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Implementing the Model in our Simulator
The Kaplan et al. model comprises a system of 17 differential equations, describing the relationship among 17 quantities that are functions of time. Each of these quantities measures the number of individuals that are in a particular state with respect to the disease. For instance, the quantity S0 designates the number of susceptible-untraced individuals at the current moment in time. Initially the value is almost 10 million, but as time goes on, this value decreases as directed by the differential equations. This decrease corresponds to individuals that become infected and individuals that enter the vaccination queue because they were identified as contacts of index cases. Because the total population (including casualties) is constant, other states necessarily increase in population as S0 decreases.
The model in "Smallpox Attack" is a continous mathematical model. We use this simulator to offer an alternate, discrete-time approximation to the solution. In our implementation, the 17 original variables are represented by 17 agents that hold the amount of population in each state. The differential equations are reflected in the rules under which the agents share the population amongst each other at every time period.
Our goal is to replicate the results of the original paper and to make the model easily accessible to those who want to experiment with it. The original article formulates the model as a system of differential equations. We hope to provide an alternate understanding of its behavior through discrete exchange of population between states.
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