Analytic study of the pine wilt disease epidemic model

Abstract

This paper presents an analytical study of the pine wilt disease epidemic model, a significant threat to forest ecosystems and agricultural economies. The model is formulated using Caputo fractional differential equations to account for memory-dependent dynamics and anomalous diffusion processes. We first establish the fundamental properties of the system, including existence, uniqueness, and stability criteria. By employing a semi-analytical approach combining the Laplace transform with iterative techniques, we derive approximate solutions and analyze their convergence. Numerical simulations for different fractional orders α demonstrate how fractional derivatives influence disease spread, providing valuable insights for more effective containment strategies