J. Korean Math. Soc. 2017; 54(3): 987-997
Online first article February 16, 2017 Printed May 1, 2017
https://doi.org/10.4134/JKMS.j160324
Copyright © The Korean Mathematical Society.
Abid Ali Lashari and Kwang Sung Lee
Stockholm University, Dongseo University
A deterministic model for the spread of pine wilt disease with asymptomatic carrier trees in the host pine population is designed and rigorously analyzed. We have taken four different classes for the trees, namely susceptible, exposed, asymptomatic carrier and infected, and two different classes for the vector population, namely susceptible and infected. A complete global analysis of the model is given, which reveals that the global dynamics of the disease is completely determined by the associated basic reproduction number, denoted by $\mathcal{R}_0$. If $\mathcal{R}_0$ is less than one, the disease-free equilibrium is globally asymptotically stable, and in such a case, the endemic equilibrium does not exist. If $\mathcal{R}_0$ is greater than one, the disease persists and the unique endemic equilibrium is globally asymptotically stable.
Keywords: mathematical model, pine wilt disease, basic reproduction number, global stability
MSC numbers: 92B05, 34D23
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