The impact of contact tracing in clustered populations

The tracing of potentially infectious contacts has become an important part of the control strategy for many infectious diseases, from early cases of novel infections to endemic sexually transmitted infections. Here, we make use of mathematical models to consider the case of partner notification for sexually transmitted infection, however these models are sufficiently simple to allow more general conclusions to be drawn. We show that, when contact network structure is considered in addition to contact tracing, standard “mass action” models are generally inadequate. To consider the impact of mutual contacts (specifically clustering) we develop an improvement to existing pairwise network models, which we use to demonstrate that ceteris paribus, clustering improves the efficacy of contact tracing for a large region of parameter space. This result is sometimes reversed, however, for the case of highly effective contact tracing. We also develop stochastic simulations for comparison, using simple re-wiring methods that allow the generation of appropriate comparator networks. In this way we contribute to the general theory of network-based interventions against infectious disease

Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis

An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models

Evidence for variation in the effective population size of animal mitochondrial DNA

Background: It has recently been shown that levels of diversity in mitochondrial DNA are remarkably constant across animals of diverse census population sizes and ecologies, which has led to the suggestion that the effective population of mitochondrial DNA may be relatively constant. Results: Here we present several lines of evidence that suggest, to the contrary, that the effective population size of mtDNA does vary, and that the variation can be substantial. First, we show that levels of mitochondrial and nuclear diversity are correlated within all groups of animals we surveyed. Second, we show that the effectiveness of selection on non-synonymous mutations, as measured by the ratio of the numbers of non-synonymous and synonymous polymorphisms, is negatively correlated to levels of mitochondrial diversity. Finally, we estimate the effective population size of mitochondrial DNA in selected mammalian groups and show that it varies by at least an order of magnitude. Conclusions: We conclude that there is variation in the effective population size of mitochondria. Furthermore we suggest that the relative constancy of DNA diversity may be due to a negative correlation between the effective population size and the mutation rate per generation

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology

The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1

Elucidating the aetiology of human Campylobacter coli infections

Peer reviewedPublisher PD

An Agent-Based Model to study the epidemiological and evolutionary dynamics of Influenza viruses

<p>Abstract</p> <p>Background</p> <p>Influenza A viruses exhibit complex epidemiological patterns in a number of mammalian and avian hosts. Understanding transmission of these viruses necessitates taking into account their evolution, which represents a challenge for developing mathematical models. This is because the phrasing of multi-strain systems in terms of traditional compartmental ODE models either requires simplifying assumptions to be made that overlook important evolutionary processes, or leads to complex dynamical systems that are too cumbersome to analyse.</p> <p>Results</p> <p>Here, we develop an Individual-Based Model (IBM) in order to address simultaneously the ecology, epidemiology and evolution of strain-polymorphic pathogens, using Influenza A viruses as an illustrative example.</p> <p>Conclusions</p> <p>We carry out careful validation of our IBM against comparable mathematical models to demonstrate the robustness of our algorithm and the sound basis for this novel framework. We discuss how this new approach can give critical insights in the study of influenza evolution.</p

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

Man Bites Mosquito: Understanding the Contribution of Human Movement to Vector-Borne Disease Dynamics

In metropolitan areas people travel frequently and extensively but often in highly structured commuting patterns. We investigate the role of this type of human movement in the epidemiology of vector-borne pathogens such as dengue. Analysis is based on a metapopulation model where mobile humans connect static mosquito subpopulations. We find that, due to frequency dependent biting, infection incidence in the human and mosquito populations is almost independent of the duration of contact. If the mosquito population is not uniformly distributed between patches the transmission potential of the pathogen at the metapopulation level, as summarized by the basic reproductive number, is determined by the size of the largest subpopulation and reduced by stronger connectivity. Global extinction of the pathogen is less likely when increased human movement enhances the rescue effect but, in contrast to classical theory, it is not minimized at an intermediate level of connectivity. We conclude that hubs and reservoirs of infection can be places people visit frequently but briefly and the relative importance of human and mosquito populations in maintaining the pathogen depends on the distribution of the mosquito population and the variability in human travel patterns. These results offer an insight in to the paradoxical observation of resurgent urban vector-borne disease despite increased investment in vector control and suggest that successful public health intervention may require a dual approach. Prospective studies can be used to identify areas with large mosquito populations that are also visited by a large fraction of the human population. Retrospective studies can be used to map recent movements of infected people, pinpointing the mosquito subpopulation from which they acquired the infection and others to which they may have transmitted it