The effect of changes in condom usage and antiretroviral treatment coverage on human immunodeficiency virus incidence in South Africa: a model-based analysis

This study aims to assess trends in human immunodeficiency virus (HIV) incidence in South Africa, and to assess the extent to which prevention and treatment programmes have reduced HIV incidence. Two models of the South African HIV epidemic, the STI (sexually transmitted infection)–HIV Interaction model and the ASSA2003 AIDS and Demographic model, were adapted. Both models were fitted to age-specific HIV prevalence data from antenatal clinic surveys and household surveys, using a Bayesian approach. Both models suggest that HIV incidence in 15–49 year olds declined significantly between the start of 2000 and the start of 2008: by 27 per cent (95% CI: 21–32%) in the STI–HIV model and by 31 per cent (95% CI: 23–39%) in the ASSA2003 model, when expressed as a percentage of incidence rates in 2000. By 2008, the percentage reduction in incidence owing to increased condom use was 37 per cent (95% CI: 34–41%) in the STI–HIV model and 23 per cent (95% CI: 14–34%) in the ASSA2003 model. Both models also estimated a small reduction in incidence owing to antiretroviral treatment by 2008. Increased condom use therefore appears to be the most significant factor explaining the recent South African HIV incidence decline.     

Competitive numerical analysis for stochastic HIV/AIDS epidemic model in a two‐sex population

This study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two‐sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H ^* holds on the stochastic HIV/AIDS epidemic model. If H ^*  < 1 then condition helps us to control disease in a two‐sex human population while H ^*  > 1 explains the persistence of disease in the two‐sex human population. Lamentably, numerical methods such as Euler–Maruyama, stochastic Euler, and stochastic Runge–Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non‐standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two‐sex population.Inspec keywords: diseases, stochastic processes, epidemics, patient treatment, finite difference methodsOther keywords: two‐sex human population, antiretroviral therapy, competitive numerical analysis, stochastic HIV‐AIDS epidemic model, structure preserving framework, stochastic nonstandard finite difference scheme, SNSFD scheme, deterministic HIV‐AIDS epidemic model     

Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth–death SIR model

The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses'' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible–infected–removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth–death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Córdoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.     

Epidemics in networks of spatially correlated three-dimensional root-branching structures

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible–infected–recovered (‘SIR’) epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.     

Disease control across urban–rural gradients

Controlling the regional re-emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban–rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases or regional lockdowns in response to local outbreaks have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test-and-trace strategies, is pivotal to reducing the overall epidemic size over a wider range of transmission scenarios. We define an ‘urban–rural gradient in epidemic size'' as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban–rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatic individuals only. Our results emphasize the importance of test-and-trace strategies and maintaining low transmission rates for efficiently controlling SARS-CoV-2 spread, both at landscape scale and in urban areas.     

Targeting vaccination against novel infections: risk,age and spatial structure for pandemic influenza in Great Britain

The emergence of a novel strain of H1N1 influenza virus in Mexico in 2009, and its subsequent worldwide spread, has focused attention to the question of optimal deployment of mass vaccination campaigns. Here, we use three relatively simple models to address three issues of primary concern in the targeting of any vaccine. The advantages of such simple models are that the underlying assumptions and effects of individual parameters are relatively clear, and the impact of uncertainty in the parametrization can be readily assessed in the early stages of an outbreak. In particular, we examine whether targeting risk-groups, age-groups or spatial regions could be optimal in terms of reducing the predicted number of cases or severe effects; and how these targeted strategies vary as the epidemic progresses. We examine the conditions under which it is optimal to initially target vaccination towards those individuals within the population who are most at risk of severe effects of infection. Using age-structured mixing matrices, we show that targeting vaccination towards the more epidemiologically important age groups (5–14 year olds and then 15–24 year olds) leads to the greatest reduction in the epidemic growth and hence reduces the total number of cases. Finally, we consider how spatially targeting the vaccine towards regions of country worst affected could provide an advantage. We discuss how all three of these priorities change as both the speed at which vaccination can be deployed and the start of the vaccination programme is varied.     

Joint modelling of serological and hospitalization data reveals that high levels of pre-existing immunity and school holidays shaped the influenza A pandemic of 2009 in The Netherlands

Obtaining a quantitative understanding of the transmission dynamics of influenza A is important for predicting healthcare demand and assessing the likely impact of intervention measures. The pandemic of 2009 provides an ideal platform for developing integrative analyses as it has been studied intensively, and a wealth of data sources is available. Here, we analyse two complementary datasets in a disease transmission framework: cross-sectional serological surveys providing data on infection attack rates, and hospitalization data that convey information on the timing and duration of the pandemic. We estimate key epidemic determinants such as infection and hospitalization rates, and the impact of a school holiday. In contrast to previous approaches, our novel modelling of serological data with mixture distributions provides a probabilistic classification of individual samples (susceptible, immune and infected), propagating classification uncertainties to the transmission model and enabling serological classifications to be informed by hospitalization data. The analyses show that high levels of immunity among persons 20 years and older provide a consistent explanation of the skewed attack rates observed during the pandemic and yield precise estimates of the probability of hospitalization per infection (1–4 years: 0.00096 (95%CrI: 0.00078–0.0012); 5–19 years: 0.00036 (0.00031–0.0044); 20–64 years: 0.0015 (0.00091–0.0020); 65+ years: 0.0084 (0.0028–0.016)). The analyses suggest that in The Netherlands, the school holiday period reduced the number of infectious contacts between 5- and 9-year-old children substantially (estimated reduction: 54%; 95%CrI: 29–82%), thereby delaying the unfolding of the pandemic in The Netherlands by approximately a week.     

Estimating epidemic coupling between populations from the time to invasion

Identifying the mechanisms by which diseases spread among populations is important for understanding and forecasting patterns of epidemics and pandemics. Estimating transmission coupling among populations is challenging because transmission events are difficult to observe in practice, and connectivity among populations is often obscured by local disease dynamics. We consider the common situation in which an epidemic is seeded in one population and later spreads to a second population. We present a method for estimating transmission coupling between the two populations, assuming they can be modelled as susceptible–infected–removed (SIR) systems. We show that the strength of coupling between the two populations can be estimated from the time taken for the disease to invade the second population. Confidence in the estimate is low if only a single invasion event has been observed, but is substantially improved if numerous independent invasion events are observed. Our analysis of this simplest, idealized scenario represents a first step toward developing and verifying methods for estimating epidemic coupling among populations in an ever-more-connected global human population.     

Transmission network of the 2014–2015 Ebola epidemic in Sierra Leone

Understanding the growth and spatial expansion of (re)emerging infectious disease outbreaks, such as Ebola and avian influenza, is critical for the effective planning of control measures; however, such efforts are often compromised by data insufficiencies and observational errors. Here, we develop a spatial–temporal inference methodology using a modified network model in conjunction with the ensemble adjustment Kalman filter, a Bayesian inference method equipped to handle observational errors. The combined method is capable of revealing the spatial–temporal progression of infectious disease, while requiring only limited, readily compiled data. We use this method to reconstruct the transmission network of the 2014–2015 Ebola epidemic in Sierra Leone and identify source and sink regions. Our inference suggests that, in Sierra Leone, transmission within the network introduced Ebola to neighbouring districts and initiated self-sustaining local epidemics; two of the more populous and connected districts, Kenema and Port Loko, facilitated two independent transmission pathways. Epidemic intensity differed by district, was highly correlated with population size (r = 0.76, p = 0.0015) and a critical window of opportunity for containing local Ebola epidemics at the source (ca one month) existed. This novel methodology can be used to help identify and contain the spatial expansion of future (re)emerging infectious disease outbreaks.     

Complexity and anisotropy in host morphology make populations less susceptible to epidemic outbreaks

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible–infected–recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to separately analyse the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.     

Making wider use of the world's most widely used vaccine: Bacille Calmette–Guérin revaccination reconsidered

Approximately 100 million newborn children receive Bacille Calmette–Guérin (BCG) annually, because vaccination is consistently protective against childhood tuberculous meningitis and miliary TB. By contrast, BCG efficacy against pulmonary TB in children and adults is highly variable, ranging from 0% to 80%, though it tends to be higher in individuals who have no detectable prior exposure to mycobacterial infections, as judged by the absence of delayed-type hypersensitivity response (a negative tuberculin skin test, TST). The duration of protection against pulmonary TB is also variable, but lasts about 10 years on average. These observations raise the possibility that BCG revaccination, following primary vaccination in infancy, could be efficacious among TST-negative adolescents as they move into adulthood, the period of highest risk for pulmonary disease. To inform continuing debate about revaccination, this paper assesses the effectiveness and cost-effectiveness of revaccinating adolescents in a setting with intense transmission—Cape Town, South Africa. For a cost of revaccination in the range US$1–10 per person, and vaccine efficacy between 10% and 80% with protection for 10 years, the incremental cost per year of healthy life recovered (disability-adjusted life years, DALY) in the vaccinated population lies between US$116 and US$9237. The intervention is about twice as cost-effective when allowing for the extra benefits of preventing transmission, with costs per DALY recovered in the range US$52–$4540. At 80% efficacy, revaccination averted 17% of cases. Under the scenarios investigated, BCG revaccination is cost-effective against international benchmarks, though not highly effective. Cost-effectiveness ratios would be more favourable if we also allow for TB cases averted by preventing transmission to HIV-positive people, for the protection of HIV-negative people who later acquire HIV infection, for the possible non-specific benefits of BCG, for the fact that some adolescents would receive BCG for the first time, and for cost sharing when BCG is integrated into an adolescent immunization programme. These findings suggest, subject to further evaluation, that BCG revaccination could be cost-effective in some settings.     

Demographic buffering: titrating the effects of birth rate and imperfect immunity on epidemic dynamics

Host demography can alter the dynamics of infectious disease. In the case of perfectly immunizing infections, observations of strong sensitivity to demographic variation have been mechanistically explained through analysis of the susceptible–infected–recovered (SIR) model that assumes lifelong immunity following recovery from infection. When imperfect immunity is incorporated into this framework via the susceptible–infected–recovered–susceptible (SIRS) model, with individuals regaining full susceptibility following recovery, we show that rapid loss of immunity is predicted to buffer populations against the effects of demographic change. However, this buffering is contrary to the dependence on demography recently observed for partially immunizing infections such as rotavirus and respiratory syncytial virus. We show that this discrepancy arises from a key simplification embedded in the SIR(S) framework, namely that the potential for differential immune responses to repeat exposures is ignored. We explore the minimum additional immunological information that must be included to reflect the range of observed dependencies on demography. We show that including partial protection and lower transmission following primary infection is sufficient to capture more realistic reduced levels of buffering, in addition to changes in epidemic timing, across a range of partially and fully immunizing infections. Furthermore, our results identify key variables in this relationship, including R₀.     

Distribution of vaccine/antivirals and the ‘least spread line’ in a stratified population

We describe a prioritization scheme for an allocation of a sizeable quantity of vaccine or antivirals in a stratified population. The scheme builds on an optimal strategy for reducing the epidemic''s initial growth rate in a stratified mass-action model. The strategy is tested on the EpiSims network describing interactions and influenza dynamics in the population of Utah, where the stratification we have chosen is by age (0–6, 7–13, 14–18, adults). No prior immunity information is available, thus everyone is assumed to be susceptible—this may be relevant, possibly with the exception of persons over 50, to the 2009 H1N1 influenza outbreak. We have found that the top priority in an allocation of a sizeable quantity of seasonal influenza vaccinations goes to young children (0–6), followed by teens (14–18), then children (7–13), with the adult share being quite low. These results, which rely on the structure of the EpiSims network, are compared with the current influenza vaccination coverage levels in the US population.     

Effects of changes in temperature on Zika dynamics and control

When a rare pathogen emerges to cause a pandemic, it is critical to understand its dynamics and the impact of mitigation measures. We use experimental data to parametrize a temperature-dependent model of Zika virus (ZIKV) transmission dynamics and analyse the effects of temperature variability and control-related parameters on the basic reproduction number (R₀) and the final epidemic size of ZIKV. Sensitivity analyses show that these two metrics are largely driven by different parameters, with the exception of temperature, which is the dominant driver of epidemic dynamics in the models. Our R₀ estimate has a single optimum temperature (≈30°C), comparable to other published results (≈29°C). However, the final epidemic size is maximized across a wider temperature range, from 24 to 36°C. The models indicate that ZIKV is highly sensitive to seasonal temperature variation. For example, although the model predicts that ZIKV transmission cannot occur at a constant temperature below 23°C (≈ average annual temperature of Rio de Janeiro, Brazil), the model predicts substantial epidemics for areas with a mean temperature of 20°C if there is seasonal variation of 10°C (≈ average annual temperature of Tampa, Florida). This suggests that the geographical range of ZIKV is wider than indicated from static R₀ models, underscoring the importance of climate dynamics and variation in the context of broader climate change on emerging infectious diseases.     

Rubella metapopulation dynamics and importance of spatial coupling to the risk of congenital rubella syndrome in Peru

Rubella is generally a mild childhood disease, but infection during early pregnancy may cause spontaneous abortion or congenital rubella syndrome (CRS), which may entail a variety of birth defects. Consequently, understanding the age-structured dynamics of this infection has considerable public health value. Vaccination short of the threshold for local elimination of transmission will increase the average age of infection. Accordingly, the classic concern for this infection is the potential for vaccination to increase incidence in individuals of childbearing age. A neglected aspect of rubella dynamics is how age incidence patterns may be moulded by the spatial dynamics inherent to epidemic metapopulations. Here, we use a uniquely detailed dataset from Peru to explore the implications of this for the burden of CRS. Our results show that the risk of CRS may be particularly severe in small remote regions, a prediction at odds with expectations in the endemic situation, and with implications for the outcome of vaccination. This outcome results directly from the metapopulation context: specifically, extinction–re-colonization dynamics are crucial because they allow for significant leakage of susceptible individuals into the older age classes during inter-epidemic periods with the potential to increase CRS risk by as much as fivefold.     

Integrating stochasticity and network structure into an epidemic model

While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.     

Synchrotron imaging reveals bone healing and remodelling strategies in extinct and extant vertebrates

Current understanding of bone healing and remodelling strategies in vertebrates has traditionally relied on morphological observations through the histological analysis of thin sections. However, chemical analysis may also be used in such interpretations, as different elements are known to be absorbed and used by bone for different physiological purposes such as growth and healing. These chemical signatures are beyond the detection limit of most laboratory-based analytical techniques (e.g. scanning electron microscopy). However, synchrotron rapid scanning–X-ray fluorescence (SRS–XRF) is an elemental mapping technique that uniquely combines high sensitivity (ppm), excellent sample resolution (20–100 µm) and the ability to scan large specimens (decimetre scale) approximately 3000 times faster than other mapping techniques. Here, we use SRS–XRF combined with microfocus elemental mapping (2–20 µm) to determine the distribution and concentration of trace elements within pathological and normal bone of both extant and extinct archosaurs (Cathartes aura and Allosaurus fragilis). Results reveal discrete chemical inventories within different bone tissue types and preservation modes. Chemical inventories also revealed detail of histological features not observable in thin section, including fine structures within the interface between pathological and normal bone as well as woven texture within pathological tissue.     

Characterization of age-related variation in corneal biomechanical properties

An experimental study has been conducted to determine the stress–strain behaviour of human corneal tissue and how the behaviour varies with age. Fifty-seven well-preserved ex vivo donor corneas aged between 30 and 99 years were subjected to cycles of posterior pressure up to 60 mm Hg while monitoring their behaviour. The corneas were mechanically clamped along their ring of scleral tissue and kept in physiological conditions of temperature and hydration. The tissue demonstrated hyper-elastic pressure-deformation and stress–strain behaviour that closely matched an exponential trend. Clear stiffening (increased resistance to deformation) with age was observed in all loading cycles, and the rate of stiffness growth was nonlinear with bias towards older specimens. With a strong statistical association between stiffness and age (p < 0.05), it was possible to develop generic stress–strain equations that were suitable for all ages between 30 and 99 years. These equations, which closely matched the experimental results, depicted corneal stiffening with age in a form suitable for implementation in numerical simulations of ocular biomechanical behaviour.     

A century of transitions in New York City's measles dynamics

Infectious diseases spreading in a human population occasionally exhibit sudden transitions in their qualitative dynamics. Previous work has successfully predicted such transitions in New York City''s historical measles incidence using the seasonally forced susceptible–infectious–recovered (SIR) model. This work relied on a dataset spanning 45 years (1928–1973), which we have extended to 93 years (1891–1984). We identify additional dynamical transitions in the longer dataset and successfully explain them by analysing attractors and transients of the same mechanistic epidemiological model.