title: Host coexistence in a model for two host-one parasitoid interactions.
abstract: Building from a continuous-time host-parasitoid model introduced by Murdoch et al. (Am Nat 129:263-282, 1987), we study the dynamics of a 2 host-parasitoid model assuming, for the sake of simplicity, that larval stages have a fixed duration. If each host is subjected to density-dependent mortality in its larval stage, we obtain explicit conditions for the existence of an equilibrium where the two host species coexist with the parasitoid. However, if host demography is density-independent, equilibrium coexistence is impossible. If at least one of the 1 host-parasitoid systems has an oscillatory dynamics (which happens under some parameter values), we found, through numerical bifurcation, that coexistence is favoured. Coexistence between the two hosts may occur along a periodic solution even without density-dependence. Models of this type may be relevant for the use of parasitoids as biocontrol agents of insect pests.
authors.affiliation: Department of Mathematics, University of Trento, Trento, Italy.
authors.forename: Valentina
authors.initials: V
authors.lastname: Clamer
authors.affiliation: Department of Mathematics, University of Trento, Trento, Italy. andrea.pugliese@unitn.it.
authors.forename: Andrea
authors.identifier: 0000-0002-3512-8560
authors.initials: A
authors.lastname: Pugliese
authors.affiliation: Department of Mathematics, Computer Science and Physics, University of Udine, Udine, Italy.
authors.forename: Davide
authors.initials: D
authors.lastname: Liessi
authors.affiliation: Department of Mathematics, Computer Science and Physics, University of Udine, Udine, Italy.
authors.forename: Dimitri
authors.initials: D
authors.lastname: Breda
mesh_terms: D000818:Animals; D006790:Host-Parasite Interactions / Q000502:physiology*; D007313:Insecta; D007814:Larva; D008954:Models, Biological; D011156:Population Density
keywords: Characteristic multipliers; Delay differential equations; Host–parasitoid model; Numerical bifurcation; Periodic solutions; Species coexistence