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Analysis of the Incidence of Poxvirus on the Dynamics between Red and Grey Squirrels

Author

Listed:
  • Fadi Barbara

    (Department of Mathematics “Giuseppe Peano”, University of Turin, via Carlo Alberto 10, 10123 Torino, Italy
    These authors contributed equally to this work.)

  • Valentina La Morgia

    (Institute for Environmental Protection and Research (ISPRA), via Ca’Fornacetta 9, 40064 Ozzano Emilia (BO), Italy
    These authors contributed equally to this work.)

  • Valerio Parodi

    (Department of Mathematics “Giuseppe Peano”, University of Turin, via Carlo Alberto 10, 10123 Torino, Italy
    These authors contributed equally to this work.)

  • Giuseppe Toscano

    (Department of Mathematics “Giuseppe Peano”, University of Turin, via Carlo Alberto 10, 10123 Torino, Italy
    These authors contributed equally to this work.)

  • Ezio Venturino

    (Department of Mathematics “Giuseppe Peano”, University of Turin, via Carlo Alberto 10, 10123 Torino, Italy
    Member of the Research Group GNCS of INdAM
    These authors contributed equally to this work.)

Abstract

A model for the interactions of the invasive grey squirrel species as asymptomatic carriers of the poxvirus with the native red squirrel is presented and analyzed. Equilibria of the dynamical system are assessed, and their sensitivity in terms of the ecosystem parameters is investigated through numerical simulations. The findings are in line with both field and theoretical research. The results indicate that mainly the reproduction rate of the alien population should be drastically reduced to repel the invasion, and to achieve disease eradication, actions must be performed to reduce the intraspecific transmission rate; also, the native species mortality plays a role: if grey squirrels are controlled, increasing it may help in the red squirrel preservation, while the invaders vanish; on the contrary, decreasing it in favorable situations, the coexistence of the two species may occur. Preservation or restoration of the native red squirrel requires removal of the grey squirrels or keeping them at low values. Wildlife managers should exert a constant effort to achieve a harsh reduction of the grey squirrel growth rate and to protect the remnant red squirrel population.

Suggested Citation

  • Fadi Barbara & Valentina La Morgia & Valerio Parodi & Giuseppe Toscano & Ezio Venturino, 2018. "Analysis of the Incidence of Poxvirus on the Dynamics between Red and Grey Squirrels," Mathematics, MDPI, vol. 6(7), pages 1-21, July.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:7:p:113-:d:155508
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    References listed on IDEAS

    as
    1. Jones, Hannah & White, Andrew & Lurz, Peter & Shuttleworth, Craig, 2017. "Mathematical models for invasive species management: Grey squirrel control on Anglesey," Ecological Modelling, Elsevier, vol. 359(C), pages 276-284.
    2. Frank Hilker & Horst Malchow, 2006. "Strange Periodic Attractors in a Prey-Predator System with Infected Prey," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(3), pages 119-134.
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