Mathematical Modeling Approach to Study Pine Wilt Disease

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.