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Mathematical Medicine and Biology Advance Access originally published online on March 22, 2005
Mathematical Medicine and Biology 2005 22(3):227-245; doi:10.1093/imammb/dqi006
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Applications of biological control in resistant host–pathogen systems

Steven M. White** and K. A. Jane White

Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK

** Present address: Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK. Email: whites{at}maths.ox.ac.uk

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

Received on 3 August 2003. revised on 21 July 2004. accepted on 6 December 2004.


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