Asya Pritsker's Final project proposal for Math 640 (Sp. 2010)

The goal of the project is to examine from an experimental and graph theoretic perspective the economic effect of an epidemic on a community. In a usual epidemiological model we divide the population into 'susceptible', 'infected'and 'recovered' and consider global rates of disease transmittance between each portion of the population. Here we will also look at producer-consumer relationships. Our community will be represented by a digraph with doubly-weighted edges. An edge pointing from one node (person) to another will indicate that one is a benefactor of the other. One set of weights will indicate the strength of the economic relationship and the other will indicated the strength of the epidemiological relationship. For our purposes it is sufficient to describe the full relationship of two people- how they depend on each other and roughly how much time they spend together.

For example a child depends on his or her parents and is very likely to infect them but it while a worker depends on his boss economically they are unlikely to infect one another. When a person gets sick, two things can happen. If they are a producer their productivity (their economic benefit to the society) goes down. If they are a consumer, their drain on the producer should go up.

We are interested in finding out which individual's illness have the greatest negative impact on the overall stability or economic growth of the society. We will analyze each graph by going through and removing every node and then running the simulation without the node. The critical node will be the one whose removal most negatively impacts the overall stability of the graph. The exact functions and epidemiological interpretation of this is still being worked out.

An even more interesting and important question but not one we will study here is how economics effect the spread of the epidemic. This is more starkly visible in severely impoverished communities where a producer getting sick can sharply decrease the likely hood of his or her dependents' survival.


Experimental Mathematics (Spring 2010) projects pages