Mathematical modelling of infectious diseases
It is possible to mathematically model the progress of most infectious diseases to discover the likely outcome of an epidemic or to help manage them by vaccination. This article uses some basic assumptions and some simple mathematics to find parameters for various infectious diseases and to use those parameters to make useful calculations about the effects of a mass vaccination programme.
Concepts
- The basic reproduction number, R0
- the number of other individuals each infected individual will infect in a population that has no immunity to the disease.
- S
- the proportion of the population (given as a decimal between 0 and 1) who are susceptible to the disease (that is, not immune).
- A
- the average age at which the disease is contracted in a given population.
- L
- the average life expectancy in a given population.
Assumptions
- We assume a rectangular age distribution, such as that which is typically found in developed countries where there is a low infact mortality and much of the population lives to the life expectancy. In developed countries this assumption is often well justified.
- We also assume homogenous mixing of the population. That is, that the individuals of the population under scrutiny assort and make contact at random and do not mix mostly in a smaller subgroup. This assumption is rarely justified as, when dealing with a country such as the UK, most people in London, say, only make contact with other Londoners. If we deal only with London, then there will be smaller subgroups such as the Turkish community or teenagers (just to give two examples) who will mix with eachother more than people outside their group. However, homogenous mixing is a necessary assumption to make the maths simple.