# Math May Distinguish Flukes from Flu Epidemic Outbreaks

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Outbreak, epidemic, or nothing to worry about? Math has the answers. Image by Decoded Science

## Is it an Epidemic? Do The Math!

For ‘G‘ closer to zero, the risk of epidemic is greater. Now, an outbreak investigation must determine ‘R‘.

In the past, this required determining the source of infection for each patient. This process may well find new patients who had not visited a doctor, and may take long enough for new patients to become ill. In short, it’s a long and expensive process. The research paper demonstrates that the proportion ‘F‘, the first case found within each cluster during an outbreak investigation, is about as reliable in predicting ‘R‘ as thoroughly investigating every patient in each cluster.

The relationship is “R=1-F”.

## Introducing the Research Paper’s Math for Recognizing Flu Epidemics

The research paper delves much more deeply into the mathematics, but its conclusion has an intuitive appeal.

Assume an equal probability that any diseased person may be the first to be diagnosed. If there are ‘n‘ people, each has a 1/n chance of being that first person.

In routine sentinel surveillance, a disease that is not easily transmitted will have a short chain; perhaps L=2. Then there is a 50% chance of first diagnosing head of the chain, the person who “caught the flu” from the animal reservoir, and we expect G=1/n approximately. Then we would find “R=(1-G)=0.5”, and decide that there is little risk of an epidemic.

On the other hand, if the disease easily passes from person to person, the chain would be longer; say L=10. The chance of randomly selecting the head of the chain is then 1/10. So “R=(1-G)=0.9”. The outbreak investigation would begin.

During the outbreak investigation, we find ‘F‘ has a similar pattern. Each cluster has n patients to be diagnosed. Each person, including the person at the head of a chain, has an equal probability, 1/n, of being the first. So F=1/n, and R=1-F in an outbreak investigation.

Naturally this intuitive appeal falls far short of the research paper’s rigour in the mathematical analysis and statistical corroboration, and this issue is too important for an intuitive approach such as we may take when calculating voter fraud statistics; the research paper shows why the results are credible.

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