An Agent Epidemic Model

Toward a general model

Objectives

An epidemic is any attribute that is passed from one person to others in societydisease, an idea, a belief, a fad, a market, a behavioral pattern.

The model demonstrated the sensitivity of factors such as virility of the infectious agent, the "reach" of the vector and the density of the population.

Also: to begin the development of a general purpose forecasting model based on the use of agents.

Premises

Very simple systems can produce complex behavior. Systems that are apparently random may be ordered. Social databases may extend epidemiology to a social

setting. Computers and agent models may provide an alternative to

the "classic" scientific approach in which system behavior is predicted by systems of equations.

Concepts

Simple rules for the behavior of agents in a simulation can produce unexpectedly complex and realistic results.

The behavior of real life systems may be so complex as to appear random but simple rules for individual elements may lead to this behavior.

Models based on agents can be run many times to create what Epstein and Axtell call a "computarium" in which social experimentation, including epidemics, may be conducted.

Some Definitions

Cellular automata models the present state of a cell in a matrix is determined by the state of cells surrounding it

In agent models, the cells are "occupied" by agents that interact with each other- even at a distance- and sometimes interact with the attributes of the cells in which they exist. Further they may move from cell to cell.

Dynamical systems models are equation-based, when solved, these equations provide forecasts.

Similarities

Output is complex but simple equations or rules. Nevertheless, inability to predict the behavior. History is essentially useless in forecasting. High sensitivity to initial conditions. Self-organization that is sometimes observed in the midst of

otherwise random appearing behavior. Evolution to non-repeating random or divergent patterns.

The Model Rules

A grid of 100 by 100: 10,000 agent sites. User specified population density User specified "reach" of the infectious vector Multiple runs each simulating a period of time. Spatial distribution of agents is randomly determined. Once an agent is infected, it stays infected, and becomes in

turn, infectious.

End of 1st Period

End of 2nd Period

End of 5th Period

1 2 3

Spread Range

Pct of Population Infected

Percentage of Population Infected after 5 Weeks(average of 10 runs for each density; population density= 17.5)

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0.2

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12.5 15 17.5 20 22.5 25

Population Density

Pct of Population Infected

Percentage of Population Infected after 5 Weeks(average of 10 runs for each density; infection range= 2)

Conclusions

We believe that a simple and accessible general-purpose model is possible.

While this version contained only susceptibles and infecteds, future versions could include infecteds that recover and are immune or die, mavens that "sell" the idea (or "overinfect"), and costs of or benefits of infection.

Such models can be used to reach a better understanding and provide a basis for experimentation with social epidemics, interactions, and markets.