The following solution was sent in by Thomas from Dalton Primary School, New York. If you repeated Thomas's experiment with the same simulation parameters you would get different results. Can you think why? It is because the results depend on probabilities. To get reliable results that we can base decisions on we need to find the average (or mean) results from many repetitions of the same experiment with exactly the same parameters.

Thomas's results are interesting because they show very different outcomes according to whether the sick people circulate in the village, or stay at home or are put in total isolation. Lewis from Highcliff Primary School also says that isolation is a good policy but when do you think it is advisable and why?

Thomas's results

I modelled a large village being affected by a very lethal and infectious disease and looked at the impact of mobility and isolation on the length of the epidemic, the number of deaths, the number of infections, and the number of recoveries. @ @

The simulation parameters were:
Grid Dimension	50
Speed	5
Initial Population	500
Initially infected	1
Initially immune	0
Days ill	8
Days before infectiousness	1
Probability of death	0.7
Probability of infection	0.7
Probability of static	0.1
Immune after illness	true
Mobility behaviour	all three options in turn: (normal, static, isolated)

The results were:

Mobility	Duration	Deaths	Not infected	Recovered

Normal	169	342	33	125
Static	35	15	481	4
Isolated	9	1	498	1

Conclusions:

1) Reduced mobility and isolation had an enormous impact on the duration of the epidemic, the number of deaths, and the infection rate.

2) Isolation was more effective than people remaining static when infected.

3) This suggests that when there is a dangerous epidemic (High infection rate, high death rate), effective public health policies would be to tell people to stay at home and to isolate those who are sick.

Ruth from Manchester High School for Girls sent us this careful investigation of a different aspect of this problem. She repeated each experiment several times and drew conclusions from the mean of several runs.

Ruth's Results:

I am investigating whether the incubation period of an illness affects how useful it is to isolate infected individuals.

The simulation parameters were:
Grid Dimension	25
Initial Population	150
Initially infected	25
Initially immune	0
Days ill	8
Probability of death	0.9
Probability of infection	0.9
Probability of static	0.1
Gain immunity	true

Independent Variables:

Days before infectious

Behaviour if ill

RESULTS

Normal when ill

	Duration	Deaths	Never Ill	Recovered
Mean	19.8	135	0.2	14.8
St. dev.	2.7	3.6	0.4	3.5

If the behaviour when ill is normal, the number of days before infectiousness makes no difference.

Isolated when ill

0 days before infectious

Duration Deaths Never Ill Recovered

Mean 9 21.6 125 3.4

St. dev. 0 1.5 0 1.5

1 days before infectious

Duration Deaths Never Ill Recovered

Mean 15.2 81.8 56.8 11.4

St. dev. 1.6 5.5 8.4 3.4

2 days before infectious

Duration Deaths Never Ill Recovered

Mean 18.6 113.4 26.8 9.8

St. dev. 4.4 7.2 6.4 4.6

3 days before infectious

Duration Deaths Never Ill Recovered

Mean 19 126.2 10.8 13

St. dev. 1.5 6.3 7.5 1.7

4 days before infectious

Duration Deaths Never Ill Recovered

Mean 19.2 129.2 4.4 16.4

St. dev. 1.9 4.1 2.2 4.2

5 days before infectious

Duration Deaths Never Ill Recovered

Mean 18.8 133 0.6 16.4

St. dev. 1.9 2.8 0.8 2.9

6 days before infectious

Duration Deaths Never Ill Recovered

Mean 21.8 133.2 0.6 16.2

St. dev. 4.7 4.2 0.8 4.5

7 days before infectious

Duration Deaths Never Ill Recovered

Mean 20 133 0.4 15.8

St. dev. 1.7 4.1 0.8 3.3

8 days before infectious

Duration Deaths Never Ill Recovered

Mean 19.6 136.8 0.2 13

St. dev. 0.8 1.7 0.4 1.7

This disease is very lethal and infectious. If nothing is done, it will kill most of the population of the town. Isolation is an effective way of reducing the death toll and duration of the epidemic.

If the time before infectiousness is a large proportion of the duration of the illness, it makes very little difference to the outcome whether or not infected people are isolated. The percentage difference between the number of deaths when isolated and not isolated is under 1.5 before infectiousness is over half the length of the illness (5 days or more) but is over 80 is almost 40 epidemic follows a similar pattern with less than 1 isolation and non-isolation for 7 or 8 days before infectiousness but over 50

These results show that, while isolating infected individuals will almost always reduce the death toll and end the epidemic sooner, it is most effective when the incubation period of the illness is relatively short. As the incubation period increases, the amount of time that infected individuals are isolated for, and therefore the amount of time they are not infecting others for, decreases, so it is not unexpected that this is the case. The results suggest that, as isolating infected people would be quite difficult and expensive, it is only worth doing so if the incubation period of the infection, when they are infectious but show no symptoms, is quite short compared to the period when they do show symptoms so would be isolated.