Using a fixed population, formula_70 in the three functions resolves that the value formula_5 should remain constant within the simulation, if a simulation is used to solve the SIR model. Alternatively, the analytic approximant can be used without performing a simulation. The model is started with values of formula_72, formula_73 and formula_74. These are the number of people in the susceptible, infected and removed categories at time equals zero. If the SIR model is assumed to hold at all times, these initial conditions are not independent. Subsequently, the flow model updates the three variables for every time point with set values for formula_75 and formula_76. The simulation first updates the infected from the susceptible and then the removed category is updated from the infected category for the next time point (t=1). This describes the flow persons between the three categories. During an epidemic the susceptible category is not shifted with this model, formula_75 changes over the course of the epidemic and so does formula_76. These variables determine the length of the epidemic and would have to be updated with each cycle.