Calculate the Basic Reproduction Number (R₀) and Effective Reproduction Number (Rₜ)
Analysis Results
Basic Reproduction Number (R₀):0
Effective Reproduction Number (Rₜ):0
Understanding Disease Transmission Rates
In epidemiology, understanding how a disease spreads through a population is critical for public health planning. The most common metrics used to measure this spread are the Basic Reproduction Number (R₀) and the Effective Reproduction Number (Rₜ).
What is R₀ (Basic Reproduction Number)?
R₀ represents the average number of people that one infected person will pass the virus to in a population where everyone is susceptible (no prior immunity or vaccination). It is calculated using three main factors:
Transmissibility (β): The probability that infection occurs during a contact between an infected person and a susceptible person.
Contact Rate (c): How many people an infected individual comes into contact with daily.
Infectious Period (d): The total number of days an individual remains capable of spreading the disease.
How to Calculate the Transmission Rate
The standard formula for calculating the transmission rate (R₀) is:
R₀ = (Probability of Transmission) × (Contact Rate) × (Duration of Infection)
To find the Effective Reproduction Number (Rₜ), which accounts for population immunity, we use:
Rₜ = R₀ × (Fraction of Population Susceptible)
Interpreting the Results
Rₜ > 1: The number of cases is increasing exponentially. An epidemic is occurring.
Rₜ = 1: The disease is stable and moving at a constant rate (Endemic). Each person infects exactly one other person.
Rₜ < 1: The number of cases is decreasing, and the disease will eventually die out in that population.
Real-World Examples
Different diseases have vastly different transmission rates based on their biology and how they are spread:
Disease
Estimated R₀
Transmission Type
Measles
12 – 18
Airborne
Seasonal Flu
0.9 – 2.1
Droplet/Contact
Ebola
1.5 – 2.5
Bodily Fluids
How to Lower the Transmission Rate
Public health interventions aim to reduce one of the three variables in the R₀ equation:
Reduce Transmissibility: Wearing masks, hand washing, and improving ventilation.
Reduce Contact Rate: Social distancing, lockdowns, or quarantining infected individuals.
Reduce Susceptibility: Vaccination programs create "herd immunity," lowering the Rₜ even if R₀ remains high.
function calculateTransmission() {
var prob = parseFloat(document.getElementById("transProb").value);
var contacts = parseFloat(document.getElementById("contactRate").value);
var duration = parseFloat(document.getElementById("durationDays").value);
var susceptible = parseFloat(document.getElementById("susceptiblePop").value);
if (isNaN(prob) || isNaN(contacts) || isNaN(duration) || isNaN(susceptible)) {
alert("Please enter valid numerical values for all fields.");
return;
}
// Formula: R0 = beta * c * d
// prob is divided by 100 because it is entered as a percentage
var r0 = (prob / 100) * contacts * duration;
// Formula: Rt = R0 * s
// susceptible is divided by 100 to get the fraction
var rt = r0 * (susceptible / 100);
// Display results
document.getElementById("r0Val").innerHTML = r0.toFixed(2);
document.getElementById("rtVal").innerHTML = rt.toFixed(2);
var statusBox = document.getElementById("trStatus");
var resultBox = document.getElementById("trResultBox");
resultBox.style.display = "block";
if (rt > 1) {
statusBox.innerHTML = "Epidemic Spread: The disease is spreading. Every 10 infected people will infect approximately " + Math.round(rt * 10) + " others. Growth is exponential.";
statusBox.className = "tr-interpretation status-danger";
} else if (rt > 0.9 && rt <= 1) {
statusBox.innerHTML = "Endemic/Stable: The disease spread is stabilizing. Each person infects roughly one other person. The outbreak is not growing significantly.";
statusBox.className = "tr-interpretation status-warning";
} else {
statusBox.innerHTML = "Declining Spread: The transmission rate is below the replacement level. The outbreak will eventually decline and disappear if current conditions persist.";
statusBox.className = "tr-interpretation status-success";
}
}