A hybrid model of the within-host dynamics post-infection with Legionnaires disease;

Understanding the incubation period of Legionnaires disease is vital for accurate source-term identification. Traditionally, researchers estimate the dose-dependent incubation period from human outbreak data, but this method suffers from the inability to estimate the exposure dose retrospectively for each case. This challenge limit the precision of incubation-period analysis using human case data. Existing within-host models, such as ordinary differential equation (ODE)-based and discrete-event stochastic approaches, estimate the dose-dependent incubation period of Legionnaires disease. However, discrete-event models, while useful, are so computationally costly that the within-host dynamics must be simplified to solely the Legionella and macrophage interactions. This simplification makes the computation feasible, but precludes cytokine interactions and adaptive immune response modelling. In this paper, we develop a new approach to model the within-host dynamics of Legionnaires disease that focuses on reducing computational cost while maintaining accuracy. Specifically, we propose a hybrid framework that integrates and improves upon existing ODE and discrete event within-host models of Legionnaires disease. By integrating the previously developed ODE and discrete-event stochastic models with stochastic differential equation (SDE) models, we create a unified system that adapts dynamically throughout the infection process. We quantify the points at which each model becomes the optimal tool for describing the infection, resulting in a flexible simulation of disease dynamics. Our hybrid model aligns with observed human incubation-period data and is the first framework of its kind in this context. This advancement offers a more robust platform for testing additional biological assumptions and improving our understanding of Legionnaires disease.