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A two-parameter, minimal-data model to predict dengue cases: the 2022-2023 outbreak in Florida, USA

This paper proposes and validates a data-parsimonious, two-parameter Bayesian framework based on the incidence-cumulative cases curve to accurately predict dengue outbreaks in data-sparse settings, demonstrating its effectiveness on the 2022-2023 Florida outbreak without relying on complex site-specific covariates.

Original authors: Saman Hosseini, Lee W. Cohnstaedt, Caterina Scoglio

Published 2026-06-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Saman Hosseini, Lee W. Cohnstaedt, Caterina Scoglio

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict how a fire will spread through a forest. Usually, to do this, you need a massive amount of data: the type of trees, the humidity, the wind speed, the exact location of every spark, and a history of how fires behaved in that specific forest for decades. If you don't have all that data, you can't make a prediction.

This paper introduces a much simpler way to predict the spread of dengue fever (a mosquito-borne disease). The authors, working with data from Florida in 2022 and 2023, built a "minimal-data" model. Instead of needing a weather report or a mosquito count, their model only needs one thing: a list of how many new people got sick each week.

Here is how their method works, broken down into simple analogies:

1. The "Parabolic" Shortcut

The core idea relies on a mathematical shape called a parabola (an upside-down U-shape).

The Old Way: Most models try to calculate every single step of the fire: how fast the wind blows, how dry the leaves are, and how many sparks there are. This is like trying to predict a fire by measuring every single leaf. It's accurate but requires too much data and is hard to move to a new forest.
The New Way: The authors proved mathematically that for dengue, the relationship between the total number of people sick so far and the number of new people getting sick this week always forms that perfect upside-down U shape.
- At the start, the curve is low (few new cases).
- It goes up to a peak (the worst week of the outbreak).
- It comes back down (the outbreak is ending).

Because this shape is so predictable, you don't need to know about the weather or the mosquitoes. You just need to see the first few weeks of the curve, fit that "U" shape to the data, and the math tells you exactly how high the peak will be and when the fire will die out.

2. The "Two-Parameter" Engine

The authors call this a "two-parameter" model. Think of it like driving a car with only two controls: Gas and Brake.

Most complex models are like driving a spaceship with 50 buttons, dials, and switches (temperature, humidity, mosquito density, etc.). If you miss one setting, the whole prediction fails.
This model only needs two numbers to work:
1. How fast the outbreak is growing.
2. The total size of the outbreak (how many people will get sick in total by the end).

By only needing these two numbers, the model is "data-parsimonious" (it saves data). It works even in places where we don't have good mosquito traps or weather stations, as long as we have a list of sick people.

3. The "Bayesian" Safety Net

The authors also built a "Bayesian" version of this model. Think of this as adding a safety margin or a "fuzziness filter."

The Problem: Sometimes, the data we get isn't perfect. Maybe a doctor missed a case, or a lab test was delayed.
The Solution: The Bayesian model doesn't just say, "We predict 10 cases." It says, "We predict 10 cases, but we are 95% sure the real number is between 8 and 12."
The Result: In the Florida tests, this "safety net" version was even more accurate than the basic version. It accounted for the fact that real-world reporting isn't always 100% perfect, giving health officials a more reliable range of what to expect.

4. Testing it in Florida

The team tested this on the 2022–2023 dengue outbreaks in Florida. Florida is a great test case because:

It has a mix of tropical and subtropical weather.
It has very strict, high-quality testing (doctors use specific lab tests to confirm dengue), so the data they used was very reliable.
It has limited long-term history of local dengue, making it a "data-sparse" environment where complex models usually fail.

The Outcome:
The model successfully predicted the outbreaks.

It could guess the total number of cases for the season just by looking at the first few weeks.
It predicted the number of new cases for the next 1 to 4 weeks with high accuracy.
It worked without needing any data about how many mosquitoes were flying around or what the temperature was.

5. Why This Matters (According to the Paper)

The paper argues that this method is a game-changer for prevention.

Lead Time: Because the model can predict the peak of the outbreak weeks in advance, health officials get a "head start."
Actionable: Instead of reacting after people get sick, officials can use this prediction to spray for mosquitoes or warn the public before the outbreak gets bad.
Portability: Because it doesn't need complex data, this "two-control" model can be used in any town or country, even those that have never had dengue before or don't have fancy weather sensors.

Summary

The paper presents a "lean" way to predict dengue. Instead of building a massive, complicated machine that needs fuel, oil, and a pilot (lots of data), they built a simple, two-wheeled bicycle. It only needs the path of the road (the list of sick people) to tell you exactly where the hill is and how high it will be. In Florida, this simple bicycle rode faster and more accurately than the complex machines.

Technical Summary: A Two-Parameter, Minimal-Data Model to Predict Dengue Cases

Problem Statement
Reliable and timely dengue forecasting is critical for enabling targeted vector control and clinical preparedness, thereby reducing preventable disease and health-system costs. However, existing forecasting approaches often rely on site-specific covariates (e.g., entomological surveillance, climate data) and complex multi-parameter models. These dependencies limit portability to data-sparse settings, introduce estimation noise, and render models inapplicable to newly infected locations lacking historical outbreak data or detailed environmental monitoring. Furthermore, many models struggle with generalizability, as predictors effective in one region may fail in another.

Methodology
The authors propose a data-parsimonious (DP) framework based on the relationship between incidence and cumulative cases (ICC). The methodology consists of three primary components:

Mathematical Justification: The paper provides a rigorous mathematical proof that the parabolic ICC structure, previously established for the basic SIR model, holds true for a substantially more complex dengue transmission model. This complex model includes two populations (human and mosquito), four serotypes (DENV-1 to DENV-4), primary and secondary infections, and distinct mild/severe disease classes. The proof demonstrates that incidence ( $\dot{C}$ ) is an inverse parabolic function of cumulative cases ( $C$ ), expressed as $\dot{C} = W C (L_0 - C)$ , where $L_0$ is the final epidemic size and $W$ is the intrinsic growth-rate constant.
Predictive Framework (Point Estimation):
- Input: The model requires only the time series of new human cases for the target season.
- Procedure: Early outbreak data is used to fit a parabola to the relationship between cumulative cases and incidence. This fit estimates the final epidemic size ( $L_0$ ). A logistic growth curve is then fitted using $L_0$ and early incidence data to project the epidemic trajectory.
- Statistical Model: Weekly cumulative cases are modeled as a left-censored Poisson random variable, where the mean is determined by the ICC curve forecast and the support is restricted to values greater than or equal to the previously reported cumulative total.
Bayesian Extension:
- To account for case-reporting and fitting uncertainty, a Bayesian model is constructed.
- Observation Model: Reported cases are treated as true incidence perturbed by additive Gaussian measurement error, with a left-truncated prior to ensure non-negativity.
- Final Size Prior: The final size parameter $L$ is assigned a left-truncated Gaussian prior, truncated below at the current cumulative reported cases.
- Inference: Markov Chain Monte Carlo (MCMC) methods (Metropolis-Hastings) are employed to sample from the joint posterior distribution of the latent true observations and the final epidemic size, generating calibrated predictive intervals.

Evaluation
The framework was evaluated using locally acquired dengue case data from Florida for the 2022–2023 period, a setting characterized by standardized clinical testing (RT-PCR/NAAT and IgM) and robust reporting. The study analyzed four distinct outbreak periods. Performance was assessed using:

Root Mean Square Error (RMSE) and Absolute Value of Error (AVE) for point predictions.
Logarithmic scores (adopted from CDC WNV challenges) to evaluate probabilistic accuracy.
MCMC diagnostics (Gelman-Rubin statistic, Geweke Z-scores, Effective Sample Size) to ensure convergence.

Key Results

Point Prediction Accuracy: The model generated 258 weekly forecasts across four outbreaks. The overall RMSE for all horizons was 5.7. Short-term forecasts (1–3 weeks ahead) demonstrated high accuracy, with RMSEs ranging from 1.51 to 3.81. Accuracy decreased for 4-week-ahead forecasts (RMSE up to 15.66), reflecting the inherent difficulty of longer-term prediction.
Bayesian Performance: The Bayesian model consistently outperformed the deterministic parabolic ICC (censored Poisson) model. For example, in the third outbreak, the Bayesian median RMSE was 1.58 compared to 4.36 for the censored Poisson model. The Bayesian approach yielded narrower, well-calibrated predictive intervals, particularly in settings with high reporting accuracy like Florida.
Ecological Correlation: The study identified a consistent 8–10 week lag between Aedes aegypti abundance and predicted dengue risk, aligning with findings from other tropical regions. This suggests the model captures the underlying transmission dynamics despite not explicitly using entomological data.

Significance and Claims
The paper claims that the proposed DP framework addresses the limitations of generalizability and data requirements in current forecasting models. By mathematically proving that the parabolic ICC relation holds for complex multi-serotype dengue models, the authors establish a theoretical basis for a two-parameter model that:

Requires Minimal Data: It functions using only the human incidence time series of the target year, eliminating the need for entomological surveillance or complex environmental covariates.
Reduces Noise: By estimating only two parameters ( $L_0$ and growth rate), it avoids the noise associated with high-dimensional parameter estimation.
Supports New Outbreaks: It is applicable to newly infected locations with limited historical data, as it does not rely on long-term outbreak histories.
Quantifies Uncertainty: The Bayesian extension provides calibrated predictive intervals that account for reporting and fitting uncertainties, offering a more robust tool for public health decision-making than point estimates alone.

The authors conclude that while the model is based on reported incidence (which underestimates true infections), its ability to reproduce outbreak timing and trajectory with high accuracy using minimal data makes it a viable tool for operational forecasting and mitigation planning, particularly in emerging endemic regions.