Abstract
The containment of the invasive species is a widespread problem in the environmental
management, with a significant economic impact. We analyze an optimal
control model which aims to find the best temporal resource allocation strategy
for the removal of an invasive species. We study the existence and uniqueness
of the optimal solution when both initial and final conditions on the state variable
are fixed. We derive and alternative optimality system in the state and control
variables and we use the phase-space analysis to provide qualitative insights into
the system dynamics and to analyze the behavior of the optimal solution. Finally,
we find the expression of the optimal solution for the free terminal time problem.
We apply these techniques to two case studies: the case of feral cats population
in Australia, where we assume a logistic growth; the control of wild-boars populations
in Italy, where we include an Allee effect in the population growth. This
work has been carried out within the H2020 project 'ECOPOTENTIAL: Improving
Future Ecosystem Benefits Through Earth Observations'. The project has received
funding from the European Union's Horizon 2020 research and innovation
programme under grant agreement No 641762.
References
[1] Baker, C. M., F. Diele, D. Lacitignola, C. Marangi, A. Martiradonna (2017). Optimal
control of invasive species through a dynamical systems approach, Discrete
and Continuous Dynamical System, under review.
[2] Baker, C.M., M. Bode (2013). Spatial control of invasive species in conservation
landscapes, Comput. Manag. Sci., 10, 331-351.
[3] Lenhart, S., J.T. Workman (2007). Optimal control applied to biological models,
Chapman & Hall/CRC, London.
Anno
2018
Tipo pubblicazione
Altri Autori
Angela Martiradonna