Mathematics Inspired by Biology by O. Diekmann R. Durrett K. P. Hadeler

By O. Diekmann R. Durrett K. P. Hadeler

The summer time university on arithmetic encouraged by means of Biology was once held at Martina Franca, Apulia, Italy in 1997. This quantity offers 5 sequence of six lectures every one. the typical subject matter is the function of constitution in shaping brief and supreme dynamics. however the kind of constitution levels from spatial (hadeler and maini within the deterministic environment, Durrett within the stochastic surroundings) to physiological (Diekmann) and order (Smith). each one contribution sketches the current scenario whereas, by means of together with a few wishful pondering, pointing at open difficulties that deserve cognizance.

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The second is that one is greatly rewarded for such preliminary work, since the determination of R0 and (an equation for) r is subsequently as easy as it can ever be. In the second example, which concerns juvenile dispersal in space, we only deal with the first aspect. We choose this example to show that the determination of u and A from more primitive model ingredients may involve the solution of a partial differential equation. Consider individuals which are characterised by their age and by their spatial position y E ]~2.

ANELLI,Pitman Research Notes in Maths 190: 67-89. [4] DIEKMANN, 0 . , M. J. R. THIEME. 1998. On the formulation and analysis of general deterministic structured population models. I. Linear Theory J. Math. Biol. 36: 349-388. , M. GYLLENBERG, H. HUANG, M. J. R. THIEME. If. Nonlinear Theory. In preparation. [6] DIBKMANN, 0 . J. METZ. 1994. On the reciprocal relationship between life histories and population dynamics. A. LEVlN, Springer LNiB 100: 263-279. , M. R. M. VERDUYN LUNEL. (preprint). A cell-cycle model revisited.

Appl. 29: 247-265. M. 1992. Markov renewal theory and its applications to Markov ergodic processes. Lect. Notes Dept. , Chalmers Univ. of Technology. R. 1988. Well-posedness of physiologically structured population models for Daphnia magna. J. Math. Biol. 26: 299-317. L. O. ZIMMERMANN. 1988. A nonlinear model of population dynamics containing an arbitrary number of continuous structure variables. SIAM. d. Appl. Math. 48: 549-591. M. DE R o o s & W. GABRmL. 1988. Cannibalism as a life boat meachanism.

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