The premise of the experiment is:

In a group of 10 people, present your findings with different mathematical models (eg, logistics, SI, SIS) or any other mathematical models.

An initial person has a virus on the first day and infects someone else on the second day.

On any given day, each person who has the virus on that day infects someone the next day.

The process is repeated daily until all the people in the group have the virus.

The total number of people who have the virus is noted each day and recorded. On any given day some people who already have the virus might come into contact with the virus again. These people will not be counted twice.

Start by randomly selecting a person to be the initial person.

On each day, anyone who has the virus already selects another person at random to infect.

If the first person selects their own number on the first day, there would be only one person who is infected on day two.

The selected students on each day may or may not have already been selected. If a student who had already been infected was selected again, that person was not counted again.

Continue the simulation until the entire group has the infection.

Collect data showing the total number of people who have the virus each day, and represent your results in tables, graphs and formulae.

Questions:

Could you outline the strategy?

Design, perform and record suitable simulations that allow you to investigate the spread of viruses in groups.

Show evidence of the application of mathematical models and strategies, including calculations, and result in using appropriate graphs, tables and formulas. Why did you choose to use these equations or formulas? What do they represent and how to solve the variables? How do you figure out the rate of infection?

Show with the use application of differentiation.

So, how long before everyone has the virus?

Investigate the way a virus spreads through a group of people and the length of time it takes for an entire group to be infected.

Investigate the factor that affects the spread of the virus. Do they always spread at the same rate? Do they always take the same amount of time to spread to everyone?

Show with the use of a calculator:

1. random number generator on the calculator
2. regression on the calculator, which will produce suitable functions.

What are the assumptions that need to be included? Why did you make them? How did they affect what you did?

Discuss the reasonableness and limitations of the results.

What are some improvements for this investigation in the future?

Could you generalise the scenario?