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

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

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

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

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

Modelling that shaped the early COVID-19 pandemic response in the UK.

Infectious disease modelling has played an integral part of the scientific evidence used to guide the response to the COVID-19 pandemic. In the UK, modelling evidence used for policy is reported to the Scientific Advisory Group for Emergencies (SAGE) modelling subgroup, SPI-M-O (Scientific Pandemic Influenza Group on Modelling-Operational). This Special Issue contains 20 articles detailing evidence that underpinned advice to the UK government during the SARS-CoV-2 pandemic in the UK between January 2020 and July 2020. Here, we introduce the UK scientific advisory system and how it operates in practice, and discuss how infectious disease modelling can be useful in policy making. We examine the drawbacks of current publishing practices and academic credit and highlight the importance of transparency and reproducibility during an epidemic emergency. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'