Robustness and Resilience of Dynamical Networks in Biology and Epidemiology

Systems in nature are extremely robust and resilient, despite uncertainties and variability: they have evolved to preserve fundamental properties and qualitative behaviours that are crucial for survival, even in hostile and ever-changing environments. Studying their nonlinear dynamic behaviour is challenging, due to their complexity and to the many parameters at play, but is crucial to understand important phenomena at all scales, including for instance cellular dynamics, onset of diseases, and epidemic spreading. Robustness and resilience capture a system’s ability to maintain and recover its functions despite uncertainties, fluctuations and perturbations, both intrinsic and extrinsic. Here, we survey the competing definitions of these concepts adopted in different disciplines. Then, given a family of uncertain dynamical networked systems characterised by a structure (the interconnection topology, along with qualitative features of the individual dynamic units and interconnections) and by uncertain or unknown parameters, we provide an overview of methodologies to assess whether a property is structural (parameter-free) or robust (preserved for parameter variations within an uncertainty bounding set) for the family, and we discuss integrated structural and probabilistic approaches for biological and epidemiological systems. Also, we introduce possible formal definitions of resilience for a family of systems consisting of stochastic perturbations of a nominal deterministic system, to probabilistically quantify the system’s ability to preserve a prescribed attractor; our proposed definitions generalise the notion of probabilistic robustness, and offer insight into well-known biological models. Finally, we provide an overview of resilience indicators and of data-driven approaches to detect resilience loss and regime shifts that build upon bifurcation analysis. These methodologies can strongly support the analysis and the control of complex uncertain systems in nature, including the analysis and the design of biomolecular feedback systems with a desired behaviour, the identification of therapeutic targets, the prediction and the control of epidemics, and the detection of tipping points and regime shifts in complex systems.