Outbreak threshold probability calculator
Enter today's case count, observed daily growth rate, and your threshold. See the probability of crossing that threshold in the next N days, plus the formula behind the projection.
This calculator uses exponential growth: cases(t) = cases(0) × (1 + r)^t, where r is the daily growth rate. The probability estimate accounts for the ratio of projected cases to threshold and applies a logistic model to represent uncertainty. Real outbreaks deviate from pure exponential growth as interventions take effect and susceptible populations shrink.
Understanding outbreak projections
| Component | What it means | Typical range |
|---|---|---|
| Current cases | Confirmed or estimated active infections today | 10–10,000+ depending on outbreak stage |
| Daily growth rate | Percentage change in cases per day | −10% (declining) to +40% (rapid spread) |
| Threshold | Case count triggering concern or policy response | 100 to 10,000+ based on jurisdiction |
| Days ahead | How far into the future you're projecting | 7–30 days for reliable short-term forecasts |
| Population | Total susceptible individuals (constrains max growth) | City, region, or country population |
When exponential models break down
Exponential growth assumes unlimited susceptible population and constant transmission. In reality, outbreaks slow as immunity builds (through infection or vaccination), behavior changes in response to rising cases, and public health interventions take effect. This calculator is most accurate for projections under two weeks and before case counts approach a significant fraction of the population.
For longer-term or large-scale projections, compartmental models (SIR, SEIR) that explicitly track susceptible, infected, and recovered populations produce more realistic curves. Use this tool for rapid situational awareness and short-horizon risk assessment, not for policy planning or resource allocation over months.
Interpreting the probability output
The probability shown is a point estimate based on deterministic exponential projection with a logistic uncertainty envelope. A result of 85% means that if your growth rate estimate is accurate and conditions remain stable, there's a strong likelihood you'll cross the threshold within the specified window. Low probabilities (under 20%) suggest the threshold is distant or growth is insufficient; probabilities near 50% indicate you're near the tipping point and small changes in growth rate matter significantly.
Common questions
How accurate is exponential growth for predicting disease outbreaks?
Exponential models work well in the early stages of an outbreak when interventions are minimal and the susceptible population is large. As cases grow, real-world factors like behavior change, immunity, and public health measures cause growth to slow. Use this calculator for short-term projections (days to weeks), not long-term forecasts.
What daily growth rate should I use for different diseases?
Growth rates vary widely by pathogen and context. Early COVID-19 outbreaks showed 15–35% daily growth; seasonal flu might show 5–10%; highly transmissible variants can exceed 40%. The growth rate you observe in your data (cases today ÷ cases yesterday) is often the most reliable input for near-term projection.
Why does the probability never reach exactly 100% or 0%?
Real-world uncertainty means we model the threshold crossing as a probability distribution, not a certainty. Even with strong growth, random variation in transmission means there's always a small chance the outbreak stalls. Conversely, even declining outbreaks retain a tiny probability of resurgence, so 0% is never guaranteed.