Efficient and flexible methods for time since infection models

TL;DR

This paper introduces efficient numerical methods for time since infection (TSI) epidemic models, enabling more accurate disease transmission simulations without significant computational cost increases, and demonstrates their application in optimal epidemic control.

Contribution

The paper presents a discretization scheme that makes TSI models computationally comparable to compartment models and offers a new approach to incorporate stages, enhancing epidemic modeling accuracy.

Findings

TSI models can be solved efficiently with proper discretization.

New staging approach decouples transmission dynamics from residence times.

Methods enable practical application in optimal epidemic control.

Abstract

Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are more faithful to the microscopic details of disease transmission can offer more reliable projections, which in turn can lead to more reliable control strategies. For example, many epidemic models describe disease progression via a series of artificial 'stages' or 'compartments' (e.g. exposed, activated, infectious, etc.) but an epidemic model that explicitly tracks time since infection (TSI) can provide a more precise description. At present, epidemic models with 'compartments' are more common than TSI models , largely due to higher computational cost and complexity typically associated with TSI models. Here, however, we show that with the right discretization scheme a TSI model is not much more difficult to solve than a comparment model with three or four 'stages' for the infected class. We also provide a new perspective for adding 'stages' to a TSI model in a way that decouples the disease transmission dynamics from the residence time distributions at each stage. These results are also generalized for age-structured TSI models in an appendix. Finally, as proof-of-principle for the efficiency of the proposed numerical methods, we provide calculations for optimal epidemic control by non-pharmaceutical intervention. Many of the tools described in this report are available through the software package 'pyross'