By Mimmo Iannelli, Andrea Pugliese (auth.)
This publication is an advent to mathematical biology for college kids with out adventure in biology, yet who've a few mathematical historical past. The paintings is concentrated on inhabitants dynamics and ecology, following a practice that is going again to Lotka and Volterra, and encompasses a half dedicated to the unfold of infectious illnesses, a box the place mathematical modeling is intensely well known. those topics are used because the sector the place to appreciate sorts of mathematical modeling and the potential that means of qualitative contract of modeling with information. The ebook additionally incorporates a collections of difficulties designed to technique extra complex questions. This fabric has been utilized in the classes on the collage of Trento, directed at scholars of their fourth yr of experiences in arithmetic. it will possibly even be used as a reference because it presents up to date advancements in numerous areas.
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Extra resources for An Introduction to Mathematical Population Dynamics: Along the trail of Volterra and Lotka
Thus π (H)Δ t = aH(Δ t − τπ (H)Δ t) from which Holling II form is derived. In type III the parameter α appears explicitly, while ν has the same dimensions as the number of individuals and is such that 1 π (ν ) = α . 2 This form of π (H) has not a mechanistic explanation as in the case of type II but is justiﬁed empirically on the basis of ﬁeld data. 32), are considered more realistic and are respectively called (see Fig. 15) hyperbolic response and sigmoidal response. In the latter the exponent θ may be set and justiﬁed in terms of the predation mechanism and its role consists in a reduction of predation at low prey density, as it is the case of a generalist predator that, having other food sources, does not care 26 1 Malthus, Verhulst and all that Fig.
1007/978-3-319-03026-5_2, © Springer International Publishing Switzerland 2014 40 2 Population models with delays ics. In fact, after Volterra’s ansatz, the need of taking into account the hereditary nature of population phenomena was pointed out since the very beginning of the mathematical modeling of population growth, and some attention has been devoted to the speciﬁc mechanisms that ask for the introduction of delays into the equations. The next section provides a short discussion to the modeling aspect of the problem, then we will consider the delayed Malthus and Verhulst models both in the concentrated case and in the distributed one.
Editeurs , Paris (1935) 4. : Sur les problèmes aux dérivées partielles et leur signiﬁcation physique, Princeton University Bulletin, 49–52 (1902) 5. : Functional Analysis and Semigroups, American Mathematical Society colloquium publications 31 (1957) 6. : The Component of Predation as Revealed by a Study of Small-Mammal Predation of the European Pine Sawﬂy, The Canadian Entomologist 91, 293–320 (1959) 7. : The functional response of predators to prey density and its role in mimicry and population regulation, Memoirs of the Entomological Society of Canada 45, 5–60 (1965) 8.