Predicting the effect of landscape structure on epidemic invasion using an analytical estimate for infection rate.

The influence of landscape structure on epidemic invasion of agricultural crops is often underestimated in the construction and analysis of epidemiological models. Computer simulations of individual-based models (IBMs) are widely used to characterize disease spread under different management scenarios but can be slow in exploring large numbers of different landscape configurations. Here, we address the problem of finding an analytical measure of the impact of the spatial structure of a crop landscape on the invasion and spread of plant pathogens.

Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models.

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel.

A unified framework for analysis of individual-based models in ecology and beyond.

Individual-based models, 'IBMs', describe naturally the dynamics of interacting organisms or social or financial agents. They are considered too complex for mathematical analysis, but computer simulations of them cannot give the general insights required. Here, we resolve this problem with a general mathematical framework for IBMs containing interactions of an unlimited level of complexity, and derive equations that reliably approximate the effects of space and stochasticity.

Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states.

Altered cellular energy metabolism is a hallmark of many diseases, one notable example being cancer. Here, we focus on the identification of the transition from healthy to abnormal metabolic states. To do this, we study the dynamics of energy production in a cell.

Generalized chronotaxic systems: time-dependent oscillatory dynamics stable under continuous perturbation.

Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in Phys. Rev.

Inverse approach to chronotaxic systems for single-variable time series.

Following the development of a new class of self-sustained oscillators with a time-varying but stable frequency, the inverse approach to these systems is now formulated. We show how observed data arranged in a single-variable time series can be used to recognize such systems. This approach makes use of time-frequency domain information using the wavelet transform as well as the recently developed method of Bayesian-based inference.

Chronotaxic systems with separable amplitude and phase dynamics.

Until recently, deterministic nonautonomous oscillatory systems with stable amplitudes and time-varying frequencies were not recognized as such and have often been mistreated as stochastic. These systems, named chronotaxic, were introduced in Phys. Rev.

Chronotaxic systems: a new class of self-sustained nonautonomous oscillators.

Nonautonomous oscillatory systems with stable amplitudes and time-varying frequencies have often been treated as stochastic, inappropriately. We therefore formulate them as a new class and discuss how they generate complex behavior. We show how to extract the underlying dynamics, and we demonstrate that it is simple and deterministic, thus paving the way for a diversity of new systems to be recognized as deterministic.