Analytic study of the pine wilt disease epidemic model

This paper presents an analytical study of the pine wilt disease epidemic model, a significantthreat to forest ecosystems and agricultural economies. The model is formulated using Caputo fractionaldifferential equations to account for memory-dependent dynamics and anomalous diffusion processes. We firstestablish the fundamental properties of the system, including existence, uniqueness, and stability criteria. Byemploying a semi-analytical approach combining the Laplace transform with iterative techniques, we deriveapproximate solutions and analyze their convergence. Numerical simulations for different fractional ordersαdemonstrate how fractional derivatives influence disease spread, providing valuable insights for more effectivecontainment strategies.