Outbreak Investigation, Epidemic Curves & R0

Describing disease occurrence

Baseline vs excess. Epidemiologists judge an outbreak against what is normally seen in that population:

• Sporadic: occasional, irregular cases with no steady pattern.
• Endemic: the usual, constant baseline level of a disease in a population, such as malaria in parts of sub-Saharan Africa.
• Epidemic (outbreak): more cases than expected for that place and time.
• Pandemic: an epidemic that has spread across countries or continents, such as 1918 influenza or COVID-19.

"Expected" is relative, so an epidemic needs no minimum count. A single case of a disease long absent from a region, such as smallpox or polio in the US, is enough to trigger a full investigation.

Attack rates and finding the source

Attack rate. Ill people ÷ people exposed (at risk) during the outbreak, usually given as a percentage. It is a cumulative incidence over a short, defined period: if 45 of 60 guests who ate the chicken salad fell ill, the attack rate among eaters is 75%. Despite its name it is a proportion, not a true rate, because its denominator has no time unit.

Food-specific attack-rate table. For each item, calculate the attack rate among those who ate it and among those who did not, then compare the two. The culprit shows the largest difference (or the highest risk ratio): high among eaters, low among non-eaters, and eaten by most of the ill. A popular food can have a high attack rate in eaters simply because nearly everyone ate it; if non-eaters got sick just as often, it is not the source.

Secondary attack rate. New cases among contacts of a primary case ÷ susceptible contacts, counted within about one incubation period. The denominator excludes the primary case and anyone already immune from vaccination or past infection. Because it counts only person-to-person spread in households, classrooms, or wards, it directly measures transmissibility.

Removing immune contacts from the denominator is the usual trap: the secondary attack rate is always calculated among contacts who could actually have been infected.

Reading the epidemic curve

The curve. An epidemic curve plots cases by date or time of symptom onset. Its shape reveals the mode of spread, and its timing, read against the pathogen's incubation period, points to when exposure happened.

Timing clues. In a point-source outbreak, the peak falls roughly one typical incubation period after the shared exposure, so the incubation period both suggests the agent and dates the exposure. Preformed toxins such as staphylococcal enterotoxin act within hours; infections that must first multiply, such as Salmonella or norovirus, usually take 12 hours or more; hepatitis A takes weeks. Legionella is inhaled from aerosolized water and does not spread person to person, so its outbreaks stay common-source rather than turning into propagated waves.

John Snow traced London's 1854 cholera outbreak to the Broad Street pump by mapping cases, the classic common-source investigation and an early spot map.

R0, Re, and herd immunity

Basic reproduction number (R0). The average number of secondary cases one infectious person causes in a fully susceptible population. It depends on three things: contact rate, probability of transmission per contact, and duration of infectiousness. Measles is among the most contagious infections (R0 about 12–18); seasonal influenza is about 1–2. R0 describes a pathogen in a particular population and setting rather than a fixed constant: crowding and behavior change it.

Effective reproduction number (Re). The actual average number of secondary cases once some people are immune or interventions are working. In the simplest model, Re = R0 × fraction susceptible.

• Re > 1: cases grow.
• Re = 1: cases hold at a steady, endemic level.
• Re < 1: the outbreak declines and fades out.

Herd immunity threshold. Setting Re below 1 means the susceptible fraction must fall below 1/R0, so the fraction immune must exceed 1 − 1/R0. An R0 of 2 needs 50% immunity; an R0 of 15 needs about 93%. When most people are immune, those who cannot be vaccinated, such as young infants and the immunocompromised, are protected indirectly.

Average coverage can hide danger: clustered vaccine refusal, low coverage, or waning immunity creates pockets where Re exceeds 1 and outbreaks ignite even when the national figure looks adequate. Because no vaccine is 100% effective, coverage must exceed the threshold itself.

Running an investigation and surveillance

Choosing the analytic study. When the exposed group is small and fully known, such as wedding guests, a cohort design lets you compute attack rates and risk ratios directly. When the population at risk cannot be enumerated, as in a community-wide outbreak, compare cases with controls and estimate the odds ratio. Control measures begin as soon as a likely source is identified; they need not wait for the analytic study.