Abstract
We investigate the characteristics of pine wilt disease by incorporating the harmonic type incident rate in an existing model. We find the threshold number for the model under consideration which plays a vital role in the dynamical behaviour of the system. Stability conditions for the possible stationary states of the system are found in terms of the threshold quantity. Our analysis shows that disease eradicates from the pine trees whenever the threshold quantity assumes values less than unity and persists otherwise. We then study the effect of various parameters of the model upon the spread of the pine wilt disease. The problem presented exhibits bifurcation, an analysis of which is a part of the current work. Under biologically meaningful conditions, we perform numerical simulations to support and verify the analytical findings of this work.
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