Handling overheads: optimal multi-method invasive species control

Implementation and acceleration of optimal control for systems biology

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.

Control of Invasive Forest Species through the Creation of a Value Chain: Acacia dealbata Biomass Recovery

In Portugal, some species are now considered invasive by law and have proliferated in recent years. Among these, Acacia dealbata stands out. This work investigated the behavior of this species, in order to characterize and evaluate its potential as raw material for biomass pellets production, while controlling its proliferation. It was found that A. dealbata has a large capacity for raw material supply, as cutting 2 ha resulted in about 140 tons of biomass. Thus, the attribution of a market value for this material could result in a reduction in the area occupied by the invasive species, once the demand for it increases, causing a pressure over the resource. This pressure on the species must be duly followed by other control measures, such as reducing the population and mitigating its proliferation. Laboratory tests have shown that both the raw material and the finished product are similar to those obtained with other species normally used for biomass pellet production, such as Pinus pinaster and Eucalyptus globulus. Thus, it can be concluded that there is a high potential for this species in the production of biomass pellets for energy, and that this may be an important contribution to controlling the proliferation of this invasive species.

Designing combination therapies using multiple optimal controls

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.