113 research outputs found
Is HIV short-sighted? Insights from a multistrain nested model
An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus
Mathematical Models for Emerging Infections in Socially Structured Populations: The Presence of Households and Workplaces
This thesis is concerned with the description and analysis of a stochastic model for
the spread of a directly transmissible infection, leading to permanent immunity af-
ter recovery, in a fully susceptible population with a social structure characterised
by the presence of households and workplaces. The model considered is highly ide-
alised, but contains the key factors affecting the spread of a directly transmissible
infection, namely those environments where frequent and intense contacts are most
likely.
Important analytical insights include the definition of a novel household re-
production number RH, representing the average number of households infected
by a single household, which is shown to overcome some of the limitations of a
previously defined reproduction number and the development of a methodology
for the approximate computation of the real-time growth rate, which is then used
for the estimation of RH from the real-time growth rate.
An efficient stochastic simulator is described and is used to gain understand-
ing of the role that local saturation effects within workplaces play in shaping the
epidemic spread and to investigate the reliability of estimates of R0 and the average
epidemic final size from the real-time growth rate when the presence of the social
structure is neglected.
The methodologies are applied to the case of pandemic influenza: its rela-
tively low infectiousness suggests that estimation of these key epidemiological quan-
tities is surprisingly accurate when the social structure is neglected and that the
additional presence of spatial constraints implying geographically localised trans-
mission has negligible effect on the overall epidemic dynamics. Despite the lack
of reliable data concerning workplaces, a realistic range of possible values for RH
is identified, but the efficacy of school closure in reducing transmission appears to
be difficult to quantify because of the unknown impact it has on transmission in
other workplace environments
Exact and approximate moment closures for non-Markovian network epidemics
Moment-closure techniques are commonly used to generate low-dimensional
deterministic models to approximate the average dynamics of stochastic systems
on networks. The quality of such closures is usually difficult to asses and the
relationship between model assumptions and closure accuracy are often
difficult, if not impossible, to quantify. Here we carefully examine some
commonly used moment closures, in particular a new one based on the concept of
maximum entropy, for approximating the spread of epidemics on networks by
reconstructing the probability distributions over triplets based on those over
pairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under
Markovian and non-Markovian assumption characterising the latent and infectious
periods. We initially study two special networks, namely the open triplet and
closed triangle, for which we can obtain analytical results. We then explore
numerically the exactness of moment closures for a wide range of larger motifs,
thus gaining understanding of the factors that introduce errors in the
approximations, in particular the presence of a random duration of the
infectious period and the presence of overlapping triangles in a network. We
also derive a simpler and more intuitive proof than previously available
concerning the known result that pair-based moment closure is exact for the
Markovian SIR model on tree-like networks under pure initial conditions. We
also extend such a result to all infectious models, Markovian and
non-Markovian, in which susceptibles escape infection independently from each
infected neighbour and for which infectives cannot regain susceptible status,
provided the network is tree-like and initial conditions are pure. This works
represent a valuable step in deepening understanding of the assumptions behind
moment closure approximations and for putting them on a more rigorous
mathematical footing.Comment: Main text (45 pages, 11 figures and 3 tables) + supplementary
material (12 pages, 10 figures and 1 table). Accepted for publication in
Journal of Theoretical Biology on 27th April 201
Real-time growth rate for general stochastic SIR epidemics on unclustered networks
Networks have become an important tool for infectious disease epidemiology.
Most previous theoretical studies of transmission network models have either
considered simple Markovian dynamics at the individual level, or have focused
on the invasion threshold and final outcome of the epidemic. Here, we provide a
general theory for early real-time behaviour of epidemics on large
configuration model networks (i.e. static and locally unclustered), in
particular focusing on the computation of the Malthusian parameter that
describes the early exponential epidemic growth. Analytical, numerical and
Monte-Carlo methods under a wide variety of Markovian and non-Markovian
assumptions about the infectivity profile are presented. Numerous examples
provide explicit quantification of the impact of the network structure on the
temporal dynamics of the spread of infection and provide a benchmark for
validating results of large scale simulations.Comment: 45 pages, 8 figures, submitted to Mathematical Biosciences on
29/11/2014; Version 2: resubmitted on 15/04/2015; accepted on 17/04/2015.
Changes: better explanations in introduction; restructured section 3.3 (3.3.3
added); section 6.3.1 added; more precise terminology; typos correcte
Reproduction numbers for epidemic models with households and other social structures II: comparisons and implications for vaccination
In this paper we consider epidemic models of directly transmissible SIR (susceptible - infective - recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproduction number R0 introduced in the companion paper of this, for which we provide a simpler, more elegant derivation. Extending previous work, we provide a complete overview of the inequalities among these reproduction numbers and resolve some open questions. Special focus is put on the exponential-growth-associated reproduction number Rr, which is loosely defined as the estimate of R0 based on the observed exponential growth of an emerging epidemic obtained when the social structure is ignored. We show that for the vast majority of the models considered in the literature Rr >= R0 when R0 >=1 and Rr <= R0 when R0 <= 1. We show that, in contrast to models without social structure, vaccination of a fraction 1-1/R0 of the population, chosen uniformly at random, with a perfect vaccine is usually insufficient to prevent large epidemics. In addition, we provide significantly sharper bounds than the existing ones for bracketing the critical vaccination coverage between two analytically tractable quantities, which we illustrate by means of extensive numerical examples
Information content of household-stratified epidemics
Household structure is a key driver of many infectious diseases, as well as a natural target for interventions such as vaccination programs. Many theoretical and conceptual advances on household-stratified epidemic models are relatively recent, but have successfully managed to increase the applicability of such models to practical problems. To be of maximum realism and hence benefit, they require parameterisation from epidemiological data, and while household-stratified final size data has been the traditional source, increasingly time-series infection data from households are becoming available. This paper is concerned with the design of studies aimed at collecting time-series epidemic data in order to maximize the amount of information available to calibrate household models. A design decision involves a trade-off between the number of households to enrol and the sampling frequency. Two commonly used epidemiological study designs are considered: cross-sectional, where different households are sampled at every time point, and cohort, where the same households are followed over the course of the study period. The search for an optimal design uses Bayesian computationally intensive methods to explore the joint parameter-design space combined with the Shannon entropy of the posteriors to estimate the amount of information in each design. For the cross-sectional design, the amount of information increases with the sampling intensity, i.e., the designs with the highest number of time points have the most information. On the other hand, the cohort design often exhibits a trade-off between the number of households sampled and the intensity of follow-up. Our results broadly support the choices made in existing epidemiological data collection studies. Prospective problem-specific use of our computational methods can bring significant benefits in guiding future study designs
Detecting HLA-infectious disease associations for multi-strain pathogens
Human Leukocyte Antigen (HLA) molecules play a vital role helping our immune system to detect the presence of pathogens. Previous work to try and ascertain which HLA alleles offer advantages against particular pathogens has generated inconsistent results. We have constructed an epidemiological model to understand why this may occur. The model captures the epidemiology of a multi strain pathogen for which the host's ability to generate immunological memory responses to particular strains depends on that host's HLA genotype. We find that an HLA allele's ability to protect against infection, as measured in a case control study, depends on the population frequency of that HLA allele. Furthermore, our capability to detect associations between HLA alleles and infection with a multi strain pathogen may be affected by the properties of the pathogen itself (i.e R0 and length of infectious period). Both host and pathogen genetics must be considered in order to identify true HLA associations. However, in the absence of detailed pathogen genetic information, a negative correlation between the frequency of an HLA type and its apparent protectiveness against disease caused by multi strain pathogen is a strong indication that the HLA type in question is well adapted to a subset of strains of that pathogen
Unsupervised identification of significant lineages of SARS-CoV-2 through scalable machine learning methods
Since its emergence in late 2019, SARS-CoV-2 has diversified into a large number of lineages and caused multiple waves of infection globally. Novel lineages have the potential to spread rapidly and internationally if they have higher intrinsic transmissibility and/or can evade host immune responses, as has been seen with the Alpha, Delta, and Omicron variants of concern. They can also cause increased mortality and morbidity if they have increased virulence, as was seen for Alpha and Delta. Phylogenetic methods provide the "gold standard" for representing the global diversity of SARS-CoV-2 and to identify newly emerging lineages. However, these methods are computationally expensive, struggle when datasets get too large, and require manual curation to designate new lineages. These challenges provide a motivation to develop complementary methods that can incorporate all of the genetic data available without down-sampling to extract meaningful information rapidly and with minimal curation. In this paper, we demonstrate the utility of using algorithmic approaches based on word-statistics to represent whole sequences, bringing speed, scalability, and interpretability to the construction of genetic topologies. While not serving as a substitute for current phylogenetic analyses, the proposed methods can be used as a complementary, and fully automatable, approach to identify and confirm new emerging variants
Evaluating the Evidence for Lymphatic Filariasis Elimination
In the global drive for elimination of lymphatic filariasis (LF), 15 countries have achieved validation of elimination as a public health problem (EPHP). Recent empirical evidence has demonstrated that EPHP does not always lead to elimination of transmission (EOT). Here we show how the probability of elimination explicitly depends on key biological parameters, many of which have been poorly characterized, leading to a poor evidence base for the elimination threshold. As more countries progress towards EPHP it is essential that this process is well-informed, as prematurely halting treatment and surveillance programs could pose a serious threat to global progress. We highlight that refinement of the weak empirical evidence base
is vital to understand drivers of elimination and inform long-term polic
- …