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Mathematical Modelling in Biosciences

Raccoon rabies epidemic spread in New York State

Luca Gerardo-Giorda

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Spread of rabies among an heterogeneous raccoons population in New York state - collaboration with J.P. Keller (U. Washington) and A. Veneziani (Emory U.).

When modeling the spread of an infectious disease among wildlife, the classical compartment models that describe space in terms of geopolitical units feature very little accuracy since wild animals do not move at geopolitical scale, and at the same time is very difficult to incorporate landscape heterogeneities.
The reference model we use is thus a Susceptible-Exposed-Infectious (SEI) system where the spatial component of the dynamics is modeled by a diffusion process, the latter being a macroscopic representation of the Brownian motion. The diffusion is designed to take into account landscape heterogeneities such as mountains and waterways.

The video shows the evolution in time of the density of susceptibles, exposed and infectious, as well as the prevalence of the disease, namely the percentage of infectious over the whole population, in the early stage of infection (first 6 years since outbreak).

The main features of the simulation are

1. The barrier effect of the waterways is obtained by reducing the diffusion in the normal direction to the waterway itself.

2. The system is advanced in time with an IMEX (implicit-explicit) scheme, where the nonlinear part is computed at the previous time step, and discretized in space with finite elements on an unstructured triangulation.

3. The computational domain is retrieved from satellite images with ImageJ software (http://rsbweb.nih.gov/ij/), and discretized by a regular triangulation with Netgen (http://www.hpfem.jku.at/netgen/), consisting of 64759 nodes and 127360 triangles.

4. The initial population is estimated according to published value in the literature (between 5 and 17 animals/km2) and by taking into account human population density, as raccoon are more keen to live in highly populated area.

5. The source terms are located in space and time in accordance with recorded cases of rabies in the period 1990-1991.

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Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)