Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission

Abstract

The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable whenever $R_0\le 1$. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.