1,216 research outputs found
Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks
This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the complexity of the model. Network clustering is incorporated into the model to provide a more accurate representation of realistic contact networks, and the accuracy of proposed closures is analysed for different levels of clustering and number of infection stages. Our results support recent findings that standard closure techniques are likely to perform better when the infectious period is constant
Spatial and stochastic epidemics : theory, simulation and control
It is now widely acknowledged that spatial structure and hence the spatial position
of host populations plays a vital role in the spread of infection. In this work
I investigate an ensemble of techniques for understanding the stochastic dynamics
of spatial and discrete epidemic processes, with especial consideration given to SIR
disease dynamics for the Levins-type metapopulation.
I present a toolbox of techniques for the modeller of spatial epidemics. The
highlight results are a novel form of moment closure derived directly from a stochastic
differential representation of the epidemic, a stochastic simulation algorithm that
asymptotically in system size greatly out-performs existing simulation methods for
the spatial epidemic and finally a method for tackling optimal vaccination scheduling
problems for controlling the spread of an invasive pathogen
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Non-Markovian epidemic dynamics on networks
The use of networks to model the spread of epidemics through structured populations is widespread. However, epidemics on networks lead to intractable exact systems with the need to coarse grain and focus on some average quantities. Often, the underlying stochastic processes are Markovian and so are the resulting mean-field models constructed as systems of ordinary differential equations (ODEs). However, the lack of memory (or memorylessness) does not accurately describe real disease dynamics. For instance, many epidemiological studies have shown that the true distribution of the infectious period is rather centred around its mean, whereas the memoryless assumption imposes an exponential distribution on the infectious period. Assumptions such as these greatly affect the predicted course of an epidemic and can lead to inaccurate predictions about disease spread. Such limitations of existing approaches to modelling epidemics on networks motivated my efforts to develop non-Markovian models which would be better suited to capture essential realistic features of disease dynamics.
In the first part of my thesis I developed a pairwise, multi-stage SIR (susceptible-infected-recovered) model. Each infectious node goes through some K 2 N infectious stages, which for K > 1 means that the infectious period is gamma-distributed. Analysis of the model provided analytic expressions for the epidemic threshold and the expected final epidemic size. Using available epidemiological data on the infectious periods of various diseases, I demonstrated the importance of considering the shape of the infectious period distribution.
The second part of the thesis expanded the framework of non-Markovian dynamics to networks with heterogeneous degree distributions with non-negligible levels of clustering. These properties are ubiquitous in many real-world networks and make model development and analysis much more challenging. To this end, I have derived and analysed a compact pairwise model with the number of equations being independent of the range of node degrees, and investigated the effects of clustering on epidemic dynamics.
My thesis culminated with the third part where I explored the relationships between several different modelling methodologies, and derived an original non-Markovian Edge-Based Compartmental Model (EBCM) which allows both transmission and recovery to be arbitrary independent stochastic processes. The major result is a rigorous mathematical proof that the message passing (MP) model and the EBCM are equivalent, and thus, the EBCM is statistically exact on the ensemble of configuration model networks. From this consideration I derived a generalised pairwise-like model which I then used to build a model hierarchy, and to show that, given corresponding parameters and initial conditions, these models are identical to MP model or EBCM.
In the final part of my thesis I considered the important problem of coupling epidemic dynamics with changes in network structure in response to the perceived risk of the epidemic. This was framed as a susceptible-infected-susceptible (SIS) model on an adaptive network, where susceptible nodes can disconnect from infected neighbours and, after some fixed time delay, connect to a random susceptible node that they are not yet connected to. This model assumes that nodes have perfect information on the state of all other nodes. Robust oscillations were found in a significant region of the parameter space, including an enclosed region known as an 'endemic bubble'. The major contribution of this work was to show that oscillations can occur in a wide region of the parameter space, this is in stark contrast with most previous research where oscillations were limited to a very narrow region of the parameter space.
Any mathematical model is a simplification of reality where assumptions must be made. The models presented here show the importance of interrogating these assumptions to ensure that they are as realistic as possible while still being amenable to analysis
Tackling complexity in biological systems: Multi-scale approaches to tuberculosis infection
Tuberculosis is an ancient disease responsible for more than a million deaths per year worldwide, whose complex infection cycle involves dynamical processes that take place at different spatial and temporal scales, from single pathogenic cells to entire hosts' populations. In this thesis we study TB disease at different levels of description from the perspective of complex systems sciences. On the one hand, we use complex networks theory for the analysis of cell interactomes of the causative agent of the disease: the bacillus Mycobacterium tuberculosis. Here, we analyze the gene regulatory network of the bacterium, as well as its network of protein interactions and the way in which it is transformed as a consequence of gene expression adaptation to disparate environments. On the other hand, at the level of human societies, we develop new models for the description of TB spreading on complex populations. First, we develop mathematical models aimed at addressing, from a conceptual perspective, the interplay between complexity of hosts' populations and certain dynamical traits characteristic of TB spreading, like long latency periods and syndemic associations with other diseases. On the other hand, we develop a novel data-driven model for TB spreading with the objective of providing faithful impact evaluations for novel TB vaccines of different types
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
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