cast disease in new zealand. New Zealand Journal of Forestry Science, 44(1):6, 2014. Heidi S Dungey, Nari M Williams, Charlie B Low, and Graham T Stovold. First evidence of genetic-based tolerance to red needle cast caused by phytophthora pluvialis in radiata pine. New Zealand Journal of Forestry Science, 44(1):31, 2014. RJ Ganley, NM Williams, CA Rolando, IA Hood, HS Dungey, PN Beets, LS Bulman, et al. Management of red needle cast, caused by phytophthora pluvialis, a new disease of radiata pine in new zealand. N. Z. Plant Protect.-SE, 67:48–53, 2014. Wake GC. Private communication, 2017. Christopher A Gilligan. An epidemiological framework for disease management. Advances in botanical research, 38:1–64, 2002. MJ Jeger. Asymptotic behaviour and threshold criteria in model plant disease epidemics. Plant Pathology, 35(3):355–361, 1986. Nurul S Abdul Latif, Graeme C Wake, Tony Reglinski, and Philip AG Elmer. Modelling induced resistance to plant diseases. Journal of theoretical biology, 347:144–150, 2014. Nurul S Abdul Latif, Graeme C Wake, Tony Reglinski, Philip AG Elmer, and Joseph T Taylor. Modeling induced resistance to plant disease using a dynamical systems approach. Frontiers in plant science, 4, 2013. Laurence V Madden, Gareth Hughes, Frank Bosch, et al. The study of plant disease epidemics. American Phytopathological Society (APS Press), 2007. CA Rolando, MA Dick, J Gardner, M Bader, NM Williams, et al. Chemical control of two phytophthora species infecting the canopy of monterey pine (pinus radiata). Forest Pathology, 47(3), 2017. Carol Rolando, Robyn Gaskin, David Horgan, Nari Williams, and Martin KF Bader. The use of adjuvants to improve uptake of phosphorous acid applied to pinus radiata needles for control of foliar phytophthora diseases. New Zealand Journal of Forestry Science, 44(1):8, 2014