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Zbl 1183.92060
Tang, Sanyi; Xiao, Yanni; Cheke, Robert A.
Dynamical analysis of plant disease models with cultural control strategies and economic thresholds. (English)
[J] Math. Comput. Simul. 80, No. 5, 894-921 (2010). ISSN 0378-4754

Summary: Plant disease models including impulsive cultural control strategies were developed and analyzed. 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 $k\geq 1$. 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.

MSC 2000:: *92C80 Plant biology
92D30 Epidemiology
93C95 Appl. of control theory
34A37 Differential equations with impulses
34C25 Periodic solutions of ODE
34D20 Lyapunov stability of ODE
93C15 Control systems governed by ODE

Keywords: plant disease; epidemiology; cultural control; economic threshold; bi-threshold value

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