# Heterogeneous immune recovery after viral response through a dynamical model of feedback-driven persistence and clearance

## TL;DR

This paper uses a mathematical model to study how immune responses and viral infections interact, showing that different immune outcomes can coexist depending on initial conditions.

## Contribution

The novel contribution is a dynamical model with six interacting modules that reveals up to five stable immune states and identifies key drivers of immune bistability and oscillations.

## Key findings

- The model shows that under continuous viral exposure, up to five stable immune states can coexist.
- Severe inflammation is mainly driven by strong activation of cellular immunity.
- The viral replication rate is critical during the transition from acute to chronic disease.

## Abstract

Viral infections trigger complex immune responses with heterogeneous outcomes shaped by nonlinear feedback. A system of ordinary differential equations is developed to investigate immune response dynamics during viral infection, incorporating six modules, including viral load, innate immunity, cellular immunity, humoral immunity, immune suppression, and IL-6. Bifurcation analysis reveals that under continuous viral exposure, when viral clearance rate and intrinsic viral death rate satisfy specific conditions, the system exhibits up to five stable equilibria. This indicates that different health and disease states may coexist depending on initial conditions, while severe inflammation mainly arises from strong activation of cellular immunity, highlighting the complexity of immune responses. Simulations of finite-time viral exposure demonstrate multi-timescale recovery characteristics, with viral load and IL-6 levels declining rapidly, while humoral immune activation and immunosuppression show delayed and sustained patterns. Furthermore, analysis of infectious period and disease duration also indicates that during transition from early acute response to chronic disease, viral replication rate plays a critical role, while immune response intensity is sensitive to both viral clearance and immune self-activation. Subsystem analysis identifies the three-component subsystem of viral load, innate immunity, and cellular immunity as core drivers of bistability and oscillations, while humoral immunity, immune suppression, and IL-6 primarily modulate response amplitude and timing. This work establishes a theoretical framework for analyzing immune response and chronic risks through feedback dynamical modelling, providing insights for intervention strategies.