Transmission scenarios for Middle East Respiratory Syndrome Coronavirus (MERS-CoV) and how to tell them apart.

Detection of human cases of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) infection internationally is a global public health concern. Rigorous risk assessment is particularly challenging in a context where surveillance may be subject to under-ascertainment and a selection bias towards more severe cases. We would like to assess whether the virus is capable of causing widespread human epidemics, and whether self-sustaining transmission is already under way. Here we review possible transmission scenarios for MERS-CoV and their implications for risk assessment and control. We discuss how existing data, future investigations and analyses may help in reducing uncertainty and refining the public health risk assessment and present analytical approaches that allow robust assessment of epidemiological characteristics, even from partial and biased surveillance data. Finally, we urge that adequate data be collected on future cases to permit rigorous assessment of the transmission characteristics and severity of MERS-CoV, and the public health threat it may pose. Going beyond minimal case reporting, open international collaboration, under the guidance of the World Health Organization and the International Health Regulations, will impact on how this potential epidemic unfolds and prospects for control.

The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions.

We present an analysis of the current foot-and-mouth disease epidemic in Great Britain over the first 2 months of the spread of the virus. The net transmission potential of the pathogen and the increasing impact of control measures are estimated over the course of the epidemic to date. These results are used to parameterize a mathematical model of disease transmission that captures the differing spatial contact patterns between farms before and after the imposition of movement restrictions. The model is used to make predictions of future incidence and to simulate the impact of additional control strategies. Hastening the slaughter of animals with suspected infection is predicted to slow the epidemic, but more drastic action, such as "ring" culling or vaccination around infection foci, is necessary for more rapid control. Culling is predicted to be more effective than vaccination.

Cross-serotype interactions and disease outcome prediction of dengue infections in Vietnam.

Dengue pathogenesis is extremely complex. Dengue infections are thought to induce life-long immunity from homologous challenges as well as a multi-factorial heterologous risk enhancement. Here, we use the data collected from a prospective cohort study of dengue infections in schoolchildren in Vietnam to disentangle how serotype interactions modulate clinical disease risk in the year following serum collection. We use multinomial logistic regression to correlate the yearly neutralizing antibody measurements obtained with each infecting serotype in all dengue clinical cases collected over the course of 6 years (2004-2009). This allowed us to extrapolate a fully discretised matrix of serotype interactions, revealing clear signals of increased risk of clinical illness in individuals primed with a previous dengue infection. The sequences of infections which produced a higher risk of dengue fever upon secondary infection are: DEN1 followed by DEN2; DEN1 followed by DEN4; DEN2 followed by DEN3; and DEN4 followed by DEN3. We also used this longitudinal data to train a machine learning algorithm on antibody titre differences between consecutive years to unveil asymptomatic dengue infections and estimate asymptomatic infection to clinical case ratios over time, allowing for a better characterisation of the population's past exposure to different serotypes.

Analytic approximation of spatial epidemic models of foot and mouth disease.

The effect of spatial heterogeneity in epidemic models has improved with computational advances, yet far less progress has been made in developing analytical tools for understanding such systems. Here, we develop two classes of second-order moment closure methods for approximating the dynamics of a stochastic spatial model of the spread of foot and mouth disease. We consider the performance of such 'pseudo-spatial' models as a function of R(0), the locality in disease transmission, farm distribution and geographically-targeted control when an arbitrary number of spatial kernels are incorporated. One advantage of mapping complex spatial models onto simpler deterministic approximations lies in the ability to potentially obtain a better analytical understanding of disease dynamics and the effects of control. We exploit this tractability by deriving analytical results in the invasion stages of an FMD outbreak, highlighting key principles underlying epidemic spread on contact networks and the effect of spatial correlations.

Refined efficacy estimates of the Sanofi Pasteur dengue vaccine CYD-TDV using machine learning.

CYD-TDV is the first licensed dengue vaccine for individuals 9-45 (or 60) years of age. Using 12% of the subjects enroled in phase-2b and phase-3 trials for which baseline serostatus was measured, the vaccine-induced protection against virologically confirmed dengue during active surveillance (0-25 months) was found to vary with prior exposure to dengue. Because age and dengue exposure are highly correlated in endemic settings, refined insight into how efficacy varies by serostatus and age is essential to understand the increased risk of hospitalisation observed among vaccinated individuals during the long-term follow-up and to develop safe and effective vaccination strategies. Here we apply machine learning to impute the baseline serostatus for subjects with post-dose 3 titres but missing baseline serostatus. We find evidence for age dependence in efficacy independent of serostatus and estimate that among 9-16 year olds, CYD-TDV is protective against serotypes 1, 3 and 4 regardless of baseline serostatus.

Approximate disease dynamics in household-structured populations.

We argue that the large-dimensional dynamical systems which frequently occur in biological models can sometimes be effectively reduced to much smaller ones. We illustrate this by applying projection operator techniques to a mean-field model of an infectious disease spreading through a population of households. In this way, we are able to accurately approximate the dynamics of the system in terms of a few key quantities greatly reducing the number of equations required. We investigate linear stability in this framework and find a new way of calculating the familiar threshold criterion for household systems.

Viral dynamics and anti-viral pharmacodynamics: rethinking in vitro measures of drug potency.

Most current assays used to quantitate the pharmacodynamic effect of anti-viral agents measure the net inhibitory effect of a drug on virus replication over several days in an in vitro cell culture. Such endpoint experiments give cumulative measures of inhibition that vary with the assay used and therefore provide suboptimal information on likely in vivo drug performance. We argue that instantaneous inhibition (proportion of cell infection prevented at a point in time) is a more robust pharmacodynamic measure, and propose techniques to estimate this quantity from endpoint data. Implications for the quantification of drug interactions are discussed.

Adherence to antiretroviral therapy and its impact on clinical outcome in HIV-infected patients.

We analyse data on patient adherence to prescribed regimens and surrogate markers of clinical outcome for 168 human immunodeficiency virus infected patients treated with antiretroviral therapy. Data on patient adherence consisted of dose-timing measurements collected for an average of 12 months per patient via electronic monitoring of bottle opening events. We first discuss how such data can be presented to highlight suboptimal adherence patterns and between-patient differences, before introducing two novel methods by which such data can be statistically modelled. Correlations between adherence and subsequent measures of viral load and CD4+T-cell counts are then evaluated. We show that summary measures of short-term adherence, which incorporate pharmacokinetic and pharmacodynamic data on the monitored regimen, predict suboptimal trends in viral load and CD4+T-cell counts better than measures based on adherence data alone.

Reduction of the HIV-1-infected T-cell reservoir by immune activation treatment is dose-dependent and restricted by the potency of antiretroviral drugs.

BACKGROUND: Treatments combining T-cell activating agents and potent antiretroviral drugs have been proposed as a possible means of reducing the reservoir of long-lived HIV-1 infected quiescent CD4 T-cells. OBJECTIVE: To analyse the effect of such therapies on HIV-1 dynamics and T-cell homeostasis. DESIGN AND METHODS: A mathematical framework describing HIV-1 dynamics and T-cell homeostasis was developed. Three patients who were kept on a particularly potent course of highly active antiretroviral therapy (HAART) were treated with the anti-CD3 monoclonal antibody OKT3 and interleukin (IL)-2. Plasma HIV-RNA, and HIV-RNA and DNA in peripheral blood mononuclear cells and lymph node mononuclear cells were measured. These results and other published studies on the use of IL-2 alone were assessed using our mathematical framework. RESULTS: We show that outcome of treatment is determined by the relative rates of depletion of the infected quiescent T-cell population by activation and of its replenishment through new infection. Which of these two processes dominates is critically dependent on both the potency of HAART and also the degree of T-cell activation induced. We demonstrate that high-level T-cell stimulation is likely to produce negative outcomes, both by failing to reduce viral reservoirs and by depleting the CD4 T-cell pool and disrupting CD4/CD8 T-cell homeostasis. In contrast, repeated low-level stimulation may both aid CD4 T-cell pool expansion and achieve a substantial reduction in the long-lived HIV-1 reservoir. CONCLUSIONS: Our analysis suggests that although treatment that activates T-cells can reduce the long-lived HIV-1 reservoir, caution should be used as high-level stimulation may result in a negative outcome.

Slower decline of plasma HIV-1 RNA following highly suppressive antiretroviral therapy in primary compared with chronic infection.

OBJECTIVES: To study the effect of highly suppressive antiretroviral therapy on the slopes of HIV-1 RNA decline in primary compared with chronic HIV-1 infection. METHODS: Slopes of HIV-1 RNA decline in plasma were compared before and after the start of highly suppressive antiretroviral therapy from five acutely infected patients who started treatment 2 to 5 weeks following the onset of clinical symptoms. Slopes of decline after the initiation of therapy were also compared with those found in 12 chronically infected individuals on the same therapy. Numbers and percentages of activated CD4 and CD8 T cells at baseline were compared as well. RESULTS: The pre-treatment slopes of HIV-1 RNA decline in the acutely infected individuals increased significantly (P = 0.0001) after the start of anti-retroviral therapy. However, these post-treatment slopes were lower than those found in the chronically infected individuals (P= 0.012). Slopes were inversely correlated (P= 0.012) with baseline HIV-1 RNA. Although the number of CD38+HLA-DR+ CD4 cells was higher in primary infection (P= 0.02), the percentage did not differ between primary and chronic infection. CONCLUSIONS: These findings indicate that antiretroviral therapy contributes significantly to the clearance of HIV-1 during primary infection. Based on the mathematical model the less steep RNA slope following the start of treatment in primary infection can be predicted to be the result of lower clearance of productively infected cells and higher burst size per cell per unit time. This may indicate a growing immune response to HIV-1 in this very early stage of infection.

Vaccination and the population structure of antigenically diverse pathogens that exchange genetic material.

Populations of antigenically diverse pathogens undergoing genetic exchange may be categorized into strains on the basis of a set of principal protective antigens. The extent to which polyvalent vaccines based on these protective antigens can alter the population structure of the pathogen is determined by the degree of cross-protection between strains. In the case where there is no cross-protection, vaccinating against a particular strain will have no effect on the others. As cross-protection increases, the strains containing the antigenic variants included in the vaccine will be diminished in prevalence, and those that do not will increase in prevalence. The rise in prevalence of the latter will become more and more exaggerated as cross-protection increases. However, beyond a critical level of cross-protection, in the absence of vaccination, the steady state of the system is asymmetric in that a certain subset of strains (with non-overlapping repertoires of antigenic variants) will dominate over the others in terms of prevalence. Under these circumstances, a vaccine consisting of the most immunogenic combinations of antigenic variants can cause a dramatic increase in frequency of a subset of rare strains.

The role of antigenic stimulation and cytotoxic T cell activity in regulating the long-term immunopathogenesis of HIV: mechanisms and clinical implications.

This paper develops a predictive mathematical model of cell infection, host immune response and viral replication that reproduces observed long-term trends in human immunodeficiency virus (HIV) pathogenesis. Cell activation induced by repeated exposure to many different antigens is proposed as the principal mechanism of providing target cells for HIV infection and, hence, of CD4+ T cell depletion, with regulation of the overall T cell pool size causing concomitant CD8 pool increases. The model correctly predicts the cross-patient variability in disease progression, the rate of which is found to depend on the efficacy of anti-HIV cytotoxic T lymphocyte responses, overall viral pathogenicity and random effects. The model also predicts a variety of responses to anti-viral therapy, including episodic residual viral replication and discordant responses and we find that such effects can be suppressed by increasing the potency of treatment.

Analysis of dam-calf pairs of BSE cases: confirmation of a maternal risk enhancement.

We investigate whether a calf born to a dam that develops bovine spongiform encephalopathy (BSE) (prior or subsequent to the birth) is itself at an enhanced risk of developing BSE. Analyses utilize the main database on reported BSE cases in the British cattle herd maintained by the Central Veterinary Laboratory in Weybridge to trace the dams of BSE-affected animals born following the ruminant feed ban in July 1988. The data reveal a significantly enhanced risk of disease in calves born to BSE-affected dams, with the risk being greatest when birth occurs after the onset of clinical signs of disease in the dam. The dependence of the maternally enhanced risk on the maternal incubation stage at birth argues for a significant component of direct maternal transmission of the aetiological agent of BSE, and offers little support for the hypothesis of genetic predisposition. Using a statistical likelihood model, we obtain estimates of the rate of direct maternal transmission by maternal incubation stage; however, biases in the available data make these values minimum estimates.

A genetic interpretation of heightened risk of BSE in offspring of affected dams.

An analysis is presented of the results of a cohort study designed to test whether or not the aetiological agent of bovine spongiform encephalopathy (BSE) in cattle can be transmitted maternally (vertically) from dam offspring. Various genetic models are fitted to the data under the assumption that the results could be explained entirely by genetic predisposition to disease (as opposed to maternal transmission) given exposure of offspring of diseased and unaffected dams to contaminated cattle feed. The analyses suggest that the results could be explained by the hypothesis of genetic predisposition, provided a large difference exists in the susceptibility of resistant and susceptible hosts, and explore the range of genotypic parameters and frequencies consistent with the limited currently available data. The results presented are broadly robust, even under the scenario that a portion of the observed maternally enhanced risk of BSE is due to a low level of maternal transmission in late incubation stage dams.

Epidemiological determinants of the pattern and magnitude of the vCJD epidemic in Great Britain.

Understanding the epidemiology and aetiology of new-variant Creutzfeldt-Jakob (vCJD) disease in humans has become increasingly important given the scientific evidence linking it to bovine spongiform encephalopathy (BSE) in cattle and hence the wide exposure of the population of Great Britain (GB) to potentially infectious tissue. The recent analysis undertaken to determine the risk to the population from dorsal route ganglia illustrated the danger in presenting point estimates rather than ranges of scenarios in the face of uncertainty. We present a mathematical template that relates the past pattern of the BSE epidemic in cattle to the future course of any vCJD epidemic in humans, and use extensive scenario analysis to explore the wide range of possible outcomes given the uncertainty in epidemiological determinants. We demonstrate that the average number of humans infected by one infectious bovine and the incubation period distribution are the two epidemiological factors that have the greatest impact on epidemic size and duration. Using the time-series of the BSE epidemic and the cases seen to date, we show that the minimum length of the incubation period is approximately nine years, and that at least 20% of the cases diagnosed to date were exposed prior to 1986. We also demonstrate that the current age distribution of vCJD cases can only arise if younger people were either exposed to a greater extent, more susceptible to infection, or have shorter incubation periods. Extensive scenario analyses show that given the information currently available, the very high degree of uncertainty in the future size of the epidemic will remain for the next 3-5 years. Furthermore, we demonstrate that this uncertainty is unlikely to be reduced by mass screening for late-stage infection.

BSE in Northern Ireland: epidemiological patterns past, present and future.

By 30 January 1998, there had been 170,259 confirmed cases of BSE in Great Britain (GB), 1766 confirmed cases in Northern Ireland (NI) (2 January 1998), and 276 confirmed cases in the Republic of Ireland (31 January 1998). Analysis of the epidemiological patterns in the NI epidemic reveals significant clustering of cases in herds and counties. The observed clustering of cases within herds results in lower per capita incidence of BSE in previously unaffected herds, providing support for the introduction of a certified herd scheme in NI. By fitting a backcalculation model to the case data, we can estimate the number of animals infected with the aetiological agent of BSE and project the number of future cases. We predict that the epidemic will decline rapidly, with approximately 99 cases (95% confidence interval 30,504) occurring in the five year period 1997-2001.

Assessment of the prevalence of vCJD through testing tonsils and appendices for abnormal prion protein.

The objective of this study was to determine the age group or groups which will provide the most information on the potential size of the vCJD epidemic in Great Britain via the sampling of tonsil and appendix material to detect the presence of abnormal prion protein (PrP(Sc)). A subsidiary aim was to determine the degree to which such an anonymous age-stratified testing programme will reduce current uncertainties in the size of the epidemic in future years. A cohort- and time-stratified model was used to generate epidemic scenarios consistent with the observed vCJD case incidence. These scenarios, together with data on the age distribution of tonsillectomies and appendectomies, were used to evaluate the optimal age group and calendar time for undertaking testing and to calculate the range of epidemic sizes consistent with different outcomes. The analyses suggested that the optimal five-year age group to test is 25-29 years, although a random sample of appendix tissue from all age groups is nearly as informative. A random sample of tonsil tissue from all age groups is less informative, but the information content is improved if sampling is restricted to tissues removed from those over ten years of age. Based on the assumption that the test is able to detect infection in the last 75% of the incubation period, zero detected infections in an initial random sample of 1000 tissues would suggest that the epidemic will be less than 870,000 cases. If infections are detected, then the model prediction suggests that both relatively small epidemics (800+ cases if one is detected or 8300+ if two are detected) and larger epidemics (21,000+ cases if three or more are detected) are possible. It was concluded that testing will be most informative if undertaken using appendix tissues or tonsil tissues removed from those over ten years of age. Large epidemics can only be excluded if a small number of infections are detected and the test is able to detect infection early in the incubation period.

Feed-borne transmission and case clustering of BSE.

An unresolved issue in the epidemiology of bovine spongiform encephalopathy (BSE) in the UK is what precisely determines the degree to which cases of disease in cattle are clustered within herds throughout the course of the epidemic. This paper presents an analysis of feed-borne transmission at the herd level and tests various models of case-clustering mechanisms, associated with heterogeneity in exposure to infectious feed, against observed epidemic pattern. We use an age-structured metapopulation framework in which the recycling of animal tissue between herds via feed producers is explicitly described. We explore two alternative assumptions for the scaling with herd size of the within-herd risk of exposure of an animal to infectious material. We find that whereas exposure heterogeneity caused by variation in feed and offal processing methods and by variation in per-animal feed uptake can explain the pattern of case clustering seen in the BSE epidemic, exposure heterogeneity due to the aggregation of infectivity within feed cannot.

Estimation of the basic reproduction number of BSE: the intensity of transmission in British cattle.

The basic reproduction number, R0, of an infectious agent is a key factor determining the rate of spread and the proportion of the host population affected. We formulate a general mathematical framework to describe the transmission dynamics of long incubation period diseases with complex pathogenesis. This is used to derive expressions for R0 of bovine spongiform encephalopathy (BSE) in British cattle, and back-calculation methods are used to estimate R0 throughout the time-course of the BSE epidemic. We show that the 1988 meat and bonemeal ban was effective in rapidly reducing R0 below 1, and demonstrate that this indicates that BSE will be unable to become endemic in the UK cattle population even when case clustering is taken into account. The analysis provides some insight into absolute infectiousness for bovine-to-bovine transmission, indicating maximally infectious animals may have infected up to 400 animals each. The relationship between R0 and the early stages of the BSE epidemic and the requirements for additional research are also discussed.

Extending backcalculation to analyse BSE data.

We review the origins of backcalculation (or back projection) methods developed for the analysis of AIDS (acquired immunodeficiency syndrome) incidence data. These techniques have been used extensively for >15 years to deconvolute clinical case incidence, given knowledge of the incubation period distribution, to obtain estimates of past HIV (human immunodeficiency virus) infection incidence and short-term predictions of future AIDS incidence. Adaptations required for the analysis of bovine spongiform encephalopathy (BSE) incidence included: stratification of BSE incidence by age as well as birth cohort; allowance for incomplete survival between infection and the onset of clinical signs of disease; and decomposition of the age- and time-related infection incidence into a time-dependent feed risk component and an age-dependent exposure/susceptibility function. The most recent methodological developments focus on the incorporation of data from clinically unaffected cattle screened using recently developed tests for preclinical BSE infection. Backcalculation-based predictions of future BSE incidence obtained since 1996 are examined. Finally, future directions of epidemiological analysis of BSE epidemics are discussed taking into account ongoing developments in the science of BSE and possible changes in BSE-related policies.