Secondary Attack Rate Calculation

Secondary Attack Rate (SAR) Calculator

function calculateSAR() { var totalContactsInput = document.getElementById('totalContacts'); var immuneContactsInput = document.getElementById('immuneContacts'); var secondaryCasesInput = document.getElementById('secondaryCases'); var resultDiv = document.getElementById('sar-result'); var sarValueDisplay = document.getElementById('sar-value'); var breakdownDisplay = document.getElementById('sar-breakdown'); var errorDiv = document.getElementById('error-message'); // Reset display resultDiv.style.display = 'none'; errorDiv.style.display = 'none'; // Get values var total = parseInt(totalContactsInput.value); var immune = parseInt(immuneContactsInput.value); var cases = parseInt(secondaryCasesInput.value); // Validation if (isNaN(total) || isNaN(cases)) { errorDiv.innerText = "Please enter valid numbers for Total Contacts and New Cases."; errorDiv.style.display = 'block'; return; } if (isNaN(immune)) { immune = 0; } if (total < 0 || immune < 0 || cases total) { errorDiv.innerText = "Immune contacts cannot exceed total exposed contacts."; errorDiv.style.display = 'block'; return; } var susceptible = total – immune; if (susceptible === 0) { errorDiv.innerText = "There are no susceptible contacts (everyone is immune), so SAR cannot be calculated (division by zero)."; errorDiv.style.display = 'block'; return; } if (cases > susceptible) { errorDiv.innerText = "New cases cannot exceed the number of susceptible contacts."; errorDiv.style.display = 'block'; return; } // Calculation var sar = (cases / susceptible) * 100; // Output sarValueDisplay.innerText = sar.toFixed(2) + "%"; breakdownDisplay.innerHTML = "Calculation Breakdown:" + cases + " (New Cases) ÷ " + susceptible + " (Susceptible Contacts) × 100″; resultDiv.style.display = 'block'; }

Understanding Secondary Attack Rate (SAR)

In epidemiology, the Secondary Attack Rate (SAR) is a critical metric used to measure the transmissibility of an infectious disease. Unlike the basic reproduction number ($R_0$), which estimates spread in a large, fully susceptible population, SAR focuses on the spread of disease within a closed group, such as a household, dormitory, or workplace, after a primary case has been introduced.

Calculating the SAR helps public health officials determine how contagious a pathogen is in close-contact settings and allows for the evaluation of intervention strategies like isolation, quarantine, and vaccination.

How is Secondary Attack Rate Calculated?

The formula for calculating SAR is relatively straightforward but requires precise data regarding the group being studied. The rate is expressed as a percentage.

Formula:
SAR (%) = ( Number of New Cases / Number of Susceptible Contacts ) × 100

To use this formula correctly, you must distinguish between "Total Contacts" and "Susceptible Contacts":

• Total Exposed Contacts: Everyone in the closed group excluding the primary case (patient zero).
• Immune Contacts: Individuals who cannot get the disease due to prior infection or vaccination.
• Susceptible Contacts: Calculated by subtracting Immune Contacts from Total Contacts. This is your denominator.
• New Secondary Cases: The number of susceptible people who became infected. This is your numerator.

Realistic Calculation Example

Let's look at a realistic scenario involving a household outbreak of influenza:

Imagine a household of 6 people. One person contracts the flu at work and brings it home (the Primary Case). This leaves 5 remaining people in the house (Total Exposed Contacts).

Out of these 5 people:

• 1 person had a flu shot and is considered immune.
• 4 people are unvaccinated and susceptible.

Over the next week, 2 of the unvaccinated family members get sick.

The Calculation:

• Susceptible Contacts = 5 (Total) – 1 (Immune) = 4
• New Cases = 2
• SAR = (2 ÷ 4) × 100 = 50%

In this example, the Secondary Attack Rate is 50%, indicating a high level of transmissibility within the household.

Why is SAR Important?

While $R_0$ gives a broad view of a pandemic, SAR provides a microscopic view of transmission efficiency. It is particularly useful for:

1. Comparing Variants: Determining if a new strain of a virus spreads more easily in households than previous strains.
2. Vaccine Efficacy: Comparing the SAR among vaccinated groups versus unvaccinated groups.
3. Policy Making: Deciding whether home quarantine is safe or if infected individuals should be isolated in dedicated facilities.

Factors Influencing Secondary Attack Rate

Several variables can increase or decrease the SAR in any given outbreak:

• Duration of Exposure: Longer contact time with the primary case increases risk.
• Environmental Factors: Poor ventilation in a home can increase SAR for airborne diseases.
• Viral Load: A primary case with a higher viral load may be more infectious.
• Hygiene Measures: Mask-wearing and hand-washing within the home can significantly lower the SAR.