1.5 Start here

In summary, it turns out that even with some initial assumptions we can very quickly build up a mathematical model to explain data. Even with these first steps we have a lot more to uncover:

• How would you determine the parameters \(k\) and \(N\) with the collected data?
• Are there other more complicated models?
• What techniques are used to determine the formulas \(I(t)\)?
• Are there other numerical techniques to approximate the solution \(I(t)\)?
• What happens to our solutions when the parameters \(k\) and \(N\) change?
• What happens to our solutions when the number of infected people change randomly for some reason?

We will study answers to these questions and more. Let’s get started!