Epidemiology metrics explained: Incidence, prevalence, R₀, CFR & attack rate

Incidence is all about what is new. It measures the number of new cases of a disease that appear in a specific population over a defined period. Think of it as a snapshot of how quickly an infectious disease spreads.

Public health officials track incidence to identify outbreaks and monitor the effectiveness of interventions like vaccination campaigns or public health advisories. A rising incidence rate can be an early warning sign that an outbreak is growing.

How is incidence calculated?

The formula for incidence is straightforward:

Incidence Rate = (Number of new cases in a time period) / (Total population at risk)

For example, if a town of 10,000 people reports 50 new cases of the flu in January, the incidence for that month is 50 per 10,000 people.

Real-world example: Influenza

In 1998, during a respiratory illness outbreak on a cruise ship, public health officials found that 58 people developed symptoms out of a population of 5,000 people at risk over a one-month period. 

Using the incidence formula, they calculated an incidence rate of 58 ÷ 5,000 = 0.0116, or 11.6 cases per 1,000 people per month. This high incidence rate prompted officials to implement outbreak control measures to prevent further spread.

If incidence is about new cases, prevalence is about the total burden of a disease. It measures the total number of individuals in a population, both new and existing cases, who have a disease at a specific point in time.

Prevalence gives a broader picture of a disease’s overall impact on a community or country. It helps healthcare systems plan for long-term care and resource allocation.

How is prevalence calculated?

The formula for prevalence is:

Prevalence = (Total number of cases (new + existing)) / (Total population)

For instance, if on a given day in that same town of 10,000 people, a total of 200 people are currently sick with the flu (including the 50 new cases and 150 existing ones), the point prevalence is 200 per 10,000 people.

Real-world example: Chronic vs. acute illness

Prevalence is particularly useful in epidemiology for understanding chronic conditions. A disease like diabetes has a high prevalence because people live with it for a long time. 

In contrast, an acute illness like the common cold has a low prevalence at any given moment because people recover quickly, even though the incidence (new cases) is very high.

Incidence vs. prevalence: what is the difference?

One way to understand incidence vs. prevalence is through traffic patterns [1].

• Incidence is the cars entering the highway at on-ramps (the new cases)
• Prevalence is the total number of cars currently driving on the highway (all active cases at that moment)
• Recoveries and deaths are cars exiting at off-ramps and reaching their destination

Let’s look at some examples.

The common flu is a disease with a high incidence but low prevalence because while a lot of people get sick fast, they also recover quickly. It’s like a lot of cars flooding onto the highway but also exiting as fast.

HIV, on the other hand, is a disease with low incidence but high prevalence. New cases are relatively rare, but people who become infected typically carry the virus for life. This is like a highway where only a few cars trickle on at the on-ramps, but once they’re there, they’re stuck with few working exits.

The basic reproduction number, R₀ (pronounced “R-naught”), estimates how contagious an infectious disease is. 

It represents the average number of people that one infected person will pass the virus on to in a population with no pre-existing immunity.

• If R₀ is less than 1, the infection will die out
• If R₀ equals 1, the infection will remain stable
• If R₀ is greater than 1, the infection will spread and cause an outbreak

Think of R₀ as a measure of how “socially active” a virus is at a party where no one has immunity:

• If R₀ equals 1, each infected person passes the virus to exactly one other person and the outbreak stays steady
• If R₀ is less than 1, the outbreak fizzles out
• R₀ is greater than 1, each person infects multiple others, causing the outbreak to snowball

Why R₀ is not a fixed number

R₀ is not a fixed biological constant for a virus. It is a changing estimate based on factors like population density, social behaviors, and environment. For example, the R₀ for a virus will be higher in a crowded city than in a rural area, simply because each person can infect more people in close quarters.

Real-world example: Measles vs. seasonal flu

Measles is extremely contagious, with an estimated R₀ of 12-18. This means one person with measles could infect 12 to 18 others in an unvaccinated population. In contrast, seasonal flu is less contagious, with an R₀ typically between 1 and 2.

The Case Fatality Rate (CFR)measures the severity of a disease by calculating the proportion of diagnosed individuals who die from it. It is a critical metric to help assess the deadliness of an outbreak and prioritize public health responses [2].

How is CFR calculated?

The formula is:

CFR = (Number of deaths from a Disease) / (Total number of diagnosed cases) x 100%

For example, If 100 people are diagnosed with a disease and 5 die, the CFR is 5%.

The challenges of getting it right

CFR can be a tricky number, especially early in an outbreak. It can be overestimated if only the most severe cases are being tested and diagnosed. Conversely, it can be underestimated if many mild or asymptomatic cases go undetected.

The CFR also depends heavily on the quality of healthcare available. A disease might have a much higher CFR in a region with a strained healthcare system. 

Because of these challenges, epidemiologists often also try to calculate the Infection Fatality Rate (IFR), which includes all infected individuals (diagnosed and undiagnosed), but this is much more difficult to estimate.

Real-world example: Ebola vs. the common cold

Ebola virus disease (EVD) has a very high CFR, with past outbreaks reaching up to 90%. In contrast, the common cold has a CFR that is effectively zero.

The attack rate is a specific type of incidence rate used for a narrowly defined population over a limited time, usually during an outbreak. It pinpoints the proportion of a group of people who were exposed to a source and became ill [3].

How is the attack rate calculated?

The formula is:

Attack Rate = (Number of people who got sick) / (Total number of people exposed) x 100%

When is it used?

The attack rate is the go-to metric for investigating localized outbreaks. Health officials use it to identify the source of an infection and understand who is most at risk in a specific setting.

Real-world example: A food poisoning outbreak

Imagine a wedding with 200 guests. Of the 100 guests who ate the chicken dish, 50 reported symptoms of food poisoning the next day. The attack rate for those who ate the chicken is 50% (50 sick / 100 exposed). This high attack rate strongly suggests the chicken was the source of the outbreak.

Incidence, prevalence, R₀, CFR, and attack rate form the essential vocabulary of disease surveillance. Together, these metrics paint a picture of an outbreak, revealing everything from how fast it spreads to how deadly the disease may be. 

When public health experts track new disease outbreaks, they rely on these measurements to make critical decisions about quarantine policies, vaccine distribution, and resource allocation.

How do scientists track disease outbreaks?

Scientists use five key epidemiology metrics to monitor outbreaks: Incidence (new cases), Prevalence (total cases), Basic Reproduction Number (R₀, or infectiousness), Case Fatality Rate (CFR, or severity), and Attack Rate (risk in a specific group).

What is the main difference between incidence and prevalence?

The main difference is that incidence tracks only new cases over a period, showing the rate of spread. Prevalence counts all existing cases (new and old) at a single point in time, showing the overall burden of a disease.

How do you calculate R0 in simple terms?

R₀ is not calculated with a simple public-facing formula. It is a complex estimate that epidemiologists derive from mathematical models. These models consider three main factors: how likely the virus is to pass between people (transmissibility), how many people an infected person contacts (contact rate), and how long they are infectious (infectious period).

When would you use an attack rate instead of incidence?

You use an attack rate for a specific, well-defined group of people over a short and contained period, like an outbreak at a party, school, or conference. You use incidence to measure new cases in a broader community (like a city or country) over a longer time frame (like a week, month, or year).

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