The following functions model the number of infected people by Measle and Hepatitis, respectively:
Where x is the time measured in any unknown unit (could be days, weeks, etc).
3) Under this assumption, the values of x must be positive or 0 because it does not make sense to evaluate what happened before the first person was infected. Time 0 represents the moment when the first infected person was detected.
4) If y or f(x) represents the number of infected people, it cannot be negative because of the nature of the situation. Cannot have -10 infected people, for example.
5) The totals assume the rate of infection will be constant. There are many situations that can affect that behavior. Isolating sick people, giving people required treatment, dying people that won't infect others anymore, etc.