Biology · Biology in Health, Food & the Environment

Transmission, epidemiological reasoning and population-level evidence

Among six fictional people, two already have a defined outcome at the start. Two of the other four develop it halfway through the year. One of the initial cases recovers. Counting new cases, time at risk and cases at the end gives three different summaries of the same complete record.

Research Design, Data & Scientific Practice introduces independent units, assignment, sampling and comparisons. Heredity, Variation & Evolution distinguishes inherited variants from traits and individual responses from population change. Energy, Enzymes & Metabolism introduces cellular reactions and material transformations. Their English chapters are available in this working manuscript; publication remains pending. The examples here use small graphs, fractions, sums and stated time windows, with each convention explained before use.

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By the end, you can

Explain why possible contact is not demonstrated transmission and calculate risk, incidence rate and prevalence with their different denominators.

A contact is an opportunity, not an established chain

For infectious disease, transmission concerns an agent moving from a source into a susceptible host setting. A possible route, a compatible agent and host, and suitable surrounding conditions matter. A contact network records possible opportunities for encounters. Its lines do not automatically mean that an agent crossed those lines or established infection.

The separate six-individual network has five possible contacts and two recorded new cases. The edges are undirected: they supply no time order or movement direction. Even a line connecting the two cases does not identify who infected whom. They could share an unrecorded source, or the recorded encounters could have been irrelevant.

Population patterns can suggest questions about transmission without settling the answers. Changes in reported cases can also reflect which people were observed and how an outcome was defined. A valid comparison needs a population and an observation window, alongside a defensible account of what the observations represent.

Possible encounters do not identify transmission

A shared contact is compatible with several histories. The network cannot distinguish transmission along an edge from an unrecorded shared source.

Read the diagram in words

Possible contacts are One–Two, One–Three, Two–Four, Three–Four and Five–Six. Two and Four have recorded new cases; the other four do not. All five links are undirected opportunities. No case source or actual transmission link is established.

Possible encounters do not identify transmission
Individual	Recorded new case
Individual One	No recorded new case in this window
Individual Two	Recorded new case
Individual Three	No recorded new case in this window
Individual Four	Recorded new case
Individual Five	No recorded new case in this window
Individual Six	No recorded new case in this window

Possible contact
Individual (1)	Individual (2)	Possible contact
Individual One	Individual Two	Possible contact
Individual One	Individual Three	Possible contact
Individual Two	Individual Four	Possible contact
Individual Three	Individual Four	Possible contact
Individual Five	Individual Six	Possible contact

Transmission direction unknown; Case source unknown: ?

Separate original six-individual opportunity network; unrelated to the six-person time account. No agent, infection probability, contact timing or source of cases is supplied.

Risk counts people; a rate counts time at risk

For a first occurrence over a specified interval, cumulative incidence, or risk, is the number of new cases divided by the number initially at risk. The time-account model starts with four people at risk and records two first events during one year. Its risk is two divided by four, or one half. Existing cases are excluded from that first-occurrence denominator.

An incidence rate instead divides new first events by the combined time spent at risk. Each person who has the event at half a year contributes half a person-year before it. Each of the two people without an event contributes one person-year. The total is three person-years, so the rate is two thirds of an event per person-year.

The risk has no time unit attached to its number, but belongs to the stated one-year interval. The rate has inverse-time units and is not a probability. It cannot simply be read as the fraction who will develop the outcome next year. Converting a rate into a future risk requires additional assumptions about how event rates and competing events change over time.

First events, time at risk and cases at the end

Risk and end prevalence happen to equal one half here, but their denominators and case definitions differ. The incidence rate has inverse-time units.

Read the diagram in words

First and Third each contribute half a person-year before a first event at half a year; Second and Fourth each contribute one year without an event. Fifth and Sixth start as cases and are excluded from the first-occurrence denominator. Fifth recovers at a quarter-year; Sixth continues. Risk is two of four, rate two per three person-years, start prevalence two of six and end prevalence three of six. If the two events move to a quarter-year, risk remains one half, time becomes 2.5 person-years and rate 0.8.

First events, time at risk and cases at the end
Individual	Start: Existing case interval	First occurrence	Recovery	Time at risk of first occurrence	Person-years at risk	Existing case interval	End: Existing case interval
Individual First	—	0.5	—	0 → 0.5	0.5	0.5 → 1	Existing case interval
Individual Second	—	—	—	0 → 1	1	—	—
Individual Third	—	0.5	—	0 → 0.5	0.5	0.5 → 1	Existing case interval
Individual Fourth	—	—	—	0 → 1	1	—	—
Individual Fifth	Existing case interval	—	0.25	—	0	0 → 0.25	—
Individual Sixth	Existing case interval	—	—	—	0	0 → 1	Existing case interval

One-year risk
Total population	People initially at risk	First occurrence	Person-years at risk	One-year risk	First events per person-year
6	4	2	3	0.5	0.6666666666666666

Point prevalence
Start / End	Existing case interval	Total population	Point prevalence
Start	2	6	0.3333333333333333
End	3	6	0.5

Earlier first-event timing
First occurrence · Years since start	Time at risk of first occurrence · Years since start	Person-years at risk	People initially at risk	First occurrence	One-year risk	First events per person-year
0.25, 0.25	1, 1	2.5	4	2	0.5	0.8

Years since start; —: No recorded event or not eligible, according to the field

Original six-person complete one-year record. No death, movement, loss to follow-up, recurrence or missing observation. Initially existing cases are excluded from the first-occurrence risk account even after recovery. All new cases persist to the end.

Prevalence concerns cases present at a stated time

Point prevalence is the fraction of the population that has the outcome at a particular time. At the start, two of the six people are cases. At the end, the two new cases and one continuing initial case remain: three of six. The recovery removes a case from the end count without erasing its earlier existence.

In this model, the entire six-person population remains present and observed. There are no deaths, arrivals, missing records or repeat events. The first-occurrence risk account follows the four initially eligible people; it does not add the recovered initial case back as a new person at risk of a first occurrence. These rules keep the denominators explicit.

Different populations can have different prevalence because of both new occurrences and how long outcomes persist, as well as movement and survival. A prevalence difference does not alone identify a transmission-rate difference. Population association also does not identify the cause of an individual's outcome. The description and the causal explanation remain separate tasks.

Worked example

Read three denominators from one timeline

Individuals First and Third have first events at half a year; Second and Fourth have none by the one-year end. Their at-risk durations are one half, one, one half and one year. Adding gives three person-years. Fifth and Sixth were already cases at the start, so neither belongs in the initial first-occurrence denominator.

The one-year risk is two new cases divided by four initially at risk, or fifty per cent. The incidence rate is two divided by three person-years, or approximately 0.667 events per person-year. These values describe different quantities and should not be substituted for each other.

Fifth recovers at one quarter of a year; Sixth remains a case. First and Third remain cases after their events. End prevalence is therefore three divided by six, or fifty per cent. Its numerical equality to the risk is incidental: the case counts and denominators differ. Start prevalence was two divided by six, or one third.

Check your understanding

Why is the first-occurrence risk two divided by four rather than two divided by six?
Show reasoning
Two people were already cases at the start and are not eligible for a first occurrence during this window. Four were initially at risk, and two of those four had the event. The full population of six is used for point prevalence instead.
If the two first events occurred at one quarter of a year while the two nonevent records remained one year long, what would change?
Show reasoning
Risk would still be two divided by four, or one half. At-risk time would become one quarter plus one plus one quarter plus one, or 2.5 person-years. The rate would be two divided by 2.5, or 0.8 events per person-year. Earlier events reduce the observed time at risk without changing this window's number of new cases.
The two new cases in the contact model share an edge. Does that establish transmission along it?
Show reasoning
No. The edge records only a possible encounter and has no time order or confirmed agent movement. Shared exposure elsewhere or another route remains possible. Connecting cases is not the same as establishing their causal transmission history.

What to carry forward

Name the cases, population and time window before calculating. Contact opportunities, risk, person-time rates and point prevalence answer different questions.

References

Resources supporting this lesson’s explanations and examples.