Bulletin of Mathematical Biology

, Volume 69, Issue 2, pp 525–537 | Cite as

Evaluating the Performance of Chemical Control in the Presence of Resistant Pathogens

  • Richard J. Hall
  • Simon Gubbins
  • Christopher A. Gilligan
Original Article


Resistance to chemical control is a major impediment to combating many socially and economically important diseases. Theoretical and experimental studies have shown that reducing the intensity of treatment can slow, or even prevent, the invasion of resistance, yet reducing treatment levels also results in a net increase in disease severity. Clearly there is a need to identify control strategies that balance the conflicting aims of resistance management and disease suppression. Using a mathematical model for the dynamics of fungicide resistance in crop pathogens, we present a broadly applicable measure of the performance of chemical control in the presence of resistant pathogen strains. We illustrate how to optimise fungicide performance with respect to the intensity of treatment as a function of the duration of treatment and the fitness of the resistant strain. We find that in the short term, fungicide performance is optimised at high levels of treatment despite rapid selection for resistance, while the long-term optimum performance is achieved when treatment renders the fungicide-sensitive and fungicide-resistant pathogens equally fit. We further present evidence that under prescribed conditions, the ratio of dose size and frequency, and the fungicide mode of action, can have a significant effect on fungicide performance.


Resistance Chemical control Fungicide performance Model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, R.M., May, R.M., 1986. The invasion, persistence and spread of infectious diseases within animal and plant communities. Phil. Trans. R. Soc. Lond. B 314, 533–570.CrossRefGoogle Scholar
  2. Austin, D.J., Anderson, R.M., 1999. Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models. Phil. Trans. R. Soc. Lond. B 354, 721–738.Google Scholar
  3. Bierman, S.M., Fitt, B.D.L., van den Bosch, F., Bateman, G.L., Jenkyn, J.F., Welham, S.J., 2002. Changes in populations of the eyespot fungi Tapesia yallundae and T. acuformis under different fungicide regimes in successive crops of winter wheat, 1984–2000. Plant Pathol. 51, 191–201.CrossRefGoogle Scholar
  4. Blower, S.M., Porco, T.C., Darby, G., 1998. Predicting and preventing the emergence of antiviral drug resistance in HSV-2. Nat. Med. 4, 673–678.CrossRefGoogle Scholar
  5. Bonhoeffer, S., Barbour, A.D., De Boer, R.J., 2002. Procedures for the reliable estimation of viral fitness from time-series data. Proc. R. Soc. Lond. B 269, 1887–1893.CrossRefGoogle Scholar
  6. Bonhoeffer, S., Lipsitch, M., Levin, B.R., 1997. Evaluating treatment protocols to prevent antibiotic resistance. Proc. Natl. Acad. Sci. USA 94, 12106–12111.CrossRefGoogle Scholar
  7. Bonhoeffer, S., Nowak, M.A., 1997. Pre-existence and emergence of drug resistance in HIV-1 infection. Proc. R. Soc. Lond. B 264, 631–637.Google Scholar
  8. Brent, K.J., 1995. Fungicide resistance in crop pathogens: How can it be managed? FRAC monograph no. 1. GCPF (now Crop Life International), Brussels (available online from www.FRAC.info).Google Scholar
  9. Brent, K.J., 2000. UK fungicide resistance research: Risk of resistance development in cereal pathogens to Qo inhibitor fungicides. MAFF, London.Google Scholar
  10. Clark, C.W., 1990. Mathematical Bioeconomics: The optimal management of renewable resources. Wiley, New York.MATHGoogle Scholar
  11. Comins, H.N., 1977. The management of pesticide resistance. J. Theor. Biol. 65, 399–420.CrossRefGoogle Scholar
  12. De Waard, M.A., Georgopoulos, S.G., Hollomon, D.W., Ishii, H., Leroux, P., Ragsdale, N.N., Schwinn, F.J., 1993. Chemical control of plant diseases: Problems and prospects. Ann. Rev. Phytopathol. 31, 403–421.CrossRefGoogle Scholar
  13. Gubbins, S., Gilligan, C.A., 1997. Persistence of host-parasite interactions in a disturbed environment. J. Theor. Biol. 188, 241–258.CrossRefGoogle Scholar
  14. Gubbins, S., Gilligan, C.A., 1999. Invasion thresholds for fungicide resistance: Deterministic and stochastic analyses. Proc. Roy. Soc. Lond. B 266, 2539–2549.CrossRefGoogle Scholar
  15. Hall, R.J., Gubbins, S., Gilligan, C.A., 2004. Invasion of drug and pesticide resistance is determined by a trade-off between relative fitness and treatment efficacy. Bull. Math. Biol. 66, 825–840.CrossRefGoogle Scholar
  16. Hastings, A., 2004. Transients: The key to long-term ecological understanding? Trends Ecol. Evol. 19, 39–45.CrossRefGoogle Scholar
  17. Hunter, T., Brent, K.J., Carter, G.A., 1984. Effects of fungicide regimes on sensitivity and control of barley mildews. Proceedings of the 1984 Crop Protection Conference—Pests and diseases, pp. 471–476.Google Scholar
  18. Laxminarayan, R., Brown, G.M., 2001. Economics of antibiotic resistance: A theory of optimal use. J. Environ. Econ. Manage. 42, 183–206.MATHCrossRefGoogle Scholar
  19. Little, S.J., McLean, A.R., Spina, C.A., Richman, D.D., Havlir, D.V., 1999. Viral dynamics of acute HIV-1 infection. J. Exp. Med. 190, 841–850.CrossRefGoogle Scholar
  20. Madden, L.V., Hughes, G., Irwin, M.E., 2000. Coupling disease-progress-curve and time-of-infection functions for predicting yield loss of crops. Phytopathol. 90, 788–800.CrossRefGoogle Scholar
  21. Marin, D.H., Romero, R.A., Guzman, M., Sutton, T.B., 2003. Black Sigatoka: An increasing threat to banana cultivation. Plant Dis. 87, 208–222.CrossRefGoogle Scholar
  22. Metcalfe, R.J., Shaw, M.W., Russell, P.E., 2000. The effect of dose and mobility on the strength of selection for DMI fungicide resistance in inoculated field experiments. Plant Pathol. 49, 546–557.CrossRefGoogle Scholar
  23. O'Hara, R.B., Nielsen, B.J., Ostergard, H., 2000. The effect of fungicide dose on the composition of laboratory populations of barley powdery mildew. Plant Pathol. 49, 558–566.CrossRefGoogle Scholar
  24. Parry, D.W., 1990. Plant pathology in agriculture. Cambridge University Press, Cambridge.Google Scholar
  25. Paveley, N.D., Sylvester-Bradley, R., Scott, R.K., Craigon, S.J., Day, W., 2001. Steps in predicting the relationship of yield on fungicide dose. Phytopathol. 91, 708–716.CrossRefGoogle Scholar
  26. Paveley, N.D., Thomas, J.M., Vaughan, T.B., Havis, N.D., Jones, D.R., 2003. Predicting effective doses for the joint action of two fungicide applications. Plant Pathol. 52, 638–647.CrossRefGoogle Scholar
  27. Pearson, H., 2002. ‘Superbug’ hurdles key drug barrier. Nature 418, 469.CrossRefGoogle Scholar
  28. Porras, L., Gisi, U., Staele-Csech, U., 1990. Selection dynamics in triazole-treated populations of Erysiphe graminis. Proceedings of the 1990 Brighton Crop Protection Conference, pp. 1163–1168.Google Scholar
  29. Schulz, U., 1994. Evaluating anti-resistance strategies for control of Erysiphe graminis f.sp. tritici. In: Heaney, S., Slawson, D., Hollomon, D.W., Smith, M., Russell, P.E., Parry, D.W. (Eds.), Fungicide resistance. BCPC, Farnham, UK, pp. 55–58.Google Scholar
  30. Shaw, M.W., 1993. Theoretical analysis of the effect of interacting activities on the rate of selection for combined resistance to fungicide mixtures. Crop Prot. 12, 120–126.CrossRefGoogle Scholar
  31. Shaw, M.W., 2000. Models of the effects of dose heterogeneity and escape on selection pressure for pesticide resistance. Phytopathology 90, 333–339.CrossRefGoogle Scholar
  32. Swinton, J., Anderson, R.M., 1995. Model frameworks for plant-pathogen interactions. In: Grenfell, B.T., Dobson, A.P. (Eds.), Ecology of infectious diseases in natural populations. Cambridge University Press, Cambridge, pp. 280–294.Google Scholar
  33. van den Bosch, F., Gilligan, C.A., 2003. Measures of durability of resistance. Phytopathology 93, 616–625.CrossRefGoogle Scholar
  34. van der Plank, J.E., 1963. Plant diseases: Epidemics and control. Academic Press, New York and London.Google Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  • Richard J. Hall
    • 1
    • 3
  • Simon Gubbins
    • 2
  • Christopher A. Gilligan
    • 1
  1. 1.Department of Plant SciencesUniversity of CambridgeCambridgeUK
  2. 2.Institute for Animal HealthCompton, NewburyUK
  3. 3.Department of Environmental Science and PolicyUniversity of CaliforniaDavisUSA

Personalised recommendations