Across the life sciences, we encounter many complex systems over which we wish to exert control. Optimal control is a science of trade-offs; between competing objectives, or in weighing up the benefits of control measures against their costs. We present here theoretical results and computational issues for two biological models to which we apply regional control strategies. In the first model, we investigate the problem of minimizing the total cost of the damages produced by an alien predator population, and of the regional control paid to reduce this population. The dynamics of the predators is described by a prey-predator system with either local or nonlocal reaction terms. A sufficient condition for the zero-stabilizability (eradicability) of predators is given in terms of the sign of the principal eigenvalue of an appropriate operator that is not self-adjoint, and a stabilizing feedback control with a very simple structure is indicated. We then approach a second model, defined by a two-component reaction-diffusion system to describe the spread of malaria. The model describes the dynamics of the infected mosquitoes and of the infected humans. The spread of the disease is controlled by three actions (controls) implemented in a subdomain of the habitat: killing mosquitoes, treating the infected humans and reducing the contact rate mosquitoes-humans. The problem of the eradicability of the disease is considered, while the cost of the controls is ignored. We prove that it is possible to decrease exponentially both the human and the vector infective population, everywhere in the relevant habitat, by acting only in a suitable subdomain. Later, the regional control problem of reducing the total cost of the damages produced by the disease, and of the intervention in a certain subdomain is treated for the finite time horizon case. The level set method is a key ingredient for both approaches. An iterative algorithm to decrease the total cost is proposed and numerical results illustrate the effectiveness of the theoretical results.