Copyright © University of Cambridge. All rights reserved.
'Epidemic Modelling' printed from http://nrich.maths.org/
This is an entirely open problem to which there are no 'correct'
answers. Indeed the answers are not even known. You are doing
genuine research. You can choose the characteristics of the disease
you want to model and study.
The environment is designed so that the researcher can use a
mathematical model to explore the possibilities of the spread of
the disease before it actually hits a real population. Doctors can
estimate the probability of death and the duration of the
infectious period for different diseases. Based on this knowledge
the public health officials may decide on advising the public
whether sick individuals should stay at home to limit the risk of
spreading the infection, or even advise that all infected
individuals are put into isolation to curb the spread of the
These projects can be carried out with only a basic knowledge of
probability and statistics or with a higher level of knowledge. The
more mathematics you use to analyse your results the more potential
value there might be in your findings.
- Decide how many individuals there are in your population.
- Decide how many individuals are infected with the disease at
- Decide on how many individuals (if any) will be vaccinated in
- Decide on the probability $p$ of catching the disease on
contact with it.
- Decide on the probability $q$ of dying and $1-q$ of recovering
from the disease.
- Decide how many days the disease lasts.
- Decide on the incubation period during which time the sick
person is in circulation and passes on the disease to others.
- Choose one of these three options: After the incubation period,
and while the illness lasts, the sick individual can either (1)
circulate in the population as normal or (2) stay at home (modelled
by remaining static) or (3) be put in isolation and have no contact
- Decide whether recovered individuals can be re-infected or not.
If not they will develop an immunity in which case they become dark
green on the display.
- Model a day as a trial during which every healthy individual
either stays in the same place or moves one square in one of 8
- Note that paths touching the edge of the board continue along
the 'reflected' direction back into the village. To avoid
collisions both individuals stop in their tracks.
- If a healthy individual, who is not immune, lands on a square
that touches the space of a sick individual, either corner to
corner or edge to edge, then the healthy individual is immediately