In this problem set, we examine a simple model for the spread of a contagious disease Our model makes the following assumptions the disease can only be transmied by humantohuman contact in a single specific population the size of the population remains constant in time (that is, no births or deaths occur and the population is cut o from the outside world) the disease confers no immunity aer someone has recovered from infection Of course, these assumptions limit the applicability of our model to reallife epidemics, but they provide a good foundation upon which more complex and accurate models can be based Let time be denoted by 0, ), measured in days From the above assumptions, the population can be divided into two groups () fraction of the population that is susceptible to infection but not actually infected at time , and () fraction of the population that is infected at time Our model requires two parameters with values in (0, 1) the infection rate and th