A Universal Convolution-Based Pre-processor to Correct the Prevalence-Incidence Gap in SIR, SEIR, and SIRS Modeling

TL;DR

This paper introduces a universal convolution-based pre-processing method to accurately transform incidence data into prevalence estimates, significantly improving epidemic model predictions across SIR, SEIR, and SIRS frameworks.

Contribution

It proposes a novel convolution protocol that corrects the prevalence-incidence mismatch, enhancing the predictive accuracy of compartmental epidemic models.

Findings

The convolution pre-processor reduces systematic biases in epidemic forecasts.

Adding complexity to models does not resolve the incidence-prevalence gap without proper data transformation.

Simulation results confirm improved accuracy in estimating epidemic parameters.

Abstract

Traditional compartmental models, including SIR, SEIR, and SIRS frameworks, remain the analytical standard for epidemic forecasting. However, real-world data validation consistently reveals significant predictive failures, such as peak underestimations of up to 50%. This research identifies a persistent fundamental methodological error: the calibration of prevalence-based (stock) models using raw daily incidence (flow) data without proper transformation. We propose an integrated protocol utilizing an exponentially weighted convolution to reconstruct active cases from reported incidence: $I(t) \approx \frac{1}{p} \int_{0}^{t} NDC(\tau) e^{-\gamma(t-\tau)} d\tau$. This transformation accounts for the recovery rate $\gamma$ and the ascertainment rate $p$. We demonstrate that increasing structural complexity, such as adding latency (SEIR) or waning immunity (SIRS), fails to resolve the incidence-prevalence gap. Simulation results show that without the proposed universal pre-processor, these advanced models inherit the systematic biases of misaligned data types, leading to significant errors in estimating latent periods and the "heavy tail" of endemicity. The proposed convolution transformation must serve as a universal prerequisite for any compartmental framework, bridging the gap between clinical reporting and mechanistic modeling.