Abstract
ABSTRACTThis work is related to qualitative behaviour of an epidemic model of pine wilt disease. More precisely, we proved that the reproductive number has sharp threshold properties. It has been shown that how vector population can be reduced by the periodic use of insecticides. Numerical simulations show that epidemic level of infected vectors becomes independent of saturation level by including the transmission through mating.
Highlights
Pine wilt disease (PWD), caused by the pinewood nematode (PWN) Bursaphelenchus xylophilus is a dramatic disease because it usually kills affected trees within a few weeks to a few months
We prove the global stability of the endemic equilibrium E∗, when the reproduction number R0 is greater than the unity
This paper presents a host–vector model for PWD with nonlinear incidence rate
Summary
Pine wilt disease (PWD), caused by the pinewood nematode (PWN) Bursaphelenchus xylophilus is a dramatic disease because it usually kills affected trees within a few weeks to a few months. Lee and Lashari [8] discussed a mathematical model with nonlinear incidence rates to describe the host–vector interaction between pines and pine sawyers carrying nematode by considering the role of incubation period during disease transmission. They did not include direct mode of transmission. Ozair et al [16] developed a PWD model considering a direct mode of transmission with standard incidence rate They did not consider those pine trees that has been infected by the nematode but still sustains the ability for oleoresin exudation.
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