100 students were registered in a school, out of which 60 children were completely immunized. On 10th May a child reported fever and rash. On subsequent case taking, she reported same symptoms for her friend who got sick in school on 8th May. Following the investigation,6 more cases of measles were reported to the Public health officer on 20th May. Calculate the secondary attack rate
Quick Answer:
The Secondary Attack Rate (SAR) measures how many susceptible contacts developed disease after exposure to a primary case. Here, the primary case is the child who got sick on 8th May (index case). The child who reported on 10th May is the secondary case. Then 6 more cases were reported - but we need to sort out who are susceptible contacts.
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Identifying the Key Variables
| Parameter | Value |
|---|---|
| Total students registered | 100 |
| Completely immunized | 60 |
| Susceptible (unimmunized) | 100 - 60 = 40 |
| Index (primary) case | Child who fell sick on 8th May (reported by the 10th May case as her friend) |
| Secondary case | Child who reported fever + rash on 10th May (exposed to index case at school) |
| Additional cases reported on 20th May | 6 |
Who Are the Susceptible Contacts?
- The index case (primary case, 8th May) is excluded from the denominator - she is the source, not a contact.
- Susceptible contacts = all unimmunized students minus the index case
- Susceptible contacts = 40 - 1 = 39
Counting Secondary Cases
Secondary cases = all cases arising from exposure to the index case among susceptible contacts:
- Child with fever/rash on 10th May = 1 secondary case
- 6 more cases reported on 20th May = 6 secondary cases
- Total secondary cases = 7
Formula
$$\text{SAR} = \frac{\text{Number of secondary cases among susceptible contacts}}{\text{Total susceptible contacts (excluding index case)}} \times 100$$
$$\text{SAR} = \frac{7}{39} \times 100$$
$$\boxed{\text{SAR} = 17.9%}$$
Summary
| Step | Value |
|---|---|
| Susceptible contacts (denominator) | 40 - 1 = 39 |
| Secondary cases (numerator) | 1 + 6 = 7 |
| Secondary Attack Rate | 7/39 × 100 = 17.9% |
Why 39 and not 40? The index (primary) case herself is removed from the denominator because SAR measures transmission from the index case to susceptible contacts - the index case cannot be her own contact.
Why not include immunized children? Immunized children are not considered "susceptible," so they are excluded from the denominator per the standard SAR definition.
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