The main task is to calculate the epidemiological parameters by comparing the output of mathematical models to data and investigate what kinds of interventions would be required in order to control the outbreak.
One of the main goals in modelling of infectious diseases is to be able to understand the Basic Reproduction Number or $R_0$, but what actually is it? The exact definition is:
The average number of secondary cases for every primary case in a completely susceptible population
This may sound complicated, but it's fairly easy to understand. As an example, imagine a person is infected and passes the infection on to two people. Then one of those people passes the infection on to one other person and the other passes it on to three people. On average each person infected two other people, so we would estimate the $R_0$ of that disease to be 2.
Use the tool below to explore the consequences of different $R_0$ values. An epidemic is simulated for three generations and who infects who are connected by lines.
Notice that if $R_0$ is below one then the epidemic is not likely to get to the third generation. If it's above one then this is possible. It turns out after a long time, if the $R_0$ is less than one then the infection is guaranteed to die out, however if it is bigger than one then there's a probability it will persist and continue to become an epidemic. Estimating the $R_0$ is therefore vitally important for public health intervention.
In this section we can consider the impact of vaccination on the number of secondary cases from one primary case. Below you can explore the consequences of randomly vaccinating the population with a perfect vaccine (one with 100% effectiveness). For a given $R_0$ see how much vaccine coverage you need before a an outbreak is very unlikely. You can also extend the number of generations of the outbreak to simulate to convince yourself whether an outbreak will occur or not.
It turns out that the relationship between an outbreak occurring and vaccination is fairly simple. If the vaccination coverage is $$1 - \frac{1}{R_0}$$ then the probability of an outbreak is zero. Look at the table below for some example diseases and their corresponding $R_0$, the theoretical optimal vaccination coverage is given next to each.
| Disease | R0 | Theoretical optimum vaccine coverage |
|---|---|---|
| Influenza | 2-3 | 50-66% |
| Pertussis (Whooping cough) | 5 | 80% |
| Polio | 5-7 | 80-86% |
| Smallpox | 5-7 | 80-86% |
| Measles | 12-18 | 92-94% |
We can see that some diseases are very highly infectious meaning the vaccine coverage needs to be very high. This is the important to understand as some people are too young, or due to problems with their immune system would be unable to receive a vaccine.
In the next two sections you can explore more closely the impact of vaccination in a model of a city population of 100,000 people. In the third section we can explore its consequences in an epidemic across a whole country. Navigate to these from the menu at the top or click on the links below.