Samuel Brand

Dynamics of infectious diseases

Modern infectious disease epidemiology has a strong history of using mathematics both for prediction and to gain a deeper understanding. However the study of infectious diseases is a highly interdisciplinary subject requiring insights from multiple disciplines, in particular a biological knowledge of the pathogen, a statistical description of the available data and a mathematical framework for prediction. Here we begin with the basic building blocks of infectious disease epidemiology--the SIS and SIR type models--before considering the progress that has been made over the recent decades and the challenges that lie ahead. Throughout we focus on the understanding that can be developed from relatively simple models, although accurate prediction will inevitably require far greater complexity beyond the scope of this review. In particular, we focus on three critical aspects of infectious disease models that we feel fundamentally shape their dynamics: heterogeneously structured populations, stochasticity and spatial structure. Throughout we relate the mathematical models and their results to a variety of real-world problems.

Computational Convergence of the Path Integral for Real Dendritic Morphologies

Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures.

The Interaction between Vector Life History and Short Vector Life in Vector-Borne Disease Transmission and Control

Epidemiological modelling has a vital role to play in policy planning and prediction for the control of vectors, and hence the subsequent control of vector-borne diseases. To decide between competing policies requires models that can generate accurate predictions, which in turn requires accurate knowledge of vector natural histories. Here we highlight the importance of the distribution of times between life-history events, using short-lived midge species as an example. In particular we focus on the distribution of the extrinsic incubation period (EIP) which determines the time between infection and becoming infectious, and the distribution of the length of the gonotrophic cycle which determines the time between successful bites. We show how different assumptions for these periods can radically change the basic reproductive ratio (R0) of an infection and additionally the impact of vector control on the infection. These findings highlight the need for detailed entomological data, based on laboratory experiments and field data, to correctly construct the next-generation of policy-informing models.

Adding tsetse control to medical activities contributes to decreasing transmission of sleeping sickness in the Mandoul focus (Chad)

Background Gambian sleeping sickness or HAT (human African trypanosomiasis) is a neglected tropical disease caused by Trypanosoma brucei gambiense transmitted by riverine species of tsetse. A global programme aims to eliminate the disease as a public health problem by 2020 and stop transmission by 2030. In the South of Chad, the Mandoul area is a persistent focus of Gambian sleeping sickness where around 100 HAT cases were still diagnosed and treated annually until 2013. Pre-2014, control of HAT relied solely on case detection and treatment, which lead to a gradual decrease in the number of cases of HAT due to annual screening of the population. Methods Because of the persistence of transmission and detection of new cases, we assessed whether the addition of vector control to case detection and treatment could further reduce transmission and consequently, reduce annual incidence of HAT in Mandoul. In particular, we investigated the impact of deploying ‘tiny targets’ which attract and kill tsetse. Before tsetse control commenced, a census of the human population was conducted and their settlements mapped. A pre-intervention survey of tsetse distribution and abundance was implemented in November 2013 and 2600 targets were deployed in the riverine habitats of tsetse in early 2014, 2015 and 2016. Impact on tsetse and on the incidence of sleeping sickness was assessed through nine tsetse monitoring surveys and four medical surveys of the human population in 2014 and 2015. Mathematical modelling was used to assess the relative impact of tsetse control on incidence compared to active and passive screening. Findings The census indicated that a population of 38674 inhabitants lived in the vicinity of the Mandoul focus. Within this focus in November 2013, the vector is Glossina fuscipes fuscipes and the mean catch of tsetse from traps was 0.7 flies/trap/day (range, 0–26). The catch of tsetse from 44 sentinel biconical traps declined after target deployment with only five tsetse being caught in nine surveys giving a mean catch of 0.005 tsetse/trap/day. Modelling indicates that 70.4% (95% CI: 51–95%) of the reduction in reported cases between 2013 and 2015 can be attributed to vector control with the rest due to medical intervention. Similarly tiny targets are estimated to have reduced new infections dramatically with 62.8% (95% CI: 59–66%) of the reduction due to tsetse control, and 8.5% (95% 8–9%) to enhanced passive detection. Model predictions anticipate that elimination as a public health problem could be achieved by 2018 in this focus if vector control and screening continue at the present level and, furthermore, there may have been virtually no transmission since 2015. Conclusion This work shows that tiny targets reduced the numbers of tsetse in this focus in Chad, which may have interrupted transmission and the combination of tsetse control to medical detection and treatment has played a major role in reducing in HAT incidence in 2014 and 2015.

The impact of temperature changes on vector-borne disease transmission: Culicoides midges and bluetongue virus

It is a long recognized fact that climatic variations, especially temperature, affect the life history of biting insects. This is particularly important when considering vector-borne diseases, especially in temperate regions where climatic fluctuations are large. In general, it has been found that most biological processes occur at a faster rate at higher temperatures, although not all processes change in the same manner. This differential response to temperature, often considered as a trade-off between onward transmission and vector life expectancy, leads to the total transmission potential of an infected vector being maximized at intermediate temperatures. Here we go beyond the concept of a static optimal temperature, and mathematically model how realistic temperature variation impacts transmission dynamics. We use bluetongue virus (BTV), under UK temperatures and transmitted by Culicoides midges, as a well-studied example where temperature fluctuations play a major role. We first consider an optimal temperature profile that maximizes transmission, and show that this is characterized by a warm day to maximize biting followed by cooler weather to maximize vector life expectancy. This understanding can then be related to recorded representative temperature patterns for England, the UK region which has experienced BTV cases, allowing us to infer historical transmissibility of BTV, as well as using forecasts of climate change to predict future transmissibility. Our results show that when BTV first invaded northern Europe in 2006 the cumulative transmission intensity was higher than any point in the last 50 years, although with climate change such high risks are the expected norm by 2050. Such predictions would indicate that regular BTV epizootics should be expected in the UK in the future.

Assessing the utility of minority variant composition in elucidating RSV transmission pathways

Reconstructing transmission pathways and defining the underlying determinants of virus diversity is critical for developing effective control measures. Whole genome consensus sequences represent the dominant virus subtype which does not provide sufficient information to resolve transmission events for rapidly spreading viruses with overlapping generations. We explored whether the within-host diversity of respiratory syncytial virus quantified from deep sequence data provides additional resolution to inform on who acquires infection from whom based on shared minor variants in samples that comprised epidemiological clusters and that shared similar genetic background. We report that RSV-A infections are characterized by low frequency diversity that occurs across the genome. Shared minor variant patterns alone, were insufficient to elucidate transmission chains within household members. However, they provided inference on potential transmission links where phylogenetic methods were uninformative of transmission when consensus sequences were identical. Interpretation of minor variant patterns was tractable only for small household outbreaks.

Human rhinovirus spatial-temporal epidemiology in rural coastal Kenya, 2015-2016, observed through outpatient surveillance

Background: Human rhinovirus (HRV) is the predominant cause of upper respiratory tract infections, resulting in a significant public health burden. The virus circulates as many different types (~160), each generating strong homologous, but weak heterotypic, immunity. The influence of these features on transmission patterns of HRV in the community is understudied. Methods: Nasopharyngeal swabs were collected from patients with symptoms of acute respiratory infection (ARI) at nine out-patient facilities across a Health and Demographic Surveillance System between December 2015 and November 2016. HRV was diagnosed by real-time RT-PCR, and the VP4/VP2 genomic region of the positive samples sequenced. Phylogenetic analysis was used to determine the HRV types. Classification models and G-test statistic were used to investigate HRV type spatial distribution. Demographic characteristics and clinical features of ARI were also compared. Results: Of 5,744 NPS samples collected, HRV was detected in 1057 (18.4%), of which 817 (77.3%) were successfully sequenced. HRV species A, B and C were identified in 360 (44.1%), 67 (8.2%) and 390 (47.7%) samples, respectively. In total, 87 types were determined: 39, 10 and 38 occurred within species A, B and C, respectively. HRV types presented heterogeneous temporal patterns of persistence. Spatially, identical types occurred over a wide distance at similar times, but there was statistically significant evidence for clustering of types between health facilities in close proximity or linked by major road networks. Conclusion: This study records a high prevalence of HRV in out-patient presentations exhibiting high type diversity. Patterns of occurrence suggest frequent and independent community invasion of different types. Temporal differences of persistence between types may reflect variation in type-specific population immunity. Spatial patterns suggest either rapid spread or multiple invasions of the same type, but evidence of similar types amongst close health facilities, or along road systems, indicate type partitioning structured by local spread.

Evaluating the performance of tools used to call minority variants from whole genome short-read data

Background: High-throughput whole genome sequencing facilitates investigation of minority virus sub-populations from virus positive samples. Minority variants are useful in understanding within and between host diversity, population dynamics and can potentially assist in elucidating person-person transmission pathways. Several minority variant callers have been developed to describe low frequency sub-populations from whole genome sequence data. These callers differ based on bioinformatics and statistical methods used to discriminate sequencing errors from low-frequency variants. Methods: We evaluated the diagnostic performance and concordance between published minority variant callers used in identifying minority variants from whole-genome sequence data from virus samples. We used the ART-Illumina read simulation tool to generate three artificial short-read datasets of varying coverage and error profiles from an RSV reference genome. The datasets were spiked with nucleotide variants at predetermined positions and frequencies. Variants were called using FreeBayes, LoFreq, Vardict, and VarScan2. The variant callers’ agreement in identifying known variants was quantified using two measures; concordance accuracy and the inter-caller concordance. Results: The variant callers reported differences in identifying minority variants from the datasets. Concordance accuracy and inter-caller concordance were positively correlated with sample coverage. FreeBayes identified the majority of variants although it was characterised by variable sensitivity and precision in addition to a high false positive rate relative to the other minority variant callers and which varied with sample coverage. LoFreq was the most conservative caller. Conclusions: We conducted a performance and concordance evaluation of four minority variant calling tools used to identify and quantify low frequency variants. Inconsistency in the quality of sequenced samples impacts on sensitivity and accuracy of minority variant callers. Our study suggests that combining at least three tools when identifying minority variants is useful in filtering errors when calling low frequency variants.

COMPLEX FLOW IN GRANULAR MEDIA

By detailed Molecular Dynamics we investigate the rheology of granular suspensions driven through a fixed plate channel by a pressure gradient in the suspending fluid. We observe various possible flow states: disordered flow, ordered flow (granular crystallization) and jammed as well as make close connections to experimental results in colloidal suspensions.