An epizootic model of an insect-fungal pathogen system
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.
KeywordsDiscrete Version Conidial Production Alfalfa Weevil Standard Analytic Technique Dependent Rate Constant
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- Brown, G. C. and G. L. Nordin. 1980. “An Epidemiological Model ofEntomophthora phytonomi-Hypera postica Populations.”Soc. invert. Pathol. Newsl. 7, 9.Google Scholar
- Kendall, D. G. 1957. “Deterministic and Stochastic Epidemics in Closed Populations.”Proc. 3rd Berkeley Symp. math. statist. Prob. 4, 149–165.Google Scholar
- Waltman, P. 1977. “Deterministic Threshold Models in the Theory of Epidemics.” InLecture Notes in Biomathematics, Ed. S. Levin, Vol. 6, p. 101.Google Scholar
- 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