Mathematical Tools for Controlling Invasive Species in Protected Areas

  • Carmela MarangiEmail author
  • Francesca Casella
  • Fasma Diele
  • Deborah Lacitignola
  • Angela Martiradonna
  • Antonello Provenzale
  • Stefania Ragni
Part of the Springer INdAM Series book series (SINDAMS, volume 38)


A challenging task in the management of Protected Areas is to control the spread of invasive species, either floristic or faunistic, and the preservation of indigenous endangered species, typically competing for the use of resources in a fragmented habitat. In this paper, we present some mathematical tools that have been recently applied to contain the worrying diffusion of wolf-wild boars in a Southern Italy Protected Area belonging to the Natura 2000 network. They aim to solve the problem according to three different and in some sense complementary approaches: (i) the qualitative one, based on the use of dynamical systems and bifurcation theory; (ii) the Z-control, an error-based neural dynamic approach; (iii) the optimal control theory. In the case of the wild-boars, the obtained results are illustrated and discussed. To refine the optimal control strategies, a further development is to take into account the spatio-temporal features of the invasive species over large and irregular environments. This approach can be successfully applied, with an optimal allocation of resources, to control an invasive alien species infesting the Alta Murgia National Park: Ailanthus altissima. This species is one of the most invasive species in Europe and its eradication and control is the object of research projects and biodiversity conservation actions in both protected and urban areas [11]. We lastly present, as a further example, the effects of the introduction of the brook trout, an alien salmonid from North America, in naturally fishless lakes of the Gran Paradiso National Park, study site of an on-going H2020 project (ECOPOTENTIAL).


Invasive species Dynamical systems Optimal control 



This work has been carried out within the H2020 project ‘ECOPOTENTIAL: Improving Future Ecosystem Benefits Through Earth Observations’, coordinated by CNR-IGG ( The project has received funding from the European Union’s Horizon 2020 research and innovation programme (grant agreement No 641762).

This work has been carried out within the LIFE Alta Murgia project (LIFE12 BIO/IT/000213— coordinated by CNR-ISPA, titled Control and eradication of the invasive and exotic plant species Ailanthus altissima in the Alta Murgia National Park, funded by the European Commission under the LIFE Programme. D.L. research work has been performed under the auspices of the Italian National Group for Mathematical Physics (GNFM-INdAM).


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Carmela Marangi
    • 1
    Email author
  • Francesca Casella
    • 2
  • Fasma Diele
    • 1
  • Deborah Lacitignola
    • 3
  • Angela Martiradonna
    • 1
  • Antonello Provenzale
    • 4
  • Stefania Ragni
    • 5
  1. 1.Istituto per le Applicazioni del Calcolo ‘M. Picone’, CNRBariItaly
  2. 2.Istituto di Scienze delle Produzioni Alimentari, CNRBariItaly
  3. 3.Dipartimento di Ingegneria Elettrica e dell’InformazioneUniversità di Cassino e del Lazio meridionaleCassinoItaly
  4. 4.Istituto di Geoscienze e Georisorse, CNRPisaItaly
  5. 5.Department of Economics and ManagementUniversity of FerraraFerraraItaly

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