Pattern formation in individual-based systems with time-varying parameters

Sensitivity of asymmetric rate-dependent critical systems to initial conditions: Insights into cellular decision making

The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision making in biological systems. We achieve this by extending previous studies that resorted to simple bifurcation normal forms, although in the present case we focus primarily on the issue of the system's sensitivity to initial conditions in the presence of two different noise distributions, Gaussian and Lévy. In addition, we also assess the impact of two-way sweeping at different rates through the critical region of a canonical Pitchfork bifurcation with a constant external asymmetry. The parallel with decision making in biocircuits is performed on this simple system since it is equivalent in its available states and dynamics to more complex genetic circuits published previously. Overall we verify that rate-dependent effects, previously reported as being important features of bifurcating systems, are specific to particular initial conditions. Processing of each starting state, which for the normal form underlying this study is akin to a classification task, is affected by the balance between sweeping speed through critical regions and the type of fluctuations added. For the heavy-tailed noise, two-way dynamic bifurcations are more efficient in processing the external signals, here understood to be jointly represented by the critical parameter profile and the external asymmetry amplitude, when compared to the system relying on escape dynamics. This is particular to the case when the system starts at an attractor not favored by the asymmetry and, in conjunction, when the sweeping amplitude is large.

Anticipating the emergence of infectious diseases

In spite of medical breakthroughs, the emergence of pathogens continues to pose threats to both human and animal populations. We present candidate approaches for anticipating disease emergence prior to large-scale outbreaks. Through use of ideas from the theories of dynamical systems and stochastic processes we develop approaches which are not specific to a particular disease system or model, but instead have general applicability. The indicators of disease emergence detailed in this paper can be classified into two parallel approaches: a set of early-warning signals based around the theory of critical slowing down and a likelihood-based approach. To test the reliability of these two approaches we contrast theoretical predictions with simulated data. We find good support for our methods across a range of different model structures and parameter values.