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Mathematical Medicine and Biology 1998 15(4):313-320; doi:10.1093/imammb/15.4.313
© 1998 by Institute of Mathematics and its Applications
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The stability of the biocontrol system in an epizootic insect-pathogen model incorporating three routes of infection

A. LAMOUR{dagger} and F. van den BOSCH

Wageningen Agricultural University Dreyenlaan 4, 6703 HA Wageningen, The Netherlands

{dagger} Email: Angelique.Lamour{at}medew.fyto.wau.nl

Instability of the internal steady state is usually observed in models of insect-pathogen interactions. Various authors have studied the effect of additional mechanisms on stability. In this paper we show that stable steady states can also occur without introducing additional mechanisms. In most models for insect-pathogen systems, increasing the efficiency of a pathogen leads to decreasing steady-state insect densities. From a biological control point of view this is ideal. However, in such situations the internal steady state usually becomes unstable, resulting in periodic insect outbreaks. The model developed in this paper shows the opposite behaviour: the more effective the disease, the more stable the insect population.

Keywords: insect; insect-pathogen interactions; infection rate; stedy states; stability


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