  We delve into the interactions between a prey-predator and a vector-borne
epidemic system, driven by agro-ecological motivations. This system involves an
ODE, two reaction--diffusion PDEs and one reaction--diffusion--advection PDE.
It has no complete variational or monotonic structure and features spatially
heterogeneous coefficients. Our initial focus is to examine the continuity of a
quantity known as ''harvest'', which depends on the time-integral of infected
vectors. We analyze its asymptotic behaviour as the domain becomes homogeneous.
Then we tackle a non-standard optimal control problem related to the linearized
harvest and conduct an analysis to establish the existence, uniqueness, and
properties of optimizers. Finally, we refine the location of optimizers under
specific initial conditions.
