Robustness and resilience of dynamical networks in biology and epidemiology

Abstract

Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve many interacting parameters, yet it is crucial for explaining processes from cellular regulation to disease onset and epidemic spreading. Robustness and resilience describe a system's ability to preserve and recover desired behaviours in the presence of intrinsic and extrinsic fluctuations. This survey reviews how different disciplines define these concepts, examines methods for assessing whether key properties of uncertain, networked dynamical systems are structural (parameter-free) or robust (preserved for parameter variations within an uncertainty bounding set), and discusses integrated structural and probabilistic techniques for biological and epidemiological models. The text introduces formal definitions of resilience for families of systems obtained by adding stochastic perturbations to a nominal deterministic model, enabling a probabilistic characterisation of the ability to remain within or return to a prescribed attractor. These definitions generalise probabilistic robustness and shed new light on classical biological examples. In addition, the survey summarises resilience indicators and data-driven tools for detecting resilience loss and regime shifts, drawing on bifurcation analysis to anticipate qualitative changes in system behaviour. Together, these methodologies support the study and control of complex natural systems, guiding the design of biomolecular feedback architectures, the identification of therapeutic targets, the forecasting and management of epidemics, and the detection of tipping points in ecological and biological networks.