Epidemics have been modeled mathematically for over a century. From Louis Pasteur's work on cholera epidemics, an advanced system of partial differential equations was developed to model the change in percentage of a population over time (Wasserman). From this early model, we get the standard categories used to describe an epidemic. The SIS (Susceptible-Infected- Susceptible) model represents diseases for which there is no immunity; once a person has been infected and recovers, he or she is susceptible to the disease once again. In the SIR (Susceptible-Infected-Removed) model, an individual resides from susceptible to infected to removed (the euphemistic "removed" includes both those with immunity and those that are dead). A more realistic SEIR or SLIR (Susceptible-Exposed/Latent-Infected-Removed) model adds an intermediate step which represents the latent period between exposure and external symptoms and thus can take into account differing degrees of infectiousness which occur during these two stages. Figure 1 shows a visual representation of the various stages used.

Figure 1. A flowchart of possible states in an epidemic model

The Repast toolkit is a set of libraries in Java, developed to support discrete multi-agent simulations. Repast was developed at _____________ a feature of Repast which influenced the decision to use it for this project is its ability to decouple the simulation from real-time visualization, which makes running long batches of simulations much faster. Repast has many graphical capabilities built in which we have used in the project itself.

         This simulation has several parameters that the user can vary. For example, NUM_INFECTED, NUM_REMOVED, and NUM_EXPOSED control the initial number of humans in each of these states. A combination of the NUM_HUMANS parameter with the four display size parameters can be used to set up a specific population density for the simulation. A detailed description of the simulation parameters is shown in the following three tables. Table 1 displays the parameters for the landscape and population of the simulation and their default values.

         When the simulation begins, the first step is to apply the parameters to set up its agents and locations. First, the environment is created. By this statement it means to set a user-controlled environment out of inputs from the user. Next, the human agents are created. Agents are chosen to be put in their own city according to the input of the user to fill the required numbers of initially infected, exposed. All other agents are initially set as susceptible to infection. The agents are initially placed randomly occupying. The numbers based on the user or in this case based on the research found for the average people size in a city. When the locations are created the humans are each assigned to a home and a workplace. Sizes of each home and workplace are drawn from an average distribution, which can be modified to mirror various home and workplace size distributions. Homes are placed randomly across the simulation area, while workplaces are confined to the top left quadrant to approximate a city. Now the simulation is ready for the tick to take over. The tick steps the simulation through time, allowing the agents to perform their programmed tasks. The term tick is the meaning of how the user will input the time for an illness to spread overtime. Meaning this could be sec, min, years, decades, millenniums, etc.

Wasserman and Faust. 1994. http://217.222.182.72/html/elexcourse/htm/lessons/L4_5.htm