Transmission Dynamics of an Influenza Model with Vaccination and Antiviral Treatment

Vaccination and antiviral treatment are two important prevention and control measures for the spread of influenza. However, the benefit of antiviral use can be compromised if drug-resistant strains arise. In this paper, we develop a mathematical model to explore the impact of vaccination and antiviral treatment on the transmission dynamics of influenza. The model includes both drug-sensitive and resistant strains. Analytical results of the model show that the quantities ℛ _SC and ℛ _RC , which represent the control reproduction numbers of the sensitive and resistant strains, respectively, provide threshold conditions that determine the competitive outcomes of the two strains. These threshold conditions can be used to gain important insights into the effect of vaccination and treatment on the prevention and control of influenza. Numerical simulations are also conducted to confirm and extend the analytic results. The findings imply that higher levels of treatment may lead to an increase of epidemic size, and the extent to which this occurs depends on other factors such as the rates of vaccination and resistance development. This suggests that antiviral treatment should be implemented appropriately.     

Population-Based Hospitalization Burden of Influenza A Virus Subtypes and Antigenic Drift Variants in Children in Hong Kong (2004–2011)

Objectives

We aim to document and analyze influenza hospitalization burden in light of antigenic changes in circulating influenza viruses in Hong Kong.

Methods

The pediatric age-specific rates of influenza A hospitalization in Hong Kong for 2004–2011 which encompassed the emergence of H1N1pdm09 were extrapolated from admissions to 2 hospitals that together catered for 72.5% of all pediatric admissions on Hong Kong Island. Influenza A was detected by immunofluorescence, culture and/or PCR on nasopharyngeal aspirates.

Results

Influenza A caused high rates of hospitalization in children with year to year fluctuations. The highest hospitalization burden was seen with H1N1pdm09 in 2009. Additional factors affecting hospitalization were the proportion of viral circulation among different subtypes, and antigenic drifts. Taking these into effect, an H3N2 dominated year was not always associated with more hospitalizations than a ‘seasonal’ H1N1 year. Hospitalization burden was higher in seasons when drifted viruses of H1N1 or H3N2 dominated. No hospitalization was documented in infants <6 months of age during years when an undrifted virus circulated (2006 for H1N1 and 2008 for H3N2) but significant hospitalization was observed with a drifted or shifted virus (2004, 2005, 2007 and 2010 for H3N2, and 2009 for H1N1pdm09).

Conclusions

We documented a consistently high pediatric hospitalization burden of influenza A. Knowledge of antigenic changes and their proportion of circulation aids in the interpretation of impact of the subtypes. Year-to-year variation in hospitalization rates in young infants appeared to correlate with antigenic variation, lending support to the role of protection from maternal antibodies.     

Chaos and Peak-to-Peak Dynamics in a Plankton–Fish Model

A plankton–fish model, comprising phosphorus, algae, zooplankton, and young fish, with light intensity and water temperature varying periodically with the seasons, is analyzed in this paper. For realistic values of the parameters the model behaves chaotically, but its dynamics within the strange attractor can be described by a few one-dimensional maps that allow one to forecast the next yearly peak of plankton or fish from the last peaks. This property is an unambiguous mark of a special form of chaos. Unfortunately, the estimate of such peak-to-peak maps from field data is possible only if plankton or young fish biomass has been sampled accurately and frequently for a paramount number of years. In conclusion, the analysis shows that it might be that plankton dynamics are characterized by an interesting and peculiar form of chaos, but that inferences from recorded data on the existence of these forms of chaos are premature.     

Influenza A H1N1 Pandemic Strain Evolution – Divergence and the Potential for Antigenic Drift Variants

The emergence of a novel A(H1N1) strain in 2009 was the first influenza pandemic of the genomic age, and unprecedented surveillance of the virus provides the opportunity to better understand the evolution of influenza. We examined changes in the nucleotide coding regions and the amino acid sequences of the hemagglutinin (HA), neuraminidase (NA), and nucleoprotein (NP) segments of the A(H1N1)pdm09 strain using publicly available data. We calculated the nucleotide and amino acid hamming distance from the vaccine strain A/California/07/2009 for each sequence. We also estimated P_epitope–a measure of antigenic diversity based on changes in the epitope regions–for each isolate. Finally, we compared our results to A(H3N2) strains collected over the same period. Our analysis found that the mean hamming distance for the HA protein of the A(H1N1)pdm09 strain increased from 3.6 (standard deviation [SD]: 1.3) in 2009 to 11.7 (SD: 1.0) in 2013, while the mean hamming distance in the coding region increased from 7.4 (SD: 2.2) in 2009 to 28.3 (SD: 2.1) in 2013. These trends are broadly similar to the rate of mutation in H3N2 over the same time period. However, in contrast to H3N2 strains, the rate of mutation accumulation has slowed in recent years. Our results are notable because, over the course of the study, mutation rates in H3N2 similar to that seen with A(H1N1)pdm09 led to the emergence of two antigenic drift variants. However, while there has been an H1N1 epidemic in North America this season, evidence to date indicates the vaccine is still effective, suggesting the epidemic is not due to the emergence of an antigenic drift variant. Our results suggest that more research is needed to understand how viral mutations are related to vaccine effectiveness so that future vaccine choices and development can be more predictive.     

Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics

Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however, so far only with flat hyper-surfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein–Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae.     

Dynamics of a Producer–Grazer Model Incorporating the Effects of Excess Food Nutrient Content on Grazer’s Growth

Modeling under the framework of ecological stoichiometric allows the investigation of the effects of food quality on food web population dynamics. Recent discoveries in ecological stoichiometry suggest that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). This phenomenon is known as the “stoichiometric knife edge.” While previous models have captured this phenomenon, they do not explicitly track P in the producer or in the media that supports the producer, which brings questions to the validity of their predictions. Here, we extend a Lotka–Volterra-type stoichiometric model by mechanistically deriving and tracking P in the producer and free P in the environment in order to investigate the growth response of Daphnia to algae of varying P:C ratios. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, lead to quantitative different predictions than previous models that neglect to track free nutrients. The full model shows that the fate of the grazer population can be very sensitive to excess nutrient concentrations. Dynamical free nutrient pool seems to induce extreme grazer population density changes when total nutrient is in an intermediate range.     

The Structural Dynamics of the Flavivirus Fusion Peptide–Membrane Interaction

Membrane fusion is a crucial step in flavivirus infections and a potential target for antiviral strategies. Lipids and proteins play cooperative roles in the fusion process, which is triggered by the acidic pH inside the endosome. This acidic environment induces many changes in glycoprotein conformation and allows the action of a highly conserved hydrophobic sequence, the fusion peptide (FP). Despite the large volume of information available on the virus-triggered fusion process, little is known regarding the mechanisms behind flavivirus–cell membrane fusion. Here, we evaluated the contribution of a natural single amino acid difference on two flavivirus FPs, FLA_G (⁹⁸DRGWGNGCGLFGK¹¹⁰) and FLA_H (⁹⁸DRGWGNHCGLFGK¹¹⁰), and investigated the role of the charge of the target membrane on the fusion process. We used an in silico approach to simulate the interaction of the FPs with a lipid bilayer in a complementary way and used spectroscopic approaches to collect conformation information. We found that both peptides interact with neutral and anionic micelles, and molecular dynamics (MD) simulations showed the interaction of the FPs with the lipid bilayer. The participation of the indole ring of Trp appeared to be important for the anchoring of both peptides in the membrane model, as indicated by MD simulations and spectroscopic analyses. Mild differences between FLA_G and FLA_H were observed according to the pH and the charge of the target membrane model. The MD simulations of the membrane showed that both peptides adopted a bend structure, and an interaction between the aromatic residues was strongly suggested, which was also observed by circular dichroism in the presence of micelles. As the FPs of viral fusion proteins play a key role in the mechanism of viral fusion, understanding the interactions between peptides and membranes is crucial for medical science and biology and may contribute to the design of new antiviral drugs.     

Investigation of Lysozyme–Antilysozyme Interactions in a Model Tetrahymena–EscherichiaCommunity

Lysozyme and antilysozyme activities present in a wide range of microorganisms determine the so-called lysozyme–antilysozyme system of hydrobionts, which greatly contribute to the formation of aquatic biocenoses. However, the mechanism of the functioning of this system in natural freshwater communities remains obscure. The experimental investigation of lysozyme–antilysozyme interactions in a model Tetrahymena–Escherichiacommunity showed that the antilysozyme activity of Escherichia colileads to incomplete phagocytosis, thus enhancing bacterial survival in a mixed culture with infusoria. The selection and reproduction of bacterial cells resistant to grazing by infusoria determine the character of host–parasite interactions and allow bacteria to survive. It was demonstrated that the antilysozyme activity of microorganisms, which is responsible for bacterial persistency in natural biocenoses, is involved in the maintenance of protozoa–bacteria communities in bodies of water.     

Spatial,Temporal and Genetic Dynamics Characteristics of Influenza B Viruses in China, 1973–2018

Annual influenza B virus epidemics and outbreaks cause severe influenza diseases in humans and pose a threat to public health. China is an important epidemic area of influenza B viruses. However, the spatial, temporal transmission pathways and the demography history of influenza B viruses in China remain unknown. We collected the haemagglutinin gene sequences sampled of influenza B virus in China between 1973 and 2018. A Bayesian Markov chain Monte Carlo phylogeographic discrete approach was used to infer the spatial and temporal phylodynamics of influenza B virus. The Bayesian phylogeographic analysis of influenza B viruses showed that the North subtropical and South subtropical zones are the origins of the Victoria and Yamagata lineage viruses, respectively. Furthermore, the South temperate and North subtropical zones acted as transition nodes in the Victoria lineage virus dispersion network and that the North subtropical and Mid subtropical zones acted as transition nodes in the Yamagata lineage virus dispersion network. Our findings contribute to the knowledge regarding the spatial and temporal patterns of influenza B virus outbreaks in China.     

Dynamics of plant–pollinator–robber systems

Plant–pollinator–robber systems are considered, where the plants and pollinators are mutualists, the plants and nectar robbers are in a parasitic relation, and the pollinators and nectar robbers consume a common limiting resource without interfering competition. My aim is to show a mechanism by which pollination–mutualism could persist when there exist nectar robbers. Through the dynamics of a plant–pollinator–robber model, it is shown that (i) when the plants alone (i.e., without pollination–mutualism) cannot provide sufficient resources for the robbers’ survival but pollination–mutualism can persist in the plant–pollinator system, the pollination–mutualism may lead to invasion of the robbers, while the pollinators will not be driven into extinction by the robbers’ invasion. (ii) When the plants alone cannot support the robbers’ survival but persistence of pollination–mutualism in the plant–pollinator system is density-dependent, the pollinators and robbers could coexist if the robbers’ efficiency in translating the plant–robber interactions into fitness is intermediate and the initial densities of the three species are in an appropriate region. (iii) When the plants alone can support the robbers’ survival, the pollinators will not be driven into extinction by the robbers if their efficiency in translating the plant–pollinator interactions into fitness is relatively larger than that of the robbers. The analysis leads to an explanation for the persistence of pollination–mutualism in the presence of nectar robbers in real situations.     

The Neuroprotective Effect of the Thr–Ser–Lys–Tyr Peptide in a Goldfish Mauthner Cell Model in vivo

The effects of the Thr–Ser–Lys–Tyr peptide, which was shown to display neuroprotective activity in cell cultures in vitro, were studied in the model of paired Mauthner cells of goldfish. It was found that intracerebral injections provided the peptide to be applied into the zone of the right Mauthner cell under the fourth ventricle of the hindbrain lead to a dose-dependent decrease in the number of spontaneous turns of the goldfish to the left. It was shown that this effect is not eliminated under long-lasting optokinetic stimulation when the fish instinctively follow stimuli with a low spatial frequency that are moving in the nasal-to-temporal direction. We used the method of three-dimensional reconstruction by serial histological sections to study the dendrite morphology of the Mauthner cells in control and experimental goldfish. It was found that optokinetic stimulation of control goldfish evokes the dystrophy of the ventral dendrite of the right Mauthner cell, which is the target of this type of stimulation. Conversely, the peptide stabilize the size of the ventral dendrite of the right Mauthner cell under stimulation. These data could be interpreted as evidence of the neuroprotective effect of the Thr–Ser–Lys–Tyr peptide in vivo.     

The Variance of Identity-by-Descent Sharing in the Wright–Fisher Model

Widespread sharing of long, identical-by-descent (IBD) genetic segments is a hallmark of populations that have experienced recent genetic drift. Detection of these IBD segments has recently become feasible, enabling a wide range of applications from phasing and imputation to demographic inference. Here, we study the distribution of IBD sharing in the Wright–Fisher model. Specifically, using coalescent theory, we calculate the variance of the total sharing between random pairs of individuals. We then investigate the cohort-averaged sharing: the average total sharing between one individual and the rest of the cohort. We find that for large cohorts, the cohort-averaged sharing is distributed approximately normally. Surprisingly, the variance of this distribution does not vanish even for large cohorts, implying the existence of “hypersharing” individuals. The presence of such individuals has consequences for the design of sequencing studies, since, if they are selected for whole-genome sequencing, a larger fraction of the cohort can be subsequently imputed. We calculate the expected gain in power of imputation by IBD and subsequently in power to detect an association, when individuals are either randomly selected or specifically chosen to be the hypersharing individuals. Using our framework, we also compute the variance of an estimator of the population size that is based on the mean IBD sharing and the variance in the sharing between inbred siblings. Finally, we study IBD sharing in an admixture pulse model and show that in the Ashkenazi Jewish population the admixture fraction is correlated with the cohort-averaged sharing.IN isolated populations, even purported unrelated individuals often share genetic material that is identical-by-descent (IBD). Traditionally, the term IBD sharing referred to coancestry at a single site (or autozygosity, in the case of a diploid individual) and was widely investigated as a measure of the degree of inbreeding in a population (Hartl and Clark 2006). Recent years have brought dramatic increases in the quantity and density of available genetic data and, together with new computational tools, these data have enabled the detection of IBD sharing of entire genomic segments (see, e.g., Purcell et al. 2007; Kong et al. 2008; Albrechtsen et al. 2009; Gusev et al. 2009; Browning and Browning 2011; Carr et al. 2011; Brown et al. 2012). The availability of IBD detection tools that are efficient enough to detect shared segments in large cohorts has resulted in numerous applications, from demographic inference (Davison et al. 2009; Palamara et al. 2012) and characterization of populations (Gusev et al. 2012a) to selection detection (Albrechtsen et al. 2010), relatedness detection and pedigree reconstruction (Huff et al. 2011; Kirkpatrick et al. 2011; Stevens et al. 2011; Henn et al. 2012), prioritization of individuals for sequencing (Gusev et al. 2012b), inference of HLA type (Setty et al. 2011), detection of haplotypes associated with a disease or a trait (Akula et al. 2011; Gusev et al. 2011; Browning and Thompson 2012), imputation (Uricchio et al. 2012), and phasing (Palin et al. 2011).Recently, some of us used coalescent theory to calculate several theoretical quantities of IBD sharing under a number of demographic histories. Then, shared segments were detected in real populations, and their demographic histories were inferred (Palamara et al. 2012). Here, we expand upon Palamara et al. (2012) to investigate additional aspects of the stochastic variation in IBD sharing. Specifically, we provide a precise calculation for the variance of the total sharing in the Wright–Fisher model, either between a random pair of individuals or between one individual and all others in the cohort.Understanding the variation in IBD sharing is an important theoretical characterization of the Wright–Fisher model, and additionally, it has several practical applications. For example, it can be used to calculate the variance of an estimator of the population size that is based on the sharing between random pairs. In a different domain, the variance in IBD sharing is needed to accurately assess strategies for sequencing study design, specifically, in prioritization of individuals to be sequenced. This is because imputation strategies use IBD sharing between sequenced individuals and genotyped, not-sequenced individuals to increase the number of effective sequences analyzed in the association study (Palin et al. 2011; Gusev et al. 2012b; Uricchio et al. 2012).In the remainder of this article, we first review the derivation of the mean fraction of the genome shared between two individuals (Palamara et al. 2012). We then calculate the variance of this quantity, using coalescent theory with recombination. We provide a number of approximations, one of which results in a surprisingly simple expression, which is then generalized to a variable population size and to the sharing of segments in a length range. We also numerically investigate the pairwise sharing distribution and provide an approximate fit. We then turn to the average total sharing between each individual and the entire cohort. We show that this quantity, which we term the cohort-averaged sharing, is approximately normally distributed, but is much wider than naively expected, implying the existence of hypersharing individuals. We consider several applications: the number of individuals needed to be sequenced to achieve a certain imputation power and the implications to disease mapping, inference of the population size based on the total sharing, and the variance of the sharing between siblings. We finally calculate the mean and the variance of the sharing in an admixture pulse model and show numerically that admixture results in a broader than expected cohort-averaged sharing. Therefore, large variance of the cohort-averaged sharing can indicate admixture. In the Ashkenazi Jewish population, we show that the cohort-averaged sharing is strongly anticorrelated with the fraction of European ancestry.     

Shedding of a Low Pathogenic Avian Influenza Virus in a Common Synanthropic Mammal – The Cottontail Rabbit

Background

Cottontails (Sylvilagus spp.) are common mammals throughout much of the U.S. and are often found in peridomestic settings, potentially interacting with livestock and poultry operations. If these animals are susceptible to avian influenza virus (AIV) infections and shed the virus in sufficient quantities they may pose a risk for movement of avian influenza viruses between wildlife and domestic animals in certain situations.

Methodology/Principal Findings

To assess the viral shedding potential of AIV in cottontails, we nasally inoculated fourteen cottontails with a low pathogenic AIV (H4N6). All inoculated cottontails shed relatively large quantities of viral RNA both nasally (≤10^6.94 PCR EID₅₀ equivalents/mL) and orally (≤10^5.09 PCR EID₅₀ equivalents/mL). However, oral shedding tended to decline more quickly than did nasal shedding. No animals showed any obvious signs of disease throughout the study. Evidence of a serological response was found in all infected rabbits at 22 days post infection in convalescent sera.

Conclusions/Significance

To our knowledge, cottontails have not been previously assessed for AIV shedding. However, it was obvious that they shed AIV RNA extensively via the nasal and oral routes. This is significant, as cottontails are widely distributed throughout the U.S. and elsewhere. These mammals are often found in highly peridomestic situations, such as farms, parks, and suburban neighborhoods, often becoming habituated to human activities. Thus, if infected these mammals could easily transport AIVs short distances.     

The Inhibitory Action of Several Bioantioxidants and Their Mixtures in a Model Hemoglobin–Hydrogen Peroxide–Luminol Chemiluminescent System

Determination of the antioxidant activities of various biological objects, for example, food, medicinal preparations, beverages, blood plasma, and other human biological fluids, is an important task for biomedical research. Chemiluminescent methods are widely used for this purpose. These methods are sensitive and rapid and make it possible to directly control the kinetics of inhibition of oxidation by an antioxidant. In the present work, a chemiluminescent model was used of free-radical oxidation of luminol, as initiated by a mixture of hemoglobin–hydrogen peroxide in an aqueous medium. The kinetics of the inhibitory effect of eight water-soluble bioantioxidants with different molecular structures and their binary mixtures was studied; the inhibition parameters of luminol oxidation by these antioxidants and their stoichiometric coefficients were determined. Features of the inhibition kinetics for glutathione are revealed. The synergistic and antagonistic effects of antioxidants in the mixtures were evaluated. The independence of chemiluminescence quenching by individual antioxidants was noted for the majority of the studied binary antioxidant mixtures, with more “active” antioxidants inhibiting oxidation earlier than less “active” ones. Mixtures of some antioxidants that strengthened or weakened each other upon interacting, thus exhibiting synergism or antagonism, were an exception.     

The Ideal Free Distribution in a Predator–Prey Model with Multifactor Taxis

Biophysics - The concept of an ideal free distribution (IFD) is analyzed for the predator–prey system in an inhomogeneous ring-shaped habitat. Diffusion–reaction–advection...     

Dynamics of Breakdown in a Low-Pressure Argon–Mercury Mixture in a Long Discharge Tube

Breakdown dynamics in the course of glow discharge ignition in a long discharge tube (80 cm in length and 25 mm in diameter) filled with argon at a pressure of 3–4 Torr and mercury vapor at room temperature was studied experimentally. Rectangular voltage pulses with amplitudes from 1 to 2.5 kV were applied to the tube anode, the cathode being grounded. Complex electrical and optical measurements of the breakdown dynamics were carried out. Breakdown begins with a primary discharge between the anode and the tube wall. In this stage, a jump in the anode current and a sharp decrease in the anode voltage are observed and prebreakdown ionization wave arises near the anode. The cathode current appears only after the ionization wave reaches the cathode. The wave propagation velocity was measured at different points along the tube axis. The wave emission spectrum contains Hg, Ar, and Ar⁺ lines. The intensities of these lines measured at a fixed point exhibit very different time behaviors. The effect of the tube shielding on the breakdown characteristics was examined. It is found that, at a sufficiently narrow gap between the shield and the tube, this effect can be substantial.     

Transmission Dynamics of Highly Pathogenic Avian Influenza at Lake Constance (Europe) During the Outbreak of Winter 2005–2006

Highly pathogenic avian influenza virus (HPAI) H5N1 poses a serious threat to domestic animals. Despite the large number of studies on influenza A virus in waterbirds, little is still known about the transmission dynamics, including prevalence, behavior, and spread of these viruses in the wild waterbird population. From January to April 2006, the HPAI H5N1 virus was confirmed in 82 dead wild waterbirds at the shores of Lake Constance. In this study, we present simple mathematical models to examine this outbreak and to investigate the transmission dynamics of HPAI in wild waterbirds. The population dynamics model of wintering birds was best represented by a sinusoidal function. This model was considered the most adequate to represent the susceptible compartment of the SIR model. The three transmission models predict a basic reproduction ratio (R ₀) with value of approximately 1.6, indicating a small epidemic, which ended with the migration of susceptible wild waterbirds at the end of the winter. With this study, we quantify for the first time the transmission of HPAI H5N1 virus at Lake Constance during the outbreak of winter 2005–2006. It is a step toward the improvement of the knowledge of transmission of the virus among wild waterbirds.