Project Title: Applications of Boolean networks to the study of the spread of an avian influenza epidemic

Adviser: Dora Matache

Description: The Highly Pathogenic Avian Influenza (HPAI) H5N1 has rapidly spread across the world devastating poultry industries. It is therefore important to predict the possible spread of this disease throughout the United States and to estimate the potential effects on agriculture and economics. We propose a Boolean Network model in which the nodes are farms that can be in one of two possible states “infected” or “not infected”. The infection can spread from one farm to other farms through wild life, human contact, equipment traveling. It is also based on geographical aspects of the locations of the farms. The goal of this project is to identify ways of modeling the probability of infection based on (some of) the previously mentioned characteristics. The models will be tested through simulations and comparison with other existing models for the spread of epidemics.

The student will perform the following tasks:

A. Become familiar with and write a brief description of relevant concepts of mathematical modeling in epidemiology and Boolean networks, based on several references such as:

Kasiyanov A., Kirkland L., Matache M.T., Random Boolean Network Model or the Spread of H5N1 Avian Influenza Virus among Poultry Flocks in Nebraska, in preparation.

Ferguson N.M. et al, Strategies for containing an emerging influenza pandemic in Southeast Asia, Nature, Vol 437|8 September 2005|doi:10.1038/nature04017.

Girvan M. et al, A simple model of epidemics with pathogen mutation, Phys. Rev. E 65, 031915 (2002).

Hethcote H.W., The mathematics of infectious diseases, SIAM review, Vol. 42 (4), 599-653 (to get familiar with the SIRS model).

Pastor-Satorras R., Vespignani A., Epidemics and immunization in scale-free networks, Contribution to "Handbook of Graphs and Networks: From the Genome to the Internet" eds. S. Bornholdt and H.G. Schuster (Wiley-VCH, Berlin, 2002)

This will help the student become familiar with the topic and will serve as an introductory section of the final research report.

B. Get familiar with the Matlab software in order to be able to write and run several programs related to the study of the dynamics of the coupled Boolean networks.

C. Actual model generation: identification of significant factors that should be included in modeling the probability of the spread of the infection from one node of the network to another; collection of reasonable assumptions from the biological perspective; implementation of all these in Matlab and simulation of the spread of disease under various scenarios; collection of statistics generated by simulations; comparison with results obtained by applying a different existing model.

D. Create a final research report to be presented at the MAM Symposium.

OTHER REQUIREMENTS: The students interested in the project above are expected to have had experience with probability theory and basic computer skills. They should become familiar with Matlab and TeX, (a popular markup text-editor for mathematical papers), as the project is under way.

NOTE: The results of this research will represent the core of a research paper that later will be sent for publication to a suitable journal.