3 research outputs found
Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks
The surveillance, analysis and ultimately the efficient long-term prediction
and control of epidemic dynamics appear to be one of the major challenges
nowadays. Detailed atomistic mathematical models play an important role towards
this aim. In this work it is shown how one can exploit the Equation Free
approach and optimization methods such as Simulated Annealing to bridge
detailed individual-based epidemic simulation with coarse-grained,
systems-level, analysis. The methodology provides a systematic approach for
analyzing the parametric behavior of complex/ multi-scale epidemic simulators
much more efficiently than simply simulating forward in time. It is shown how
steady state and (if required) time-dependent computations, stability
computations, as well as continuation and numerical bifurcation analysis can be
performed in a straightforward manner. The approach is illustrated through a
simple individual-based epidemic model deploying on a random regular connected
graph. Using the individual-based microscopic simulator as a black box
coarse-grained timestepper and with the aid of Simulated Annealing I compute
the coarse-grained equilibrium bifurcation diagram and analyze the stability of
the stationary states sidestepping the necessity of obtaining explicit closures
at the macroscopic level under a pairwise representation perspective
Modeling epidemics on adaptively evolving networks: a data-mining perspective
The exploration of epidemic dynamics on dynamically evolving ("adaptive")
networks poses nontrivial challenges to the modeler, such as the determination
of a small number of informative statistics of the detailed network state (that
is, a few "good observables") that usefully summarize the overall (macroscopic,
systems level) behavior. Trying to obtain reduced, small size, accurate models
in terms of these few statistical observables - that is, coarse-graining the
full network epidemic model to a small but useful macroscopic one - is even
more daunting. Here we describe a data-based approach to solving the first
challenge: the detection of a few informative collective observables of the
detailed epidemic dynamics. This will be accomplished through Diffusion Maps, a
recently developed data-mining technique. We illustrate the approach through
simulations of a simple mathematical model of epidemics on a network: a model
known to exhibit complex temporal dynamics. We will discuss potential
extensions of the approach, as well as possible shortcomings.Comment: 24 pages, 8 figures, submitted to Virulenc
Perspectives on the relationship between local interactions and global outcomes in spatially explicit models of systems of interacting individuals
Understanding the behaviour of systems of interacting individuals is a key aim of much research in the social sciences and beyond, and a wide variety of modelling paradigms have been employed in pursuit of this goal. Often, systems of interest are intrinsically spatial, involving interactions that occur on a local scale or according to some specific spatial structure. However, while it is recognised that spatial factors can have a significant impact on the global behaviours exhibited by such systems, in practice, models often neglect spatial structure or consider it only in a limited way, in order to simplify interpretation and analysis. In the particular case of individual-based models used in the social sciences, a lack of consistent mathematical foundations inevitably casts doubt on the validity of research conclusions. Similarly, in game theory, the lack of a unifying framework to encompass the full variety of spatial games presented in the literature restricts the development of general results and can prevent researchers from identifying important similarities between models. In this thesis, we address these issues by examining the relationship between local interactions and global outcomes in spatially explicit models of interacting individuals from two different conceptual perspectives. First, we define and analyse a family of spatially explicit, individual-based models, identifying and explaining fundamental connections between their local and global behaviours. Our approach represents a proof of concept, suggesting that similar methods could be effective in identifying such connections in a wider range of models. Secondly, we define a general model for spatial games of search and concealment, which unites many existing games into a single framework, and we present theoretical results on its optimal strategies. Our model represents an opportunity for the development of a more broadly applicable theory of spatial games, which could facilitate progress and highlight connections within the field