The usual method would be to:

1. define the differential equations

2. solve the differential equations

3. solve the constants of integration from your knowledge of the number of infections today, the rate of infection today any your knowledge that at time equals infinity the entire population will have survived the infection and will be immune.

However, the language in your question is not very precise, so I wonder if you are required to give a precise answer. Have you studied numerical methods?

A quick spreadsheet assuming that at day 1 there is just one infected person suggests that there would be 2100 infected people at about day 20. The infection rate for the next few days would be about 1000 per day, the maximum infected people about 10,000 would occur in about a week (i.e. day 27) and within a month there would be no infections because everyone has become sick and recovered.

The chief scientist is probably familiar with Excel but he/she has probably forgotten everything they ever knew about solving differential equations.