Riv. Mat. Univ. Parma, Vol. 12, No. 2, 2021

Ezio Venturino [a] and Sharon Zytynska [b]

Modelling multispecies interactions and horizontal transmission of aphid bacterial symbionts
Pages: 327-383
Received: 24 July 2021
Accepted in revised form: 7 December 2021
Mathematics Subject Classification: 92D40, 92D45, 92D25.
Keywords: Mathematical models, dynamical systems, equilibria, stability, aphids, pests, parasitoid wasps.
[a]: University of Torino, via Carlo Alberto 10, Member of the INdAM research group GNCS, Torino, 10123, Italy.
[c]: University of Liverpool, Department of Evolution, Ecology and Behaviour, Biosciences Building, Crown Street, Liverpool, L69 7ZB, UK.

EV has been partially supported by the project "Metodi numerici e computazionali per le scienze applicate" of the Dipartimento di Matematica "Giuseppe Peano". SZ has been supported by the British Ecological Society (SR16/1069) and a UKRI-BBSRC David Phillips Fellowship (BB/S010556/1). This research has been partially supported by the The European COST Action: FA 1405 - Food and Agriculture: Using three-way interactions between plants, microbes and arthropods to enhance crop protection and production.
Abstract: In this paper we formulate a model for the investigation of the infection of aphids by bacteria that protect them against parasitoid wasps. The model accounts for the possible transmission mechanisms that can originate in the environment. This includes horizontal transmission via parasitoid wasps and also short-term release of bacteria into the immediate environment after ladybird feeding. Mathematically, this corresponds to setting up a nonlinear dynamical system comprising all the relevant populations, and describing their possible mutual interactions via ordinary differential equations. A considerable effort is exerted in assessing the system's equilibria for feasibility and stability. The main theoretical result concerns the latter issue, for which the full set of the Routh-Hurwitz conditions are established analytically.

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