.calc-container {
max-width: 800px;
margin: 20px auto;
padding: 25px;
background-color: #f9fbfd;
border: 1px solid #e1e4e8;
border-radius: 8px;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-title {
text-align: center;
color: #2c3e50;
margin-bottom: 25px;
font-size: 24px;
font-weight: 700;
}
.input-group {
margin-bottom: 20px;
display: flex;
flex-direction: column;
}
.input-group label {
font-weight: 600;
margin-bottom: 8px;
color: #34495e;
}
.input-group input {
padding: 12px;
border: 1px solid #cbd5e0;
border-radius: 6px;
font-size: 16px;
transition: border-color 0.2s;
}
.input-group input:focus {
border-color: #3498db;
outline: none;
}
.input-hint {
font-size: 12px;
color: #7f8c8d;
margin-top: 5px;
}
.calc-btn {
width: 100%;
padding: 14px;
background-color: #3498db;
color: white;
border: none;
border-radius: 6px;
font-size: 18px;
font-weight: 600;
cursor: pointer;
transition: background-color 0.2s;
margin-top: 10px;
}
.calc-btn:hover {
background-color: #2980b9;
}
.result-box {
margin-top: 25px;
padding: 20px;
background-color: #ffffff;
border: 1px solid #e1e4e8;
border-radius: 6px;
display: none;
}
.result-header {
font-size: 14px;
text-transform: uppercase;
letter-spacing: 1px;
color: #7f8c8d;
text-align: center;
}
.result-value {
font-size: 42px;
font-weight: 800;
color: #2c3e50;
text-align: center;
margin: 10px 0;
}
.result-status {
text-align: center;
font-weight: 600;
padding: 8px;
border-radius: 4px;
margin-bottom: 15px;
}
.status-green { background-color: #d4edda; color: #155724; }
.status-yellow { background-color: #fff3cd; color: #856404; }
.status-red { background-color: #f8d7da; color: #721c24; }
.metric-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 15px;
margin-top: 15px;
border-top: 1px solid #eee;
padding-top: 15px;
}
.metric-item {
text-align: center;
}
.metric-label {
font-size: 13px;
color: #666;
}
.metric-val {
font-size: 18px;
font-weight: 700;
color: #2c3e50;
}
.article-content {
max-width: 800px;
margin: 40px auto;
line-height: 1.6;
color: #333;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
}
.article-content h2 { color: #2c3e50; margin-top: 30px; }
.article-content h3 { color: #34495e; margin-top: 25px; }
.article-content ul { padding-left: 20px; }
.article-content li { margin-bottom: 10px; }
.formula-box {
background: #f1f4f8;
padding: 15px;
border-left: 4px solid #3498db;
font-family: monospace;
margin: 20px 0;
}
function calculateR0() {
var transmissibilityInput = document.getElementById('transmissibility').value;
var contactRateInput = document.getElementById('contactRate').value;
var durationInput = document.getElementById('duration').value;
// Validation
if (transmissibilityInput === "" || contactRateInput === "" || durationInput === "") {
alert("Please fill in all fields to calculate R₀.");
return;
}
var tau = parseFloat(transmissibilityInput); // Percentage
var c = parseFloat(contactRateInput);
var d = parseFloat(durationInput);
if (isNaN(tau) || isNaN(c) || isNaN(d) || tau < 0 || c < 0 || d 1
var hit = 0;
var hitText = "N/A";
if (r0 > 1) {
hit = 1 – (1 / r0);
hitText = (hit * 100).toFixed(1) + "%";
} else {
hitText = "N/A (R₀ ≤ 1)";
}
// DOM Updates
var resultBox = document.getElementById('result');
var r0Display = document.getElementById('r0Display');
var statusDisplay = document.getElementById('statusDisplay');
var secInfDisplay = document.getElementById('secondaryInfections');
var herdDisplay = document.getElementById('herdImmunity');
r0Display.innerHTML = r0.toFixed(2);
secInfDisplay.innerHTML = Math.round(r0);
herdDisplay.innerHTML = hitText;
// Status Logic
resultBox.style.display = "block";
statusDisplay.className = "result-status"; // Reset classes
if (r0 < 1) {
statusDisplay.innerHTML = "Status: Declining Spread (Contained)";
statusDisplay.classList.add("status-green");
} else if (r0 === 1) {
statusDisplay.innerHTML = "Status: Endemic (Stable)";
statusDisplay.classList.add("status-yellow");
} else {
statusDisplay.innerHTML = "Status: Epidemic Growth (Spreading)";
statusDisplay.classList.add("status-red");
}
}
How to Calculate Reproductive Rate (R₀)
Understanding how to calculate the reproductive rate, commonly known as R₀ (R-naught), is fundamental in epidemiology and population biology. It provides a mathematical estimate of how contagious an infectious disease is and helps public health officials determine the intensity of interventions required to stop an outbreak.
What is the Basic Reproductive Number (R₀)?
The Basic Reproductive Number, R₀, represents the average number of secondary infections produced by a single infected individual introduced into a completely susceptible population. It is a metric used to measure the transmission potential of a disease.
- R₀ < 1: On average, each infected person passes the disease to fewer than one other person. The disease will eventually die out.
- R₀ = 1: Each infected person passes it to exactly one other person. The disease becomes endemic and remains stable in the population.
- R₀ > 1: Each infected person passes it to more than one person. The infection spreads exponentially, leading to an epidemic or pandemic.
The Calculation Formula
While complex statistical models are often used to estimate R₀ based on real-world data, the fundamental mathematical formula is derived from three key biological and behavioral factors:
R₀ = τ × c × d
Where:
- τ (Tau) – Transmissibility: The probability of infection being transmitted during a contact between an infected individual and a susceptible individual.
- c – Contact Rate: The average rate of contact between susceptible and infected individuals (e.g., contacts per day).
- d – Duration: The length of time an infected individual remains infectious (contagious).
Example Calculation
Let's assume we are analyzing a hypothetical virus with the following characteristics:
- There is a 10% probability (0.10) of transmission when an infected person comes into contact with a susceptible person.
- The average person has 5 contacts per day.
- The disease remains infectious for 7 days.
Using the formula:
R₀ = 0.10 (probability) × 5 (contacts/day) × 7 (days)
R₀ = 3.5
In this scenario, every one infected person would, on average, infect 3.5 other people. Since the result is greater than 1, this indicates a spreading epidemic.
R₀ vs. Effective Reproductive Number (Rₜ)
It is important to distinguish between the basic reproductive number (R₀) and the effective reproductive number (Rₜ or R-effective). R₀ assumes a completely susceptible population (no immunity, no vaccines, no interventions). However, as an outbreak progresses, people gain immunity or change their behavior (social distancing, masks).
Rₜ measures the reproduction rate at a specific point in time t, accounting for the current state of the population. If interventions reduce the contact rate (c) or vaccines reduce the susceptible population, Rₜ can drop below 1 even if the intrinsic R₀ of the virus remains high.
Herd Immunity Threshold
R₀ is also used to calculate the Herd Immunity Threshold (HIT), which is the percentage of the population that needs to be immune to stop the spread of the disease. The formula is:
HIT = 1 – (1 / R₀)
For a disease with an R₀ of 3.5, the herd immunity threshold would be approximately 71%. This means 71% of the population must be immune (via vaccination or prior infection) to contain the spread.