Lesson 5 of 5 / Infection, vaccination and disease spread
R0, outbreaks, epidemics and pandemics
What does R0 predict, and what does it leave out?
I can explain basic reproduction number and scales of disease spread.
I can explain R0 and the interpretation of outbreak progression.Syllabus
Syllabus 9477, Extension A(j). Explain R0 and the interpretation of outbreak progression.
I can distinguish outbreak, epidemic and pandemic.Syllabus
Syllabus 9477, Extension A(k). Distinguish outbreak, epidemic and pandemic.
About 7 min
Make a guess. You are not marked.
A disease has R0 = 3. Does every infected person infect exactly three others?
Show the answer
It is an average.
Some people infect many and some none. R0 is the mean number of secondary cases in a fully susceptible population.
The key idea
R0 is an expected number of secondary infections in a fully susceptible population under specified conditions, not a fixed property of the virus alone.
Connect cause and consequence
What happens when the expected number crosses 1?
R effective = 3 x 0.5 = 1.50
| Generation | Expected count |
|---|---|
| 0 | 10.00 |
| 1 | 15.00 |
| 2 | 22.50 |
| 3 | 33.75 |
| 4 | 50.63 |
R effective is above 1, so expected new infections grow. Fractional values are expectations over comparable situations, not fractions of an actual person. Generations are not necessarily days.
Assumptions: homogeneous mixing, perfect immunity and constant conditions over these generations, with no depletion of susceptible people. This short-run arithmetic illustration uses R effective = R0 x susceptible fraction; R0 itself refers to a fully susceptible population.
Explanation
The basic reproduction number, R0, is the average number of secondary infections generated by one infectious case in a wholly susceptible population under specified conditions. It reflects contact opportunities, transmission probability and infectious duration. It has no unit of time and is not the same as the number currently infected.
In a simple model, R0 above 1 permits initial growth, while below 1 favours decline. Chance events, heterogeneous contact patterns and changing behaviour mean a small outbreak can still end even when the expected value exceeds 1. R0 is not an exact prediction that every person infects the same integer number.
As immunity or interventions change conditions, the effective reproduction number describes actual transmission more appropriately. Under a deliberately simplified homogeneous model with perfect immunity, R_effective = R0 x susceptible fraction. Real vaccine effectiveness and uneven mixing can change this relationship.
An outbreak is an occurrence of cases above what is expected in a particular setting; an epidemic is a larger increase above the expected level in a population or region. A pandemic is an epidemic spread across multiple countries or continents with broad sustained transmission. These terms describe spread, not automatically the severity of each case.
Step by step
- 1
State the population assumption
Do not use R0 as if immunity is absent when it is not.
- 2
Interpret the threshold
Expected growth differs from a guaranteed individual outcome.
- 3
Separate scale and severity
A spread label does not specify case fatality.
Worked example
Work through the evidence
A hypothetical agent has R0 = 3. If half the population is perfectly immune with homogeneous mixing, estimate R_effective.
One way to explain it
3 x 0.5 = 1.5, so the simple model still permits growth. This assumes perfect protection and uniform mixing.
Why this answer works
- Use the susceptible fraction, not the immune fraction directly.
- A real intervention assessment needs its actual effectiveness and contact structure.
Watch out for this
A student says: "R0 = 3 means every infected person infects exactly three people each day." What is wrong with this?
Show the answer
It is an average total secondary-infection count under stated conditions, not a daily fixed count for every person.
Check your understanding
Which statement about a pandemic is correct?
Show the answer
It describes extensive international spread of an epidemic.
The category concerns the distribution of transmission.
Exam-style questions
Check your understanding
In a simple model, a disease has R0 = 5. What proportion of the population must be immune to stop its spread?
Show the answer
80%
The threshold is 1 - 1/R0 = 1 - 1/5 = 0.8, or 80%.
Quick recall
What does R0 predict, and what does it leave out?