Monday 3th June 2013, 09.0013.00 Marino Gatto 
Introduction and basics of stochastic processes —
Why space matters in biology. The
importance of networks. Discrete organisms and interacting
particle systems (IPS).
Markov chains in discrete and continuous time. Random walks and birthdeath processes. Extinction risk in Malthusian and densitydependent populations.
References

Wednesday 5th June 2013, 09.0013.00 Marino Gatto 
Reactiondiffusion equations and travelling waves —
Random walks and diffusion. Advectiondiffusion equation.
Diffusion and Malthusian growth in unbounded and bounded domains.
Critical domain size. Diffusionreaction equation in nonlinear densitydependent populations.
Wave fronts. Front celerity. Telegraph equation. Diffusive instability.
References

Friday 7th June 2013, 09.0013.00 Renato Casagrandi, Lorenzo Mari & Paco Melià 
Models for movement ecology: multilayered networks and
coupled physicalbiological models —
What movement ecology is and why it is important. Eulerian vs Lagrangian approaches to study the movement
of organisms. Two paradigmatic and important cases: the spread of an invasive species (the zebra mussel Dreissena polymorpha)
along river networks and the long journey of eels (Anguilla anguilla) from the Sargasso sea to Europe.
References

Monday 10th June 2013, 09.0013.00 Renato Casagrandi & Lorenzo Mari 
From meanfield to spatially realistic epidemiological models —
The classical SIRlike approaches and their use in waterborne diseases (e.g. cholera).
Modelling the spread along river systems via PDEs or via realistic
networks. Dealing with real epidemics by mathematical models: the Haitian and
South African epidemics.
References

Wednesday 12th June 2013, 09.0013.00 Renato Casagrandi & Marino Gatto 
Population extinction in spatially explicit landscapes —
Site and bond lattice models. Definition of percolation as a spatial stochastic process. Percolation thresholds.
Interacting particle systems (IPS) and contact processes. Local vs global survival and relationships with percolation.
Fragmented populations: introduction and problems. Metapopulations as IPS's. The contact process and the meanfield approximation. Extinction risk in metapopulations. Various approaches: Markov chains, moment closure, stochastic cellular automata. The influence of landscape structure. Reserve design.
References

The course is free and open primarily to Politecnico di Milano PhDs, but also to other researchers interested in the presented topics. Please fill in the following participation form if you want to participate:
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