1. Spread of Diseases Modelling Mathematically

2. Spread of Diseases Hello mathematician, What you are about to read is classified information. As you are aware Ebola has been spreading rapidly throughout the world. What has not been made public is that Ebola has been around since 1976 in Western Africa. Since then there has been three separate epidemics with the current one being the largest. So far there has been 13,268 cases reported resulting in 4960 deaths. However a new and potentially dangerous infectious disease has broken out in the UK. As you are a mathematician the government are urgently seeking your help and we are asking you to forecast how the disease will spread. We have been carefully monitoring those people already infected and their friends and families. Their data show that an infected person typically goes on to infect either one or two others. We need you to carry out some experiments and report back to us your findings.

3. Spread of Diseases

5. TASK 1: Carry out the experiment at least five times, drawing a diagram for each experiment. Work out the total number of infected people at the end of each experiment. Using the information from one of the experiments draw a graph (see above) of ‘ the number of infected people ’ against ‘ generation ’ How many infected people do you have at the end? Repeat the simulation several times. In general, do you think that the infection will go on spreading, or will it die out of its own accord? STRETCH AND CHALLENGE - What is the average number of sick people at the end of the experiment? What is the average number of sick people each person effects (Epidemiologists call the average number an infected person infects the basic reproduction ratio of the disease)? Which average did you use and why? What do you think would happen if you continued repeating this process over a longer period of time? Can you prove this?

6. Spread of Diseases TASK 2: Carry out the experiment at least five times, drawing a diagram for each experiment. Work out the total number of infected people at the end of each experiment. Using the information from one of the experiments draw a graph (see above) of ‘the number of infected people’ against ‘generation’ How many infected people do you have at the end? Repeat the simulation several times. In general, do you think that the infection will go on spreading, or will it die out of its own accord? STRETCH AND CHALLENGE - What is the average number of sick people at the end of the experiment? What is the average number of sick people each person effects (Epidemiologists call the average number an infected person infects the basic reproduction ratio of the disease)? Which average did you use and why? What do you think would happen if you continued repeating this process over a longer period of time? Can you prove this?

7. Spread of Diseases Write a short paragraph reporting you findings back to the government. PLENARY How can YOU help the battle against Ebola? So far £98 million has been raised to fight Ebola and help care for those with the disease. This is only a fraction of the amount needed. If you would like to donate (with parents/carers permission) then you can go to one of the following websites http://www.redcross.org.uk/en/Donate-Now www.oxfam.org.uk/ebola_crisis_appeal www.unicef.org.uk/Donate-Ebola