Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 4, Issue 1


Published
on

June 21, 2019


Pages

79-92


DOI

Article

Can aphids be controlled by fungus? A mathematical model

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Authors

Nicholas F. Britton Affiliation:
Centre for Mathematical Biology and Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK
, Iulia Martina Bulai Affiliation:
Department of Information Engineering, via Gradenigo, 6/B, University of Padova, 35131, Padova - Member of the INdAM research group GNCS, Italy
, Stéphanie Saussure Affiliation:
Norwegian Institute of Bioeconomy Research, Postboks 115, NO-1431 Ås; Norwegian University of Life Sciences, P.O. Box 5003, NO-1432, Ås, Norway
, Niels Holst Affiliation:
Department of Agroecology - Entomology and Plant Pathology, Århus University, Forsøgsvej 1, 4200, Slagelse, Denmark
and Ezio Venturino Affiliation:
Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, via Carlo Alberto 10, 10123, Torino - Member of the INdAM research group GNCS, Italy


Abstract

The control of insect pests in agriculture is essential for food security. Chemical controls typically damage the environment and harm beneficial insects such as pollinators, so it is advantageous to identify targetted biological controls. Since predators are often generalists, pathogens or parasitoids are more likely to serve the purpose. Here, we model a fungal pathogen of aphids as a potential means to control of these important pests in cereal crops. Typical plant herbivore pathogen models are set up on two trophic levels, with dynamic variables the plant biomass and the uninfected and infected herbivore populations. Our model is unusual in that (i) it has to be set up on three trophic levels to take account of fungal spores in the environment, but (ii) the aphid feeding mechanism leads to the plant biomass equation becoming uncoupled from the system. The dynamical variables are therefore the uninfected and infected aphid population and the environmental fungal concentration. We carry out an analysis of the dynamics of the system. Assuming that the aphid population can survive in the absence of disease, the fungus can only persist (and control is only possible) if (i) the host grows sufficiently strongly in the absence of infection, and (ii) the pathogen transmission parameters are sufficiently large. If it does persist the fungus does not drive the aphid population to extinction, but controls it below its disease-free steady state value, either at a new coexistence steady state or through oscillations. Whether this control is sufficient for agricultural purposes will depend on the detailed parameter values for the system.


Keywords

three-way interactions, pest control, mathematical model, pathogenic fungi, aphids, crops, AMS 2010 MSC primary: 92D40, secondary: 92D25, 92D30


Citation

Britton, N. F., Bulai, I. M., Saussure, S., Holst, N., & Venturino, E. (2019). Can aphids be controlled by fungus? a mathematical model. Applied Mathematics and Nonlinear Sciences, 4(1), 79–92. https://doi.org/10.2478/AMNS.2019.1.00009

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