We can represent how individuals move from one category to another in the following way: 3 r317 R where 5 > 0 is the infection rate, and 'y > 0 is the recovery rate. We assume that the individuals in all classes are wellmixed, i.e., every pair of individuals has an equal probability of coming into contact with one another. In this case, our system can be described by a system of rst order differential equations for the variables 8(t), I (t), R(t), called the SIR Model, given by S'=SI (1) ream71 (2) R'=vI (3) The physical interpretation of the different terms in each equation is the following. 0 Equation (1) states that the number of susceptible individuals decreases at a rate proportional to the number of susceptible individuals times the infected individuals. This product is proportional to the number of encounters between susceptible and infected individuals. 0 All the susceptible individuals who became infected move to the class of infected people, therefore, in equation (2) we have that the number of infected individuals increases at the same rate that the number of susceptible individuals decreasesthe rst term. The second term in equation (2) represents the number of infected individuals decreasing because of the people who are recovering and moving into the class of recovered individuals. This number is proportional to the number of infected peolpe, with a constant of proportionality, 77the recovery rate. 0 Equation (3) says that the rate of change of the recovered individuals, R', is proportional to the number of infected individuals, I, where the proportionality constant is the recovery rate, 7. This equation means that for a given unit of time, a proportion 7 of the infected individuals move to the class of recovered individuals