Inferring transmission routes for foot-and-mouth disease virus within a cattle herd using approximate Bayesian computation.

To control an outbreak of an infectious disease it is essential to understand the different routes of transmission and how they contribute to the overall spread of the pathogen. With this information, policy makers can choose the most efficient methods of detection and control during an outbreak. Here we assess the contributions of direct contact and environmental contamination to the transmission of foot-and-mouth disease virus (FMDV) in a cattle herd using an individual-based model that includes both routes. Model parameters are inferred using approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC) applied to data from transmission experiments and the 2007 epidemic in Great Britain. This demonstrates that the parameters derived from transmission experiments are applicable to outbreaks in the field, at least for closely related strains. Under the assumptions made in the model we show that environmental transmission likely contributes a majority of infections within a herd during an outbreak, although there is a lot of variation between simulated outbreaks. The accumulation of environmental contamination not only causes infections within a farm, but also has the potential to spread between farms via fomites. We also demonstrate the importance and effectiveness of rapid detection of infected farms in reducing transmission between farms, whether via direct contact or the environment.

The role of Type I interferons in the pathogenesis of foot-and-mouth disease virus in cattle: A mathematical modelling analysis.

Type I interferons (IFN) are the first line of immune response against infection. In this study, we explore the interaction between Type I IFN and foot-and-mouth disease virus (FMDV), focusing on the effect of this interaction on epithelial cell death. While several mathematical models have explored the interaction between interferon and viruses at a systemic level, with most of the work undertaken on influenza and hepatitis C, these cannot investigate why a virus such as FMDV causes extensive cell death in some epithelial tissues leading to the development of lesions, while other infected epithelial tissues exhibit negligible cell death. Our study shows how a model that includes epithelial tissue structure can explain the development of lesions in some tissues and their absence in others. Furthermore, we show how the site of viral entry in an epithelial tissue, the viral replication rate, IFN production, suppression of viral replication by IFN and IFN release by live cells, all have a major impact on results.

Control of Brucella melitensis in endemic settings: A simulation study in the Nile Delta, Egypt.

Small ruminant brucellosis remains endemic in many low- and middle-income countries (LMICs), where it poses a major economic and public health burden. Lack of resources to support long-term vaccination, inherent characteristics of small ruminant production systems such as mixing of different flocks for grazing and limitations of the vaccines currently available, which can induce abortion in pregnant animals, have all hindered the effectiveness of control programmes. In the current study, the likely effect of different control scenarios on the seroprevalence of brucellosis among the small ruminant population in a hypothetical area of an endemic region was simulated using compartmental models. The model accounts for variability in transmission rates between villages and also simulates control scenarios that target villages with high seroprevalence. Our results show that vaccination of young replacement animals only can effectively reduce the prevalence of small ruminant brucellosis in endemic settings if a high vaccination coverage is achieved. On the other hand, test-and-slaughter alone is not a promising strategy for control of small ruminant brucellosis under husbandry practices typical of endemic low-resource settings. Furthermore, results show the potential success of some strategies requiring a relatively low overall vaccination coverage such as the vaccination of 50% of young replacements and 25% of adult animals each year. Control strategies selectively targeting high initial seroprevalence villages (p > 10%) did not decrease the overall seroprevalence to acceptable levels in most of the examined scenarios. Scenario analysis showed that the efficacy of the simulated control strategies can be improved mostly by decreasing the proportion of between-village trade and also by improving the performance of the used serological tests and increasing vaccine efficacy.

Using Mathematical Modelling to Explore Hypotheses about the Role of Bovine Epithelium Structure in Foot-And-Mouth Disease Virus-Induced Cell Lysis.

Foot-and-mouth disease (FMD) is a highly contagious disease of cloven-hoofed animals. FMD virus (FMDV) shows a strong tropism for epithelial cells, and FMD is characterised by cell lysis and the development of vesicular lesions in certain epithelial tissues (for example, the tongue). By contrast, other epithelial tissues do not develop lesions, despite being sites of viral replication (for example, the dorsal soft palate). The reasons for this difference are poorly understood, but hypotheses are difficult to test experimentally. In order to identify the factors which drive cell lysis, and consequently determine the development of lesions, we developed a partial differential equation model of FMDV infection in bovine epithelial tissues and used it to explore a range of hypotheses about epithelium structure which could be driving differences in lytic behaviour observed in different tissues. Our results demonstrate that, based on current parameter estimates, epithelial tissue thickness and cell layer structure are unlikely to be determinants of FMDV-induced cell lysis. However, differences in receptor distribution or viral replication amongst cell layers could influence the development of lesions, but only if viral replication rates are much lower than current estimates.

Arenavirus budding resulting from viral-protein-associated cell membrane curvature.

Viral replication occurs within cells, with release (and onward infection) primarily achieved through two alternative mechanisms: lysis, in which virions emerge as the infected cell dies and bursts open; or budding, in which virions emerge gradually from a still living cell by appropriating a small part of the cell membrane. Virus budding is a poorly understood process that challenges current models of vesicle formation. Here, a plausible mechanism for arenavirus budding is presented, building on recent evidence that viral proteins embed in the inner lipid layer of the cell membrane. Experimental results confirm that viral protein is associated with increased membrane curvature, whereas a mathematical model is used to show that localized increases in curvature alone are sufficient to generate viral buds. The magnitude of the protein-induced curvature is calculated from the size of the amphipathic region hypothetically removed from the inner membrane as a result of translation, with a change in membrane stiffness estimated from observed differences in virion deformation as a result of protein depletion. Numerical results are based on experimental data and estimates for three arenaviruses, but the mechanisms described are more broadly applicable. The hypothesized mechanism is shown to be sufficient to generate spontaneous budding that matches well both qualitatively and quantitatively with experimental observations.

Within-group contact of cattle in dairy barns and the implications for disease transmission.

The prevention, control and reduction of livestock diseases require a good understanding of how the underlying causative agents are transmitted. On livestock premises the rate of spread is strongly determined by the contact, both direct and indirect, between infectious and susceptible individuals. Here we consider contact amongst barn-housed dairy cattle, one of the most important UK livestock sectors. A novel observational study of faecal spread indicates that the level of contact an individual animal can have with other herd members via this transmission pathway is very high (80 ± 4% within sub-units). Additional observational studies indicate the possible level of direct physical contact an animal has with other group members (an approximate Poisson distribution with a mean rate of 14.4 distinct individuals per hour), and the potential for indirect transfer via inanimate objects by considering the proportion of the herd that touched a given gatepost in the milking parlour each day (43 ± 6%). Results suggest that mixing may be considered homogeneous for certain pathogens, but that the spread of diseases transmitted along only specific routes requires the incorporation of within group contact structures.

Direct observation of membrane insertion by enveloped virus matrix proteins by phosphate displacement.

Enveloped virus release is driven by poorly understood proteins that are functional analogs of the coat protein assemblies that mediate intracellular vesicle trafficking. We used differential electron density mapping to detect membrane integration by membrane-bending proteins from five virus families. This demonstrates that virus matrix proteins replace an unexpectedly large portion of the lipid content of the inner membrane face, a generalized feature likely to play a role in reshaping cellular membranes.

Modelling the influence of foot-and-mouth disease vaccine antigen stability and dose on the bovine immune response.

Foot and mouth disease virus causes a livestock disease of significant global socio-economic importance. Advances in its control and eradication depend critically on improvements in vaccine efficacy, which can be best achieved by better understanding the complex within-host immunodynamic response to inoculation. We present a detailed and empirically parametrised dynamical mathematical model of the hypothesised immune response in cattle, and explore its behaviour with reference to a variety of experimental observations relating to foot and mouth immunology. The model system is able to qualitatively account for the observed responses during in-vivo experiments, and we use it to gain insight into the incompletely understood effect of single and repeat inoculations of differing dosage using vaccine formulations of different structural stability.

Models to capture the potential for disease transmission in domestic sheep flocks.

Successful control of livestock diseases requires an understanding of how they spread amongst animals and between premises. Mathematical models can offer important insight into the dynamics of disease, especially when built upon experimental and/or field data. Here the dynamics of a range of epidemiological models are explored in order to determine which models perform best in capturing real-world heterogeneities at sufficient resolution. Individual based network models are considered together with one- and two-class compartmental models, for which the final epidemic size is calculated as a function of the probability of disease transmission occurring during a given physical contact between two individuals. For numerical results the special cases of a viral disease with a fast recovery rate (foot-and-mouth disease) and a bacterial disease with a slow recovery rate (brucellosis) amongst sheep are considered. Quantitative results from observational studies of physical contact amongst domestic sheep are applied and results from the differently structured flocks (ewes with newborn lambs, ewes with nearly weaned lambs and ewes only) compared. These indicate that the breeding cycle leads to significant changes in the expected basic reproduction ratio of diseases. The observed heterogeneity of contacts amongst animals is best captured by full network simulations, although simple compartmental models describe the key features of an outbreak but, as expected, often overestimate the speed of an outbreak. Here the weights of contacts are heterogeneous, with many low weight links. However, due to the well-connected nature of the networks, this has little effect and differences between models remain small. These results indicate that simple compartmental models can be a useful tool for modelling real-world flocks; their applicability will be greater still for more homogeneously mixed livestock, which could be promoted by higher intensity farming practices.

Interdisciplinary approaches to zoonotic disease.

Zoonotic infections are on the increase worldwide, but most research into the biological, environmental and life science aspects of these infections has been conducted in separation. In this review we bring together contemporary research in these areas to suggest a new, symbiotic framework which recognises the interaction of biological, economic, psychological, and natural and built environmental drivers in zoonotic infection and transmission. In doing so, we propose that some contemporary debates in zoonotic research could be resolved using an expanded framework which explicitly takes into account the combination of motivated and habitual human behaviour, environmental and biological constraints, and their interactions.

Relationship between clinical signs and transmission of an infectious disease and the implications for control.

Control of many infectious diseases relies on the detection of clinical cases and the isolation, removal, or treatment of cases and their contacts. The success of such "reactive" strategies is influenced by the fraction of transmission occurring before signs appear. We performed experimental studies of foot-and-mouth disease transmission in cattle and estimated this fraction at less than half the value expected from detecting virus in body fluids, the standard proxy measure of infectiousness. This is because the infectious period is shorter (mean 1.7 days) than currently realized, and animals are not infectious until, on average, 0.5 days after clinical signs appear. These results imply that controversial preemptive control measures may be unnecessary; instead, efforts should be directed at early detection of infection and rapid intervention.

Modelling foot-and-mouth disease virus dynamics in oral epithelium to help identify the determinants of lysis.

Foot-and-mouth disease virus (FMDV) causes an economically important disease of cloven-hoofed livestock; of interest here is the difference in lytic behaviour that is observed in bovine epithelium. On the skin around the feet and tongue, the virus rapidly replicates, killing cells, and resulting in growing lesions, before eventually being cleared by the immune response. In contrast, there is usually minimal lysis in the soft palate, but virus may persist in tissue long after the animal has recovered from the disease. Persistence of virus has important implications for disease control, while identifying the determinant of lysis in epithelium is potentially important for the development of prophylactics. To help identify which of the differences between oral and pharyngeal epithelium are responsible for such dramatically divergent FMDV dynamics, a simple model has been developed, in which virus concentration is made explicit to allow the lytic behaviour of cells to be fully considered. Results suggest that localised structuring of what are fundamentally similar cells can induce a bifurcation in the behaviour of the system, explicitly whether infection can be sustained or results in mutual extinction, although parameter estimates indicate that more complex factors may be involved in maintaining viral persistence, or that there are as yet unquantified differences between the intrinsic properties of cells in these regions.

Quantifying the risk of localised animal movement bans for foot-and-mouth disease.

The maintenance of disease-free status from Foot-and-Mouth Disease is of significant socio-economic importance to countries such as the UK. The imposition of bans on the movement of susceptible livestock following the discovery of an outbreak is deemed necessary to prevent the spread of what is a highly contagious disease, but has a significant economic impact on the agricultural community in itself. Here we consider the risk of applying movement restrictions only in localised zones around outbreaks in order to help evaluate how quickly nation-wide restrictions could be lifted after notification. We show, with reference to the 2001 and 2007 UK outbreaks, that it would be practical to implement such a policy provided the basic reproduction ratio of known infected premises can be estimated. It is ultimately up to policy makers and stakeholders to determine the acceptable level of risk, involving a cost benefit analysis of the potential outcomes, but quantifying the risk of spread from different sized zones is a prerequisite for this. The approach outlined is relevant to the determination of control zones and vaccination policies and has the potential to be applied to future outbreaks of other diseases.

Predicting infection risk of airborne foot-and-mouth disease.

Foot-and-mouth disease is a highly contagious disease of cloven-hoofed animals, the control and eradication of which is of significant worldwide socio-economic importance. The virus may spread by direct contact between animals or via fomites as well as through airborne transmission, with the latter being the most difficult to control. Here, we consider the risk of infection to flocks or herds from airborne virus emitted from a known infected premises. We show that airborne infection can be predicted quickly and with a good degree of accuracy, provided that the source of virus emission has been determined and reliable geo-referenced herd data are available. A simple model provides a reliable tool for estimating risk from known sources and for prioritizing surveillance and detection efforts. The issue of data information management systems was highlighted as a lesson to be learned from the official inquiry into the UK 2007 foot-and-mouth outbreak: results here suggest that the efficacy of disease control measures could be markedly improved through an accurate livestock database incorporating flock/herd size and location, which would enable tactical as well as strategic modelling.

WITHDRAWN: Foot-and-mouth disease: How much airborne virus do animals exhale?

This article has been withdrawn at the request of the Editor. The Publisher apologizes for any inconvenience this may cause. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.

Population models of sperm-dependent parthenogenesis.

Organisms that reproduce by sperm-dependent parthenogenesis are asexual clones that require sperm of a sexual host to initiate egg production, without the genome of the sperm contributing genetic information to the zygote. Although sperm-dependent parthenogenesis has some of the disadvantages of sex (requiring a mate) without the counterbalancing advantages (mixing of parental genotypes), it appears amongst a wide variety of species. We develop initial models for the density-dependent dynamics of animal populations with sperm-dependent parthenogenesis (pseudogamy or gynogenesis), based on the known biology of the common Enchytraeid worm Lumbricillus lineatus. Its sperm-dependent parthenogenetic populations are reproductive parasites of the hermaphrodite sexual form. Our logistic models reveal two alternative requirements for coexistence at density-dependent equilibria: (i) If the two forms differ in competitive ability, the form with the lower intrinsic birth rate must be compensated by a more than proportionately lower competitive impact from the other, relative to intraspecific competition, (ii) If the two forms differ in their intrinsic capacity to exploit resources, the sperm-dependent parthenogen must be superior in this respect and must have a lower intrinsic birth rate. In general for crowded environments we expect a sperm-dependent parthenogen to compete strongly for limiting resources with the sexual sibling species. Its competitive impact is likely to be weakened by its genetic uniformity, however, and this may suffice to cancel any advantage of higher intrinsic growth rate obtained from reproductive investment only in egg production. We discuss likely thresholds of coexistence for other sperm-dependent parthenogens. The fish Poeciliopsis monacha-lucida likewise obtains an intrinsic growth advantage from reduced investment in male gametes, and so its persistence is likely to depend on it being a poor competitor. The planarian Schmidtea polychroa obtains no such intrinsic benefit because it produces fertile sperm, and its persistence may depend on superior resource exploitation.

Mathematical methods relevant to the study of wound healing.

Over recent years there has been a growing interest in the application of mathematical techniques and methods to improve understanding of clinical problems. Mathematical methods permit accurate description and quantification of observations and processes. Wound healing is a clinical problem that needs support in order to improve management and understanding of the mechanisms that may disarrange healing processes. This article attempts to provide an overview of currently available methods that have a direct relevance to the management of lower extremity wounds. Mathematics can provide valuable assistance and insight to clinical understanding, but only if applied correctly. It is hoped that examples of good practice will promote the utilization of this versatile tool.