Transmission dynamics of pine wilt disease in Qinling Mountains region based on multi-scale spatiotemporal characteristics

A dynamic model of pine wilt disease was constructed for Qinling Mountains region based on multi-scale spatiotemporal characteristics．Model's well-posedness was systematically analyzed．A nonlocal time-delayed reaction-diffusion system model was used to derive a next-generation operator \mathcalL , and basic reproduction number R₀ was defined as spectral radius of this operator, there by clarifying intrinsic relationship between basic reproduction number and model's equilibrium points stability．Based on this, Euler-Lagrange equations with gradient projection iterative algorithm were employed to simulate optimal solutions at different elevations, revealing mechanism by which elevation factors influence control strategies．Results have indicated that basic reproduction number is a critical parameter determining model's transmission dynamics and equilibrium state stability, and significant differences existed in optimal allocation of control intensity under varying elevation conditions．Prevention and control strategies proposed based on functional optimization method could provide theoretical guidance for regional management of pine wilt disease．