Curves in epidemiologyLife path is full of Curves thus the Epidemiology too.

Dr. Bhoj R SinghAct. Head of Division of Epidemiology

Indian Veterinary Research Institute, Izatnagar-243122, IndiaEmail: brs1762@ivri.res.in

Curves• Depiction of frequency distribution in

graphical format is a curve.

Characteristics of frequency distribution:• Central value (most common: the arithmetic

mean, the median, and the mode. Rare: the midrange and the geometric mean)

• Variance (the range, variance, and the standard deviation)

• Shape (Symmetric, Skewed)

B=Symmetrical, normal; A= Positively skewed, skewed to right; C= Skewed to left, negatively skewed

Types of Curves

• Epidemic curves• Survival curves

• Cumulative frequency (incidence curves)• Distribution curves

Epidemic curve

• An epidemic curve isn’t a curve at all, but a histogram that shows cases of disease during a disease outbreak or epidemic by their date of onset.

• the number of cases on the vertical axis and time on the horizontal axis (The duration of the epidemic is shown along the x-axis in equal time periods).

Epidemic (outbreak) and Hypodemic (sudden banishment of a disease from a

population)

The X axis

• Time line• Intervals are decided on the basis of incubation period

and length of illness.• Hours for an outbreak of C. perfringens gastroenteritis,

or 3-5 days for an outbreak of hepatitis A. As a general rule, we make the intervals less than one-fourth of the incubation period of the disease shown. The x axis begins before the first case of the outbreak, and show any cases of the same disease which occurred during the pre-epidemic period. These cases may represent background or unrelated cases.

Cumulative frequency/ survival curves

Interpreting the Epidemic curve• An epidemic curve which has a steep upslope and a more gradual

down slope (a log-normal curve) indicates a point source epidemic in which susceptible are exposed to the same source over a relative brief period. In fact, any sudden rise in the number of cases suggests sudden exposure to a common source. In a point source epidemic, all the cases occur within one incubation period.

• If the duration of exposure is prolonged, the epidemic is called a continuous common source epidemic, and the epidemic curve will have a plateau instead of a peak.

• Intermittent common source epidemics produce irregularly jagged epidemic curves which reflect the intermittency and duration of exposure, and the number of individuals exposed.

• Animal to animal spread – a propagated epidemic – should have a series of progressively taller peaks one incubation period apart, but in reality few produce this classic pattern.

Point source

0

5

10

15

20

No of cases

Time

Duration ~ Incubation time

Continous source

Mean IP

0

5

10

15

20

1 4 7 10 13 16 19 22 25 28 31 34 37

No of cases

Weeks

Is it Continuous source Outbreak?

Intermittent sourceNo of cases

Time (days)

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Propagated epidemic Animal-to-Animal transmission

0

5

10

Zeit

No of cases

Generation

time

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Is it propagated outbreak?

Middle East respiratory syndrome corona virus

Probable exposure time

0

5

10

15

Time

1 Median onset time

23

50% 50%Probable exposure time

Median incubation time: Intervall between first and last disease onsetNo of cases

1 2 3 4 5 6 7 8 9 10 11 12 1314 15 16 17 18 19 20 21 22

Probable exposure period

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 TimeProbable exposure period

minimum incubation time

Maximum incubation time

No of cases

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Two ways of making epicurves in Excel

• The ”square method”– Turn a work sheet in to squares– Fill in each patient as a square

• The ”chart method”– Make a table of onset times– Use the chart wizard– Make a histogram (by removing intervals between

bars in a bar chart)

Applications of epidemic curves• Time components of an outbreak• Shows

– Start – End – Duration – Peak– Outliers

• Help to frame hypothèses on– Route of transmission– Probable exposure period– Iincubation time

• Refining the estimate of the point in time of occurrence of a focal point source

• Identifying multiple possible sources of exposure• Distinguishing primary and secondary cases• Unmasking outbreak source through epidemic curve segmentation