Journal Article

Applications of biological control in resistant host–pathogen systems

Steven M. White and K. A. Jane White

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 22, issue 3, pages 227-245
Published in print September 2005 | ISSN: 1477-8599
Published online September 2005 | e-ISSN: 1477-8602 | DOI:
Applications of biological control in resistant host–pathogen systems

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  • Applied Mathematics
  • Biomathematics and Statistics


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Insect pest species can have devastating effects on crops. Control of these insect pests is usually achieved by using chemical insecticides. However, there has been much cause for concern with their overuse. Consequently, research has been carried out into alternative forms of control, in particular biological control methods. Recent laboratory studies have indicated that these natural forms of control can induce resistant strains of insect pest. In this paper we present a discrete-time host–pathogen model to describe the interaction between a host (insect species) that can develop a resistant strain and a pathogen (biological control) that can be externally applied to the system. For this model we use a single-state variable for the host population. We show that the proportion of resistants in the population impacts on the viability of the host population. Moreover, when the host population does persist, we explore the interaction between host susceptibility and host population levels. The different scenarios which arise are explained ecologically in terms of trade-offs in intrinsic growth rates, disease susceptibility and intraspecific host competition for the resistant subclass.

Keywords: biological control; resistance; host–pathogen models

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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