A multiscale framework integrating within-host infection kinetics with airborne transmission dynamics

TL;DR

This paper introduces a novel multiscale mathematical framework that links within-host infection kinetics with airborne transmission dynamics, enabling comprehensive analysis of disease spread in indoor environments.

Contribution

It develops a coupled ODE-PDE model that integrates individual infection processes with airborne pathogen movement, including a reduced nonlinear ODE model derived via asymptotic analysis.

Findings

Derived a tractable nonlinear ODE model capturing spatial heterogeneity.

Proved existence, uniqueness, and boundedness of solutions.

Recovered classical viral dynamics in the well-mixed limit.

Abstract

Coupling within-host infection dynamics with population-level transmission remains a major challenge in infectious disease modeling, especially for airborne pathogens with potential to spread indoor. The frequent emergence of such diseases highlight the need for integrated frameworks that capture both individual-level infection kinetics and between-host transmission. While analytical models for each scale exist, tractable approaches that link them remain limited. In this study, we present a novel multiscale mathematical framework that integrates within-host infection kinetics with airborne transmission dynamics. The model represents each host as a patch and couples a system of ordinary differential equations (ODEs) describing in-host infection kinetics with a diffusion-based partial differential equation (PDE) for airborne pathogen movement in enclosed spaces. These scales are linked through boundary conditions on each patch boundary, representing viral shedding and inhalation. Using matched asymptotic analysis in the regime of intermediate diffusivity, we derived a nonlinear ODE model from the coupled ODE-PDE system that retains spatial heterogeneity through Neumann Green's functions. We established the existence, uniqueness, and boundedness of solutions to the reduced model and analyzed within-host infection kinetics as functions of the airborne pathogen diffusion rate and host spatial configuration. In the well-mixed limit, the model recovers the classical target cell limited viral dynamics framework. Overall, the proposed multiscale modeling approach enables the simultaneous study of transient within-host infection dynamics and population-level disease spread, providing a tractable yet biologically grounded framework for investigating airborne disease transmission in indoor environments.