Spatiotemporal dynamics of a facultative predation-parasitism model for Pine Wilt Disease with top-hat nonlocal perception

Sclerodermus guani is a facultative natural enemy with dual functional responses of predation and parasitism, which has been widely used in the biological control of Monochamus saltuarius, the vector insect of Pine Wilt Disease (PWD). However, most existing studies treat its predation and parasitism behaviors in isolation and ignore the synergistic effect of the dual functions. Based on this, we innovatively construct a facultative predation-parasitism reaction-diffusion model with top-hat nonlocal perception, dual predation-parasitism functional responses, and parasitic time delay, and we systematically analyze the spatiotemporal dynamic behaviors of the model. Theoretical analysis shows that, in the absence of time delay, the nonlocal perception intensity $\eta$ and perception range $R$ can induce local over-predation of the host by natural enemies and population collapse, forming stable spatially nonhomogeneous steady-state solutions. When the parasitic time delay exceeds the critical value, the delay effect leads to periodic population oscillation. The synergistic effect of nonlocal perception and time delay induces Turing-Hopf bifurcation, presenting complex spatiotemporally coupled patterns. Numerical simulations based on parameters with realistic biological backgrounds verify the correctness of the theoretical analysis, and intuitively demonstrate the dynamic modes corresponding to different parameters, including local asymptotic stability, stable spatially nonhomogeneous steady-state solutions, and spatially nonhomogeneous periodic solutions. The results reveal the regulation mechanism of top-hat nonlocal perception and parasitic time delay on the spatiotemporal dynamics of the Monochamus saltuarius-Sclerodermus guani system. They not only enrich the spatiotemporal dynamics theory of facultative predation-parasitism systems, but also provide a quantitative mathematical basis for optimizing the release timing and release strategy of Sclerodermus guani in prevention and control as well as lay a theoretical foundation for the biological control of PWD.