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

Bursting endemic bubbles in an adaptive network

The spread of an infectious disease is known to change people’s behavior, which in turn affects the spread of disease. Adaptive network models that account for both epidemic and behavioral change have found oscillations, but in an extremely narrow region of the parameter space, which contrasts with intuition and available data. In this paper we propose a simple susceptible-infected-susceptible epidemic model on an adaptive network with time-delayed rewiring, and show that oscillatory solutions are now present in a wide region of the parameter space. Altering the transmission or rewiring rates reveals the presence of an endemic bubble - an enclosed region of the parameter space where oscillations are observed

Sublethal effect modelling for environmental risk assessment of chemicals : Problem definition, model variants, application and challenges

Bioenergetic models, and specifically dynamic energy budget (DEB) theory, are gathering a great deal of interest as a tool to predict the effects of realistically variable exposure to toxicants over time on an individual animal. Here we use aquatic ecological risk assessment (ERA) as the context for a review of the different model variants within DEB and the closely related DEBkiss theory (incl. reserves, ageing, size & maturity, starvation). We propose a coherent and unifying naming scheme for all current major DEB variants, explore the implications of each model's underlying assumptions in terms of its capability and complexity and analyse differences between the models (endpoints, mathematical differences, physiological modes of action). The results imply a hierarchy of model complexity which could be used to guide the implementation of simplified model variants. We provide a decision tree to support matching the simplest suitable model to a given research or regulatory question. We detail which new insights can be gained by using DEB in toxicokinetic-toxicodynamic modelling, both generally and for the specific example of ERA, and highlight open questions. Specifically, we outline a moving time window approach to assess time-variable exposure concentrations and discuss how to account for cross-generational exposure. Where possible, we suggest valuable topics for experimental and theoretical research

Mean-field models for non-Markovian epidemics on networks

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission themessage passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length

Differentiation of Chronic Lymphocytic Leukemia B Cells into Immunoglobulin Secreting Cells Decreases LEF-1 Expression

Lymphocyte enhancer binding factor 1 (LEF-1) plays a crucial role in B lineage development and is only expressed in B cell precursors as B cell differentiation into mature B and plasma cells silences its expression. Chronic lymphocytic leukemia (CLL) cells aberrantly express LEF-1 and its expression is required for cellular survival. We hypothesized that modification of the differentiation status of CLL cells would result in loss of LEF-1 expression and eliminate the survival advantage provided by its aberrant expression. In this study, we first established a methodology that induces CLL cells to differentiate into immunoglobulin (Ig) secreting cells (ISC) using the TLR9 agonist, CpG, together with cytokines (CpG/c). CpG/c stimulation resulted in dramatic CLL cell phenotypic and morphologic changes, expression of cytoplasmic Ig, and secretion of light chain restricted Ig. CpG/c stimulation also resulted in decreased CLL cell LEF-1 expression and increased Blimp-1 expression, which is crucial for plasma cell differentiation. Further, Wnt pathway activation and cellular survival were impaired in differentiated CLL cells compared to undifferentiated CLL cells. These data support the notion that CLL can differentiate into ISC and that this triggers decreased leukemic cell survival secondary to the down regulation of LEF-1 and decreased Wnt pathway activation

Psychological factors in leg ulceration: a case-control study

<p><b>Summary Background:</b>  There is increasing recognition of the role that psychological status plays in the development and outcomes of chronic disease, but little understanding of its importance in chronic leg ulceration.</p> <p><b>Objectives:</b>  To examine psychological health and perceived social support in patients with chronic leg ulceration.</p> <p><b>Methods:</b>  Patients with leg ulceration within a defined population were matched for age and gender (1 : 1) with community controls in a matched case–control study. Analysis was by conditional logistic regression and matched t-test analysis.</p> <p><b>Results:</b>  Ninety-five patients (60 women and 35 men; 59% aged over 75 years) were identified and matched to the same number of controls. Cases had significantly poorer health-related quality of life in all domains of the Nottingham Health Profile (all P ≤ 0·001), compared with controls. Levels of depression (Hospital Anxiety and Depression Scale) were significantly greater in the patient group (mean 5·3 vs. 3·6, P < 0·001). Social support (Medical Outcomes Study Social Support Survey scale) showed significantly fewer social networks and less perceived social support in patients than controls (P = 0·008). Patients used significantly fewer coping strategies (COPE scale) than controls, particularly with regard to problem-focused coping strategies.</p> <p><b>Conclusions:</b>  Patients with leg ulceration experience poor psychological health with a greater risk of depression, less perceived social support and greater social isolation. Systems of care should offer an environment that reduces social isolation and increases support to this patient group.</p&gt