Dynamical analysis of plant disease models with cultural control strategies and economic thresholds

Sanyi Tang, Yanni Xiao and Robert A. Cheke

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 80, issue 5, 894-921

Abstract: In this paper plant disease models including impulsive cultural control strategies were developed and analyzed. The sufficient conditions under which the infected plant free periodic solution with fixed moments is globally stable are obtained. For the model with an economic threshold (ET) of infected plants, detailed investigations imply that the number of healthy plants either goes to extinction or tends to infinity, and the maximum value of infected plants is always less than the given ET. In order to prevent the healthy plant population going to extinction, we further propose a bi-threshold-value model, which has richer dynamical behavior including order 1-k or order k-1 periodic solutions with k≥1. Under certain parameter spaces, the infected plant free periodic solution is globally stable for the bi-threshold-value model. The modeling methods and analytical analysis presented can serve as an integrating measure to identify, evaluate and design appropriate plant disease control strategies.

Keywords: Plant disease; Epidemiology; Cultural control; Economic threshold; Bi-threshold value (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2010:i:5:p:894-921

DOI: 10.1016/j.matcom.2009.10.004

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