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PREDATOR–PREY MODEL WITH AGE STRUCTURE

Part of: Systems of linear integral equations

Published online by Cambridge University Press:  02 November 2017

J. PROMRAK Open the ORCID record for J. PROMRAK [Opens in a new window] ,
G. C. WAKE  and
C. RATTANAKUL
J. PROMRAK
Affiliation:
Department of Mathematics, Faculty of Science, Mahidol University, Thailand email jpjairaj@gmail.com
G. C. WAKE
Affiliation:
Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand email g.c.wake@massey.ac.nz
C. RATTANAKUL*
Affiliation:
Department of Mathematics, Faculty of Science, Mahidol University, Thailand Centre of Excellence in Mathematics, Commission on Higher Education, Thailand email chontita.rat@mahidol.ac.th
*
✉ chontita.rat@mahidol.ac.th
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Abstract

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Mealybug is an important pest of cassava plant in Thailand and tropical countries, leading to severe damage of crop yield. One of the most successful controls of mealybug spread is using its natural enemies such as green lacewings, where the development of mathematical models forecasting mealybug population dynamics improves implementation of biological control. In this work, the Sharpe–Lotka–McKendrick equation is extended and combined with an integro-differential equation to study population dynamics of mealybugs (prey) and released green lacewings (predator). Here, an age-dependent formula is employed for mealybug population. The solutions and the stability of the system are considered. The steady age distributions and their bifurcation diagrams are presented. Finally, the threshold of the rate of released green lacewings for mealybug extermination is investigated.

Keywords

Sharpe–Lotka–McKendrick equationpredator–prey modelsteady age distributionmealybugs

MSC classification

Primary: 45F99: None of the above, but in this section

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 155 - 166
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2017 Australian Mathematical Society

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