Abstract:
This study is conducted to discuss the host-vector epidemic models of pine wilt disease
qualitatively. We examine the features by including the harmonic type incidence rate.
The value of the basic reproduction number R0 of the model under consideration is
evaluated by using the next generation matrix approach. Two possible stationary
states have been discussed. The first is a disease-free state, while the second is diseaseendemic.
We investigate the stationary state’s stability conditions in terms of R0. Our
investigation demonstrates that whenever R0 adopts values smaller than one, a diseasefree
stationary state is locally asymptotically stable and disease disappears from pine
trees. The geometric approach method for global stability is used to demonstrate the
existence of a distinct endemic equilibrium if R0 is greater than unity and is globally
asymptotically stable under certain parameter value constraints.
Auxiliary work is presented in the chapter 4, including the effect of η that is transmission
rate among bark beetles through mating. We discuss the equilibrium of the
new model along with stability of these equilibrium. Important parameters that play
vital role in disease dynamics are also identified.
