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.     

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.     

On spatially explicit models of cholera epidemics

We generalize a recently proposed model for cholera epidemics that accounts for local communities of susceptibles and infectives in a spatially explicit arrangement of nodes linked by networks having different topologies. The vehicle of infection (Vibrio cholerae) is transported through the network links that are thought of as hydrological connections among susceptible communities. The mathematical tools used are borrowed from general schemes of reactive transport on river networks acting as the environmental matrix for the circulation and mixing of waterborne pathogens. Using the diffusion approximation, we analytically derive the speed of propagation for travelling fronts of epidemics on regular lattices (either one-dimensional or two-dimensional) endowed with uniform population density. Power laws are found that relate the propagation speed to the diffusion coefficient and the basic reproduction number. We numerically obtain the related, slower speed of epidemic spreading for more complex, yet realistic river structures such as Peano networks and optimal channel networks. The analysis of the limit case of uniformly distributed population sizes proves instrumental in establishing the overall conditions for the relevance of spatially explicit models. To that extent, the ratio between spreading and disease outbreak time scales proves the crucial parameter. The relevance of our results lies in the major differences potentially arising between the predictions of spatially explicit models and traditional compartmental models of the susceptible–infected–recovered (SIR)-like type. Our results suggest that in many cases of real-life epidemiological interest, time scales of disease dynamics may trigger outbreaks that significantly depart from the predictions of compartmental models.     

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.     

North–South divide: contrasting impacts of climate change on crop yields in Scotland and England

Effects of climate change on productivity of agricultural crops in relation to diseases that attack them are difficult to predict because they are complex and nonlinear. To investigate these crop–disease–climate interactions, UKCIP02 scenarios predicting UK temperature and rainfall under high- and low-CO₂ emission scenarios for the 2020s and 2050s were combined with a crop-simulation model predicting yield of fungicide-treated winter oilseed rape and with a weather-based regression model predicting severity of phoma stem canker epidemics. The combination of climate scenarios and crop model predicted that climate change will increase yield of fungicide-treated oilseed rape crops in Scotland by up to 0.5 t ha⁻¹ (15%). In contrast, in southern England the combination of climate scenarios, crop, disease and yield loss models predicted that climate change will increase yield losses from phoma stem canker epidemics to up to 50 per cent (1.5 t ha⁻¹) and greatly decrease yield of untreated winter oilseed rape. The size of losses is predicted to be greater for winter oilseed rape cultivars that are susceptible than for those that are resistant to the phoma stem canker pathogen Leptosphaeria maculans. Such predictions illustrate the unexpected, contrasting impacts of aspects of climate change on crop–disease interactions in agricultural systems in different regions.     

Modelling cholera epidemics: the role of waterways,human mobility and sanitation

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000–2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.     

Strong seasonality produces spatial asynchrony in the outbreak of infectious diseases

Models for infectious diseases usually assume a fixed demographic structure. Yet, a disease can spread over a region encountering different local demographic variations that may significantly alter local dynamics. Spatial heterogeneity in the resulting dynamics can lead to important differences in the design of surveillance and control strategies. We illustrate this by exploring the north–south gradient in the seasonal demography of raccoon rabies over the eastern USA. We find that the greater variance in the timing of spring births characteristic of southern populations can lead to the spatial synchronization of southern epidemics, while the narrow birth-pulse associated with northern populations can lead to an irregular patchwork of epidemics. These results indicate that surveillance in the southern states can be reduced relative to northern locations without loss of detection ability. This approach could yield significant savings in vaccination programmes. The importance of seasonality in many widely distributed diseases indicates that our findings will find applications beyond raccoon rabies.     

Yield stress of duplex stainless steel specimens estimated using a compound Hall–Petch equation

In this study, the 0.2% yield stress of duplex stainless steel was evaluated using a compound Hall–Petch equation. The compound Hall–Petch equation was derived from four types of duplex stainless steel, which contained 0.2–64.4 wt% δ-ferrite phase, had different chemical compositions and were annealed at different temperatures. Intragranular yield stress was measured with an ultra-microhardness tester and evaluated with the yield stress model proposed by Dao et al. Grain size, volume fraction and texture were monitored by electron backscattering diffraction measurement. The k_γ constant in the compound equation for duplex stainless steel agrees well with that for γ-phase SUS316L steel in the temperature range of 1323–1473 K. The derived compound Hall–Petch equation predicts that the yield stress will be in good agreement with the experimental results for the Cr, Mn, Si, Ni and N solid-solution states. We find that the intragranular yield stress of the δ-phase of duplex stainless steel is rather sensitive to the chemical composition and annealing conditions, which is attributed to the size misfit parameter.     

Disease transmission in territorial populations: the small-world network of Serengeti lions

Territoriality in animal populations creates spatial structure that is thought to naturally buffer disease invasion. Often, however, territorial populations also include highly mobile, non-residential individuals that potentially serve as disease superspreaders. Using long-term data from the Serengeti Lion Project, we characterize the contact network structure of a territorial wildlife population and address the epidemiological impact of nomadic individuals. As expected, pride contacts are dominated by interactions with neighbouring prides and interspersed by encounters with nomads as they wander throughout the ecosystem. Yet the pride–pride network also includes occasional long-range contacts between prides, making it surprisingly small world and vulnerable to epidemics, even without nomads. While nomads increase both the local and global connectivity of the network, their epidemiological impact is marginal, particularly for diseases with short infectious periods like canine distemper virus. Thus, territoriality in Serengeti lions may be less protective and non-residents less important for disease transmission than previously considered.     

Invasion,persistence and control in epidemic models for plant pathogens: the effect of host demography

Many epidemiological models for plant disease include host demography to describe changes in the availability of susceptible tissue for infection. We compare the effects of using two commonly used formulations for host growth, one linear and the other nonlinear, upon the outcomes for invasion, persistence and control of pathogens in a widely used, generic model for botanical epidemics. The criterion for invasion, reflected in the basic reproductive number, R₀, is unaffected by host demography: R₀ is simply a function of epidemiological parameters alone. When, however, host growth is intrinsically nonlinear, unexpected results arise for persistence and the control of disease. The endemic level of infection (I_∞) also depends upon R₀. We show, however, that the sensitivity of I_∞ to changes in R₀ > 1 depends upon which underlying epidemiological parameter is changed. Increasing R₀ by shortening the infectious period results in a monotonic increase in I_∞. If, however, an increase in R₀ is driven by increases in transmission rates or by decreases in the decay of free-living inoculum, I_∞ first increases (R₀ < 2), but then decreases (R₀ > 2). This counterintuitive result means that increasing the intensity of control can result in more endemic infection.     

Resonance of human brain under head acceleration

Although safety standards have reduced fatal head trauma due to single severe head impacts, mild trauma from repeated head exposures may carry risks of long-term chronic changes in the brain''s function and structure. To study the physical sensitivities of the brain to mild head impacts, we developed the first dynamic model of the skull–brain based on in vivo MRI data. We showed that the motion of the brain can be described by a rigid-body with constrained kinematics. We further demonstrated that skull–brain dynamics can be approximated by an under-damped system with a low-frequency resonance at around 15 Hz. Furthermore, from our previous field measurements, we found that head motions in a variety of activities, including contact sports, show a primary frequency of less than 20 Hz. This implies that typical head exposures may drive the brain dangerously close to its mechanical resonance and lead to amplified brain–skull relative motions. Our results suggest a possible cause for mild brain trauma, which could occur due to repetitive low-acceleration head oscillations in a variety of recreational and occupational activities.     

Active vacuum brazing of CNT films to metal substrates for superior electron field emission performance

The joining of macroscopic films of vertically aligned multiwalled carbon nanotubes (CNTs) to titanium substrates is demonstrated by active vacuum brazing at 820 °C with a Ag–Cu–Ti alloy and at 880 °C with a Cu–Sn–Ti–Zr alloy. The brazing methodology was elaborated in order to enable the production of highly electrically and thermally conductive CNT/metal substrate contacts. The interfacial electrical resistances of the joints were measured to be as low as 0.35 Ω. The improved interfacial transport properties in the brazed films lead to superior electron field-emission properties when compared to the as-grown films. An emission current of 150 μA was drawn from the brazed nanotubes at an applied electric field of 0.6 V μm⁻¹. The improvement in electron field-emission is mainly attributed to the reduction of the contact resistance between the nanotubes and the substrate. The joints have high re-melting temperatures up to the solidus temperatures of the alloys; far greater than what is achievable with standard solders, thus expanding the application potential of CNT films to high-current and high-power applications where substantial frictional or resistive heating is expected.     

Rapid removal of lead(II) ions from water using iron oxide–tea waste nanocomposite – a kinetic study

Lead (Pb) ions are a major concern to the environment and human health as they are contemplated cumulative poisons. In this study, facile synthesis of magnetic iron oxide–tea waste nanocomposite is reported for adsorptive removal of lead ions from aqueous solutions and easy magnetic separation of the adsorbent afterwards. The samples were characterised by scanning electron microscopy, Fourier transform‐infrared spectroscopy, X‐ray diffraction, and Braunner–Emmet–Teller nitrogen adsorption study. Adsorptive removal of Pb(II) ions from aqueous solution was followed by ultraviolet–visible (UV–Vis) spectrophotometry. About 95% Pb(II) ion removal is achieved with the magnetic tea waste within 10 min. A coefficient of regression R ²  ≃ 0.99 and adsorption density of 18.83 mg g⁻¹ was found when Pb(II) ions were removed from aqueous solution using magnetic tea waste. The removal of Pb(II) ions follows the pseudo‐second‐order rate kinetics. External mass transfer principally regulates the rate‐limiting phenomena of adsorption of Pb(II) ions on iron oxide–tea waste surface. The results strongly imply that magnetic tea waste has promising potential as an economic and excellent adsorbent for the removal of Pb(II) from water.Inspec keywords: visible spectra, scanning electron microscopy, mass transfer, ultraviolet spectra, X‐ray diffraction, nanocomposites, lead, adsorption, magnetic separation, iron compounds, nanofabrication, Fourier transform infrared spectraOther keywords: FeO, Pb, time 10.0 min, X‐ray diffraction, Fourier transform‐infrared spectroscopy, scanning electron microscopy, adsorbent, magnetic separation, rapid removal, Braunner–Emmet–Teller nitrogen adsorption, iron oxide–tea waste surface, magnetic tea waste, aqueous solution, adsorptive removal, magnetic iron oxide–tea waste nanocomposite, lead(II) ions     

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.     

Towards elucidating the connection between epithelial–mesenchymal transitions and stemness

Epithelial cells undergoing epithelial-to-mesenchymal transitions have often been shown to behave as cancer stem cells, but the precise molecular connection remains elusive. At the genetic level, stemness is governed by LIN28/let-7 double inhibition switch, whereas EMT/MET is controlled by miR-200/ZEB double inhibition circuit and LIN28 is inhibited by miR-200, coupling the two modules. Here, using a specially devised theoretical framework to investigate the dynamics of the LIN28/let-7 system, we show that it can operate as a three-way switch (between low, high and intermediate LIN28 levels termed the D, U and hybrid D/U states) similar to the three-way operation of the miR-200/ZEB circuit that allows for the existence of a hybrid epithelial/mesenchymal (E/M) phenotype. We find significant correspondence between the existence of the three states of the two circuits: E–D, M–U and E/M–D/U. Incorporating the activation of OCT4 by LIN28, we find that the hybrid E/M phenotype has high likelihood (when compared with either the E or M states) to gain stemness. Combining the LIN28/let-7 regulation by NF-κB and c-MYC, we find that NF-κB, but not c-MYC, elevates the likelihood of E/M phenotype to gain stemness. Our results are consistent with emerging concept that partial EMT can lead to stemness.     

The interaction of seasonal forcing and immunity and the resonance dynamics of malaria

Theory has emphasized the importance of both intrinsic factors such as host immunity and extrinsic drivers such as climate in determining disease dynamics. In particular, seasonality may lead to multi-annual cycles in prevalence, but the likelihood of this depends on the role of acquired immunity. Some diseases including malaria have immunity that falls between the classic susceptible–infectious–removed and susceptible–infectious–susceptible models. Here, we investigate the general conditions promoting the subharmonic resonance behaviour that may lead to multi-annual cycles in a general malaria dynamical model. Utilizing two complementary approaches to bifurcation analyses, we show that resonance is promoted by processes shortening the length of the infectious period and that subharmonic cycles are favoured in situations with strong seasonality in transmission but at intermediate levels of endemicity. We discuss the implications of our results for understanding prevalence patterns in long-term malaria datasets from Kenya that show multi-annual cycles and one from Thailand that does not and discuss the possible implications of treatment.     

Electrodeposition of zinc–silica composite coatings: challenges in incorporating functionalized silica particles into a zinc matrix

Zinc is a well-known sacrificial coating material for iron and co-deposition of suitable particles is of interest for further improving its corrosion protection performance. However, incorporation of particles that are well dispersible in aqueous electrolytes, such as silica particles, is extremely difficult. Here, we report a detailed study of Zn–SiO₂ nanocomposite coatings deposited from a zinc sulfate solution at pH 3. The effect of functionalization of the silica particles on the electro-codeposition was investigated. The best incorporation was achieved for particles modified with SiO₂–SH, dithiooxamide or cysteamine; these particles have functional groups that can strongly interact with zinc and therefore incorporate well into the metal matrix. Other modifications (SiO₂–NH₃⁺, SiO₂–Cl and N,N-dimethyldodecylamine) of the silica particles lead to adsorption and entrapment only.     

Time and dose-dependent risk of pneumococcal pneumonia following influenza: a model for within-host interaction between influenza and Streptococcus pneumoniae

A significant fraction of seasonal and in particular pandemic influenza deaths are attributed to secondary bacterial infections. In animal models, influenza virus predisposes hosts to severe infection with both Streptococcus pneumoniae and Staphylococcus aureus. Despite its importance, the mechanistic nature of the interaction between influenza and pneumococci, its dependence on the timing and sequence of infections as well as the clinical and epidemiological consequences remain unclear. We explore an immune-mediated model of the viral–bacterial interaction that quantifies the timing and the intensity of the interaction. Taking advantage of the wealth of knowledge gained from animal models, and the quantitative understanding of the kinetics of pathogen-specific immunological dynamics, we formulate a mathematical model for immune-mediated interaction between influenza virus and S. pneumoniae in the lungs. We use the model to examine the pathogenic effect of inoculum size and timing of pneumococcal invasion relative to influenza infection, as well as the efficacy of antivirals in preventing severe pneumococcal disease. We find that our model is able to capture the key features of the interaction observed in animal experiments. The model predicts that introduction of pneumococcal bacteria during a 4–6 day window following influenza infection results in invasive pneumonia at significantly lower inoculum size than in hosts not infected with influenza. Furthermore, we find that antiviral treatment administered later than 4 days after influenza infection was not able to prevent invasive pneumococcal disease. This work provides a quantitative framework to study interactions between influenza and pneumococci and has the potential to accurately quantify the interactions. Such quantitative understanding can form a basis for effective clinical care, public health policies and pandemic preparedness.     

Strain amplification in bone mechanobiology: a computational investigation of the in vivo mechanics of osteocytes

The osteocyte is believed to act as the main sensor of mechanical stimulus in bone, controlling signalling for bone growth and resorption in response to changes in the mechanical demands placed on our bones throughout life. However, the precise mechanical stimuli that bone cells experience in vivo are not yet fully understood. The objective of this study is to use computational methods to predict the loading conditions experienced by osteocytes during normal physiological activities. Confocal imaging of the lacunar–canalicular network was used to develop three-dimensional finite element models of osteocytes, including their cell body, and the surrounding pericellular matrix (PCM) and extracellular matrix (ECM). We investigated the role of the PCM and ECM projections for amplifying mechanical stimulation to the cells. At loading levels, representing vigorous physiological activity (3000 µɛ), our results provide direct evidence that (i) confocal image-derived models predict 350–400% greater strain amplification experienced by osteocytes compared with an idealized cell, (ii) the PCM increases the cell volume stimulated more than 3500 µɛ by 4–10% and (iii) ECM projections amplify strain to the cell by approximately 50–420%. These are the first confocal image-derived computational models to predict osteocyte strain in vivo and provide an insight into the mechanobiology of the osteocyte.