Bulletin of Mathematical Biology

, Volume 44, Issue 5, pp 731–739 | Cite as

An epizootic model of an insect-fungal pathogen system

  • Grayson C. Brown
  • Gerald L. Nordin


A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population. Because of piecewise continuous behavior under some parametric conditions, it is concluded that standard phase orbits can be misleading. Using a different analytic approach yields a simple system of finite difference equations. Both the continuous and discrete versions are compared to classical forms. The continuous version differs from a classical one in possessing a second derivative dependent on population density. The discrete version differs in maintaining positive, non-zero populations of both infectives and susceptibles in finite time.


Discrete Version Conidial Production Alfalfa Weevil Standard Analytic Technique Dependent Rate Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Brown, G. C. and G. L. Nordin. 1980. “An Epidemiological Model ofEntomophthora phytonomi-Hypera postica Populations.”Soc. invert. Pathol. Newsl. 7, 9.Google Scholar
  2. Gani, J. 1978. “Some Problems with Epidemic Theory.”J. R. statist. Soc. Ser. A 141, 323–347.MATHMathSciNetGoogle Scholar
  3. Hoog, F. de, J. Gani and D. J. Gates. 1979. “A Threshold Theorem for the General Epidemic in Discrete Time.”J. math. Biol. 8, 113–121.MATHMathSciNetCrossRefGoogle Scholar
  4. Kendall, D. G. 1957. “Deterministic and Stochastic Epidemics in Closed Populations.”Proc. 3rd Berkeley Symp. math. statist. Prob. 4, 149–165.Google Scholar
  5. Kermack, W. D. and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.”J. R. statist. Soc., Ser. A. 115, 700–721.MATHGoogle Scholar
  6. Waltman, P. 1977. “Deterministic Threshold Models in the Theory of Epidemics.” InLecture Notes in Biomathematics, Ed. S. Levin, Vol. 6, p. 101.Google Scholar
  7. Watson, P. L., R. J. Barney, J. V. Maddox and E. J. Armbrust. 1981. “Sporulation and Mode of Infection ofEntomophthora phytonomi, a Pathogen of the Alfalfa Weevil.”Environ. Entomol. 10, 305–306.Google Scholar

Copyright information

© Society for Mathematical Biology 1982

Authors and Affiliations

  • Grayson C. Brown
    • 1
  • Gerald L. Nordin
    • 1
  1. 1.Department of EntomologyUniversity of KentuckyLexingtonUSA

Personalised recommendations