Stage-structured transmission of phocine distemper virus in the Dutch 2002 outbreak

Heterogeneities in transmission among hosts can be very important in shaping infectious disease dynamics. In mammals with strong social organization, such heterogeneities are often structured by functional stage: juveniles, subadults and adults. We investigate the importance of such stage-related heterogeneities in shaping the 2002 phocine distemper virus (PDV) outbreak in the Dutch Wadden Sea, when more than 40 per cent of the harbour seals were killed. We do this by comparing the statistical fit of a hierarchy of models with varying transmission complexity: homogeneous versus heterogeneous mixing and density- versus frequency-dependent transmission. We use the stranding data as a proxy for incidence and use Poisson likelihoods to estimate the ‘who acquires infection from whom’ (WAIFW) matrix. Statistically, the model with strong heterogeneous mixing and density-dependent transmission was found to best describe the transmission dynamics. However, patterns of incidence support a model of frequency-dependent transmission among adults and juveniles. Based on the maximum-likelihood WAIFW matrix estimates, we use the next-generation formalism to calculate an R₀ between 2 and 2.5 for the Dutch 2002 PDV epidemic.     

Inferring Epidemiological Dynamics with Bayesian Coalescent Inference: The Merits of Deterministic and Stochastic Models

Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe epidemic progression. These include inference approaches derived from Kingman’s coalescent theory. Here, we use recently described coalescent theory for epidemic dynamics to develop stochastic and deterministic coalescent susceptible–infected–removed (SIR) tree priors. We implement these in a Bayesian phylogenetic inference framework to permit joint estimation of SIR epidemic parameters and the sample genealogy. We assess the performance of the two coalescent models and also juxtapose results obtained with a recently published birth–death-sampling model for epidemic inference. Comparisons are made by analyzing sets of genealogies simulated under precisely known epidemiological parameters. Additionally, we analyze influenza A (H1N1) sequence data sampled in the Canterbury region of New Zealand and HIV-1 sequence data obtained from known United Kingdom infection clusters. We show that both coalescent SIR models are effective at estimating epidemiological parameters from data with large fundamental reproductive number R₀ and large population size S₀. Furthermore, we find that the stochastic variant generally outperforms its deterministic counterpart in terms of error, bias, and highest posterior density coverage, particularly for smaller R₀ and S₀. However, each of these inference models is shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with R₀ close to one or with small effective susceptible populations.     

Modeling and Statistical Analysis of the Spatio-Temporal Patterns of Seasonal Influenza in Israel

Background

Seasonal influenza outbreaks are a serious burden for public health worldwide and cause morbidity to millions of people each year. In the temperate zone influenza is predominantly seasonal, with epidemics occurring every winter, but the severity of the outbreaks vary substantially between years. In this study we used a highly detailed database, which gave us both temporal and spatial information of influenza dynamics in Israel in the years 1998–2009. We use a discrete-time stochastic epidemic SIR model to find estimates and credible confidence intervals of key epidemiological parameters.

Findings

Despite the biological complexity of the disease we found that a simple SIR-type model can be fitted successfully to the seasonal influenza data. This was true at both the national levels and at the scale of single cities.The effective reproductive number R_e varies between the different years both nationally and among Israeli cities. However, we did not find differences in R_e between different Israeli cities within a year. R _e was positively correlated to the strength of the spatial synchronization in Israel. For those years in which the disease was more “infectious”, then outbreaks in different cities tended to occur with smaller time lags. Our spatial analysis demonstrates that both the timing and the strength of the outbreak within a year are highly synchronized between the Israeli cities. We extend the spatial analysis to demonstrate the existence of high synchrony between Israeli and French influenza outbreaks.

Conclusions

The data analysis combined with mathematical modeling provided a better understanding of the spatio-temporal and synchronization dynamics of influenza in Israel and between Israel and France. Altogether, we show that despite major differences in demography and weather conditions intra-annual influenza epidemics are tightly synchronized in both their timing and magnitude, while they may vary greatly between years. The predominance of a similar main strain of influenza, combined with population mixing serve to enhance local and global influenza synchronization within an influenza season.     

Antiviral effect of flavonol glycosides isolated from the leaf of Zanthoxylum piperitum on influenza virus

The ethanol extract of Zanthoxylum piperitum (L.) DC. showed in vitro antiviral activity against influenza A virus. Three flavonol glycosides were isolated from the EtOAc fraction of Z. piperitum leaf by means of activity-guided chromatographic separation. Structures of isolated compounds were identified as quercetin 3-O-β-D-galactopyranoside (1), quercetin 3-O-α-L-rhamnopyranoside (2), kaempferol 3-O-α-L-rhamnopyranoside (3) by comparing their spectral data with literature values. The anti-influenza viral activity of isolates was evaluated using a plaque reduction assay against influenza A/NWS/33 (H1N1) virus. The compounds also were subjected to neuraminidase inhibition assay in influenza A/NWS/33 virus. Compounds 1–3 exhibited antiviral activity against an influenza A virus in vitro, and inhibited the neuraminidase activity at relatively high concentrations.     

Improving data interpretation of fragmentary data-sets on invertebrate dispersal with permutation tests

Biological data often tend to have heterogeneous, discontinuous non-normal distributions. Statistical non-parametric tests, like the Mann–Whitney U-test or the extension for more than two samples, the Kruskal–Wallis test, are often used in these cases, although they assume certain preconditions which are often ignored. We developed a permutation test procedure that uses the ratio of the interquartile distances and the median differences of the original non-classified data to assess the properties of the real distribution more appropriately than the classical methods. We used this test on a heterogeneous, skewed biological data set on invertebrate dispersal and showed how different the reactions of the Kruskal–Wallis test and the permutation approach are. We then evaluated the new testing procedure with reproducible data that were generated from the normal distribution. Here, we tested the influence of four different experimental trials on the new testing procedure in comparison to the Kruskal–Wallis test. These trials showed the impact of data that were varying in terms of (a) negative correlation between variances and means of the samples, (b) changing variances that were not correlated with the means of the samples, (c) constant variances and means, but different sample sizes and in trials (d) we evaluated the testing power of the new procedure. Due to the different test statistics, the permutation test reacted more sensibly to the data presented in trials (a) and c) and non-uniformly in trial (b). In the evaluation of the testing power, no significant differences between the Kruskal–Wallis test and the new permutation testing procedure could be detected. We consider this test to be an alternative for working on heterogeneous data where the preconditions of the classical non-parametric tests are not met.     

A mathematical model of avian influenza with half-saturated incidence

The widespread impact of avian influenza viruses not only poses risks to birds, but also to humans. The viruses spread from birds to humans and from human to human In addition, mutation in the primary strain will increase the infectiousness of avian influenza. We developed a mathematical model of avian influenza for both bird and human populations. The effect of half-saturated incidence on transmission dynamics of the disease is investigated. The half-saturation constants determine the levels at which birds and humans contract avian influenza. To prevent the spread of avian influenza, the associated half-saturation constants must be increased, especially the half-saturation constant H _m for humans with mutant strain. The quantity H _m plays an essential role in determining the basic reproduction number of this model. Furthermore, by decreasing the rate β _m at which human-to-human mutant influenza is contracted, an outbreak can be controlled more effectively. To combat the outbreak, we propose both pharmaceutical (vaccination) and non-pharmaceutical (personal protection and isolation) control methods to reduce the transmission of avian influenza. Vaccination and personal protection will decrease β _m, while isolation will increase H _m. Numerical simulations demonstrate that all proposed control strategies will lead to disease eradication; however, if we only employ vaccination, it will require slightly longer to eradicate the disease than only applying non-pharmaceutical or a combination of pharmaceutical and non-pharmaceutical control methods. In conclusion, it is important to adopt a combination of control methods to fight an avian influenza outbreak.     

Characterizing the epidemiology of the 2009 influenza A/H1N1 pandemic in Mexico

Background

Mexico''s local and national authorities initiated an intense public health response during the early stages of the 2009 A/H1N1 pandemic. In this study we analyzed the epidemiological patterns of the pandemic during April–December 2009 in Mexico and evaluated the impact of nonmedical interventions, school cycles, and demographic factors on influenza transmission.

Methods and Findings

We used influenza surveillance data compiled by the Mexican Institute for Social Security, representing 40% of the population, to study patterns in influenza-like illness (ILIs) hospitalizations, deaths, and case-fatality rate by pandemic wave and geographical region. We also estimated the reproduction number (R) on the basis of the growth rate of daily cases, and used a transmission model to evaluate the effectiveness of mitigation strategies initiated during the spring pandemic wave. A total of 117,626 ILI cases were identified during April–December 2009, of which 30.6% were tested for influenza, and 23.3% were positive for the influenza A/H1N1 pandemic virus. A three-wave pandemic profile was identified, with an initial wave in April–May (Mexico City area), a second wave in June–July (southeastern states), and a geographically widespread third wave in August–December. The median age of laboratory confirmed ILI cases was ∼18 years overall and increased to ∼31 years during autumn (p<0.0001). The case-fatality ratio among ILI cases was 1.2% overall, and highest (5.5%) among people over 60 years. The regional R estimates were 1.8–2.1, 1.6–1.9, and 1.2–1.3 for the spring, summer, and fall waves, respectively. We estimate that the 18-day period of mandatory school closures and other social distancing measures implemented in the greater Mexico City area was associated with a 29%–37% reduction in influenza transmission in spring 2009. In addition, an increase in R was observed in late May and early June in the southeast states, after mandatory school suspension resumed and before summer vacation started. State-specific fall pandemic waves began 2–5 weeks after school reopened for the fall term, coinciding with an age shift in influenza cases.

Conclusions

We documented three spatially heterogeneous waves of the 2009 A/H1N1 pandemic virus in Mexico, which were characterized by a relatively young age distribution of cases. Our study highlights the importance of school cycles on the transmission dynamics of this pandemic influenza strain and suggests that school closure and other mitigation measures could be useful to mitigate future influenza pandemics. Please see later in the article for the Editors'' Summary     

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.     

Modeling influenza seasonality in the tropics and subtropics

Climate drivers such as humidity and temperature may play a key role in influenza seasonal transmission dynamics. Such a relationship has been well defined for temperate regions. However, to date no models capable of capturing the diverse seasonal pattern in tropical and subtropical climates exist. In addition, multiple influenza viruses could cocirculate and shape epidemic dynamics. Here we construct seven mechanistic epidemic models to test the effect of two major climate drivers (humidity and temperature) and multi-strain co-circulation on influenza transmission in Hong Kong, an influenza epidemic center located in the subtropics. Based on model fit to long-term influenza surveillance data from 1998 to 2018, we found that a simple model incorporating the effect of both humidity and temperature best recreated the influenza epidemic patterns observed in Hong Kong. The model quantifies a bimodal effect of absolute humidity on influenza transmission where both low and very high humidity levels facilitate transmission quadratically; the model also quantifies the monotonic but nonlinear relationship with temperature. In addition, model results suggest that, at the population level, a shorter immunity period can approximate the co-circulation of influenza virus (sub)types. The basic reproductive number R₀ estimated by the best-fit model is also consistent with laboratory influenza survival and transmission studies under various combinations of humidity and temperature levels. Overall, our study has developed a simple mechanistic model capable of quantifying the impact of climate drivers on influenza transmission in (sub)tropical regions. This model can be applied to improve influenza forecasting in the (sub)tropics in the future.     

Generation of Influenza Virus from Avian Cells Infected by Salmonella Carrying the Viral Genome

Domestic poultry serve as intermediates for transmission of influenza A virus from the wild aquatic bird reservoir to humans, resulting in influenza outbreaks in poultry and potential epidemics/pandemics among human beings. To combat emerging avian influenza virus, an inexpensive, heat-stable, and orally administered influenza vaccine would be useful to vaccinate large commercial poultry flocks and even migratory birds. Our hypothesized vaccine is a recombinant attenuated bacterial strain able to mediate production of attenuated influenza virus in vivo to induce protective immunity against influenza. Here we report the feasibility and technical limitations toward such an ideal vaccine based on our exploratory study. Five 8-unit plasmids carrying a chloramphenicol resistance gene or free of an antibiotic resistance marker were constructed. Influenza virus was successfully generated in avian cells transfected by each of the plasmids. The Salmonella carrier was engineered to allow stable maintenance and conditional release of the 8-unit plasmid into the avian cells for recovery of influenza virus. Influenza A virus up to 10⁷ 50% tissue culture infective doses (TCID₅₀)/ml were recovered from 11 out of 26 co-cultures of chicken embryonic fibroblasts (CEF) and Madin-Darby canine kidney (MDCK) cells upon infection by the recombinant Salmonella carrying the 8-unit plasmid. Our data prove that a bacterial carrier can mediate generation of influenza virus by delivering its DNA cargoes into permissive host cells. Although we have made progress in developing this Salmonella influenza virus vaccine delivery system, further improvements are necessary to achieve efficient virus production, especially in vivo.     

Estimating transmission probability in schools for the 2009 H1N1 influenza pandemic in Italy

Background

Epidemic models are being extensively used to understand the main pathways of spread of infectious diseases, and thus to assess control methods. Schools are well known to represent hot spots for epidemic spread; hence, understanding typical patterns of infection transmission within schools is crucial for designing adequate control strategies. The attention that was given to the 2009 A/H1N1pdm09 flu pandemic has made it possible to collect detailed data on the occurrence of influenza-like illness (ILI) symptoms in two primary schools of Trento, Italy.

Results

The data collected in the two schools were used to calibrate a discrete-time SIR model, which was designed to estimate the probabilities of influenza transmission within the classes, grades and schools using Markov Chain Monte Carlo (MCMC) methods. We found that the virus was mainly transmitted within class, with lower levels of transmission between students in the same grade and even lower, though not significantly so, among different grades within the schools. We estimated median values of R ₀ from the epidemic curves in the two schools of 1.16 and 1.40; on the other hand, we estimated the average number of students infected by the first school case to be 0.85 and 1.09 in the two schools.

Conclusions

The discrepancy between the values of R ₀ estimated from the epidemic curve or from the within-school transmission probabilities suggests that household and community transmission played an important role in sustaining the school epidemics. The high probability of infection between students in the same class confirms that targeting within-class transmission is key to controlling the spread of influenza in school settings and, as a consequence, in the general population.

     

The effects of human movement on the persistence of vector-borne diseases

With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of transmission. We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian models that mimic human commuting behavior and (ii) Eulerian models that mimic human migration. We determine the basic reproduction number R₀ for both modeling approaches. We show that for both approaches that if the disease-free equilibrium is stable (R₀<1) then it is globally stable and if the disease-free equilibrium is unstable (R₀>1) then there exists a unique positive (endemic) equilibrium that is globally stable among positive solutions. Finally, we prove in general that Lagrangian and Eulerian modeling approaches are not equivalent. The modeling approaches presented provide a framework to explore spatial vector-borne disease dynamics and control in heterogeneous environments. As an example, we consider two patches in which the disease dies out in both patches when there is no movement between them. Numerical simulations demonstrate that the disease becomes endemic in both patches when humans move between the two patches.     

Four new cytotoxic oligosaccharidic derivatives of 12-oleanene from Lysimachia heterogenea Klatt

Cytotoxicity-guided phytochemical analysis on the extract of Lysimachia heterogenea Klatt led to the isolation of 3β,16β-12-oleanene-3,16,23,28-tetrol (1) and its four new oligosaccharidic derivatives heterogenosides A, B, C, and D (2–5). Their structural elucidation was mainly based on NMR and mass spectral data. The time course experimental results indicated that unlike the likely lysis activity of heterogenosides B–D, heterogenoside A showed a significantly time-dependent cytotoxicity.     

In vitro inhibition of mumps virus by retinoids

Background

Foot-and-mouth disease virus (FMDV) initiates infection via recognition of one of at least four cell-surface integrin molecules α_vβ₁, α_vβ₃, α_vβ₆, or α_vβ₈ by a highly conserved Arg-Gly-Asp (RGD) amino acid sequence motif located in the G-H loop of VP1. Within the animal host, the α_vβ₆ interaction is believed to be the most relevant. Sub-neutralizing levels of soluble secreted α_vβ₆ (ssα_vβ₆) was used as a selective pressure during passages in vitro to explore the plasticity of that interaction.

Results

Genetically stable soluble integrin resistant (SIR) FMDV mutants derived from A24 Cruzeiro were selected after just 3 passages in cell culture in the presence of sub-neutralizing levels of ssα_vβ₆. SIR mutants were characterized by: replication on selective cell lines, plaque morphology, relative sensitivity to ssα_vβ₆ neutralization, relative ability to utilize α_vβ₆ for infection, as well as sequence and structural changes. All SIR mutants maintained an affinity for α_vβ₆. Some developed the ability to attach to cells expressing heparan sulfate (HS) proteoglycan, while others appear to have developed affinity for a still unknown third receptor. Two classes of SIR mutants were selected that were highly or moderately resistant to neutralization by ssα_vβ₆. Highly resistant mutants displayed a G145D substitution (RGD to RDD), while moderately resistant viruses exhibited a L150P/R substitution at the conserved RGD + 4 position. VP1 G-H loop homology models for the A-type SIR mutants illustrated potential structural changes within the integrin-binding motif by these 2 groups of mutations. Treatment of O1 Campos with ssα_vβ₆ resulted in 3 SIR mutants with a positively charged VP3 mutation allowing for HS binding.

Conclusions

These findings illustrate how FMDV particles rapidly gain resistance to soluble receptor prophylactic measures in vitro. Two different serotypes developed distinct capsid mutations to circumvent the presence of sub-neutralizing levels of the soluble cognate receptor, all of which resulted in a modified receptor tropism that expanded the cell types susceptible to FMDV. The identification of some of these adaptive mutations in known FMDV isolates suggests these findings have implications beyond the cell culture system explored in these studies.     

Theory of early warning signals of disease emergenceand leading indicators of elimination

Anticipating infectious disease emergence and documenting progress in disease elimination are important applications for the theory of critical transitions. A key problem is the development of theory relating the dynamical processes of transmission to observable phenomena. In this paper, we consider compartmental susceptible–infectious–susceptible (SIS) and susceptible–infectious–recovered (SIR) models that are slowly forced through a critical transition. We derive expressions for the behavior of several candidate indicators, including the autocorrelation coefficient, variance, coefficient of variation, and power spectra of SIS and SIR epidemics during the approach to emergence or elimination. We validated these expressions using individual-based simulations. We further showed that moving-window estimates of these quantities may be used for anticipating critical transitions in infectious disease systems. Although leading indicators of elimination were highly predictive, we found the approach to emergence to be much more difficult to detect. It is hoped that these results, which show the anticipation of critical transitions in infectious disease systems to be theoretically possible, may be used to guide the construction of online algorithms for processing surveillance data.     

Coupling effects on turning points of infectious diseases epidemics in scale-free networks

Background

Pandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network. The Susceptible-Infective-Recovered (SIR) model describes spreading phenomena using two spreading factors; contagiousness (β) and recovery rate (γ). Some network models are trying to reflect the social network, but the real structure is difficult to uncover.

Methods

We have developed a spreading phenomenon simulator that can input the epidemic parameters and network parameters and performed the experiment of disease propagation. The simulation result was analyzed to construct a new marker VRTP distribution. We also induced the VRTP formula for three of the network mathematical models.

Results

We suggest new marker VRTP (value of recovered on turning point) to describe the coupling between the SIR spreading and the Scale-free (SF) network and observe the aspects of the coupling effects with the various of spreading and network parameters. We also derive the analytic formulation of VRTP in the fully mixed model, the configuration model, and the degree-based model respectively in the mathematical function form for the insights on the relationship between experimental simulation and theoretical consideration.

Conclusions

We discover the coupling effect between SIR spreading and SF network through devising novel marker VRTP which reflects the shifting effect and relates to entropy.

     

Physiological analysis on oscillatory behavior of glucose-insulin regulation by model with delays

Despite temporally forced transmission driving many infectious diseases, analytical insight into its role when combined with stochastic disease processes and non-linear transmission has received little attention. During disease outbreaks, however, the absence of saturation effects early on in well-mixed populations mean that epidemic models may be linearised and we can calculate outbreak properties, including the effects of temporal forcing on fade-out, disease emergence and system dynamics, via analysis of the associated master equations. The approach is illustrated for the unforced and forced SIR and SEIR epidemic models. We demonstrate that in unforced models, initial conditions (and any uncertainty therein) play a stronger role in driving outbreak properties than the basic reproduction number R₀, while the same properties are highly sensitive to small amplitude temporal forcing, particularly when R₀ is small. Although illustrated for the SIR and SEIR models, the master equation framework may be applied to more realistic models, although analytical intractability scales rapidly with increasing system dimensionality. One application of these methods is obtaining a better understanding of the rate at which vector-borne and waterborne infectious diseases invade new regions given variability in environmental drivers, a particularly important question when addressing potential shifts in the global distribution and intensity of infectious diseases under climate change.     

Simulations of cross-amyloid aggregation of amyloid-β and islet amyloid polypeptide fragments

Amyloid-β (Aβ) and islet amyloid polypeptide (IAPP) are small peptides, classified as amyloids, that have the potential to self-assemble and form cytotoxic species, such as small soluble oligomers and large insoluble fibrils. The formation of Aβ aggregates facilitates the progression of Alzheimer’s disease (AD), while IAPP aggregates induce pancreatic β-cell apoptosis, leading to exacerbation of type 2 diabetes (T2D). Cross-amyloid interactions between Aβ and IAPP have been described both in vivo and in vitro, implying the role of Aβ or IAPP as modulators of cytotoxic self-aggregation of each species, and suggesting that Aβ-IAPP interactions are a potential molecular link between AD and T2D. Using molecular dynamics (MD) simulations, “hotspot” regions of the two peptides were studied to understand the formation of hexamers in a heterogeneous and homogeneous peptide-containing environment. Systems of only Aβ_(16–22) peptides formed antiparallel, β-barrel-like structures, while systems of only IAPP_(20–29) peptides formed stacked, parallel β-sheets and had relatively unstable aggregation structures after 2 μs of simulation time. Systems containing both Aβ and IAPP (1:1 ratio) hexamers showed antiparallel, β-barrel-like structures, with an interdigitated arrangement of Aβ_(16–22) and IAPP_(20–29). These β-barrel structures have features of cytotoxic amyloid species identified in previous literature. Ultimately, this work seeks to provide atomistic insight into both the mechanism behind cross-amyloid interactions and structural morphologies of these toxic amyloid species.     

Interaction of fast and slow dynamics in endocrine control systems with an application to β-cell dynamics

Endocrine dynamics spans a wide range of time scales, from rapid responses to physiological challenges to with slow responses that adapt the system to the demands placed on it. We outline a non-linear averaging procedure to extract the slower dynamics in a way that accounts properly for the non-linear dynamics of the faster time scale and is applicable to a hierarchy of more than two time scales, although we restrict our discussion to two scales for the sake of clarity. The procedure is exact if the slow time scale is infinitely slow (the dimensionless ε-quantity is the period of the fast time scale fluctuation times an upper bound to the slow time scale rate of change). However, even for an imperfect separation of time scales we find that this construction provides an excellent approximation for the slow-time dynamics at considerably reduced computational cost. Besides the computation advantage, the averaged equation provided a qualitative insight into the interaction of the time scales. We demonstrate the procedure and its advantages by applying the theory to the model described by Toli? et al. [I.M. Toli?, E. Mosekilde, J. Sturis, Modeling the insulin–glucose feedback system: the significance of pulsatile insulin secretion, J. Theor. Biol. 207 (2000) 361–375.] for ultradian dynamics of the glucose–insulin homeostasis feedback system, extended to include β-cell dynamics. We find that the dynamics of the β-cell mass are dependent not only on the glycemic load (amount of glucose administered to the system), but also on the way this load is applied (i.e. three meals daily versus constant infusion), effects that are lost in the inappropriate methods used by the earlier authors. Furthermore, we find that the loss of the protection against apoptosis conferred by insulin that occurs at elevated levels of insulin has a functional role in keeping the β-cell mass in check without compromising regulatory function. We also find that replenishment of β-cells from a rapidly proliferating pool of cells, as opposed to the slow turn-over which characterises fully differentiated β-cells, is essential to the prevention of type 1 diabetes.     

Quantifying the Routes of Transmission for Pandemic Influenza

Motivated by the desire to assess nonpharmaceutical interventions for pandemic influenza, we seek in this study to quantify the routes of transmission for this disease. We construct a mathematical model of aerosol (i.e., droplet-nuclei) and contact transmission of influenza within a household containing one infected. An analysis of this model in conjunction with influenza and rhinovirus data suggests that aerosol transmission is far more dominant than contact transmission for influenza. We also consider a separate model of a close expiratory event, and find that a close cough is unlikely (≈1% probability) to generate traditional droplet transmission (i.e., direct deposition on the mucous membranes), although a close, unprotected and horizontally-directed sneeze is potent enough to cause droplet transmission. There are insufficient data on the frequency of close expiratory events to assess the relative importance of aerosol transmission and droplet transmission, and it is prudent to leave open the possibility that droplet transmission is important until proven otherwise. However, the rarity of close, unprotected and horizontally-directed sneezes—coupled with the evidence of significant aerosol and contact transmission for rhinovirus and our comparison of hazard rates for rhinovirus and influenza—leads us to suspect that aerosol transmission is the dominant mode of transmission for influenza.