Backward bifurcation, equilibrium and stability phenomena in a three-stage extended BRSV epidemic model

In this paper we consider the phenomenon of backward bifurcation in epidemic modelling illustrated by an extended model for Bovine Respiratory Syncytial Virus (BRSV) amongst cattle. In its simplest form, backward bifurcation in epidemic models usually implies the existence of two subcritical endemic equilibria for R 0 < 1, where R 0 is the basic reproductive number, and a unique supercritical endemic equilibrium for R 0 > 1. In our three-stage extended model we find that more complex bifurcation diagrams are possible. The paper starts with a review of some of the previous work on backward bifurcation then describes our three-stage model. We give equilibrium and stability results, and also provide some biological motivation for the model being studied. It is shown that backward bifurcation can occur in the three-stage model for small b, where b is the common per capita birth and death rate. We are able to classify the possible bifurcation diagrams. Some realistic numerical examples are discussed at the end of the paper, both for b small and for larger values of b

In Vivo Evaluation of Indium-111-Labeled 800CW as a Necrosis-Avid Contrast Agent.

Current clinical measurements for tumor treatment efficiency rely often on changes in tumor volume measured as shrinkage by CT or MRI, which become apparent after multiple lines of treatment and pose a physical and psychological burden on the patient. Detection of therapy-induced cell death in the tumor can be a fast measure for treatment efficiency. However, there are no reliable clinical tools for detection of tumor necrosis. Previously, we studied the necrosis avidity of cyanine-based fluorescent dyes, which suffered long circulation times before tumor necrosis could be imaged due to low hydrophilicity. We now present the application of radiolabeled 800CW, a commercially available cyanine with high hydrophilicity, to image tumor necrosis in a mouse model. We conjugated 800CW to DOTA via a PEG linker, for labeling with single-photon emission-computed tomography isotope indium-111, yielding [ <sup>111</sup> In]In-DOTA-PEG <sub>4</sub> -800CW. We then investigated specific [ <sup>111</sup> In]In-DOTA-PEG <sub>4</sub> -800CW uptake by dead cells in vitro, using both fluorescence and radioactivity as detection modalities. Finally, we investigated [ <sup>111</sup> In]In-DOTA-PEG <sub>4</sub> -800CW uptake into necrotic tumor regions of a 4T1 breast tumor model in mice. We successfully prepared a precursor and developed a reliable procedure for labeling 800CW with indium-111. We detected specific [ <sup>111</sup> In]In-DOTA-PEG <sub>4</sub> -800CW uptake by dead cells, using both fluorescence and radioactivity. Albeit with a tumor uptake of only 0.37%ID/g at 6 h post injection, we were able to image tumor necrosis with a tumor to background ratio of 7:4. Fluorescence and radioactivity in cryosections from the dissected tumors were colocalized with tumor necrosis, confirmed by TUNEL staining. [ <sup>111</sup> In]In-DOTA-PEG <sub>4</sub> -800CW can be used to image tumor necrosis in vitro and in vivo. Further research will elucidate the application of [ <sup>111</sup> In]In-DOTA-PEG <sub>4</sub> -800CW or other radiolabeled hydrophilic cyanines for the detection of necrosis caused by chemotherapy or other anti-cancer therapies. This can provide valuable prognostic information in treatment of solid tumors

Necrosis binding of Ac-Lys⁰(IRDye800CW)-Tyr³-octreotate: a consequence from cyanine-labeling of small molecules.

There is a growing body of nuclear contrast agents that are repurposed for fluorescence-guided surgery. New contrast agents are obtained by substituting the radioactive tag with, or adding a fluorescent cyanine to the molecular structure of antibodies or peptides. This enables intra-operative fluorescent detection of cancerous tissue, leading to more complete tumor resection. However, these fluorescent cyanines can have a remarkable influence on pharmacokinetics and tumor uptake, especially when labeled to smaller targeting vectors such as peptides. Here we demonstrate the effect of cyanine-mediated dead cell-binding of Ac-Lys <sup>0</sup> (IRDye800CW)-Tyr <sup>3</sup> -octreotate (800CW-TATE) and how this can be used as an advantage for fluorescence-guided surgery. Binding of 800CW-TATE could be blocked with DOTA <sup>0</sup> -Tyr <sup>3</sup> -octreotate (DOTA-TATE) on cultured SSTR <sub>2</sub> -positive U2OS cells and was absent in SSTR <sub>2</sub> negative U2OS cells. However, strong binding was observed to dead cells, which could not be blocked with DOTA-TATE and was also present in dead SSTR <sub>2</sub> negative cells. No SSTR <sub>2</sub> -mediated binding was observed in frozen tumor sections, possibly due to disruption of the cells in the process of sectioning the tissue before exposure to the contrast agent. DOTA-TATE blocking resulted in an incomplete reduction of 61.5 ± 5.8% fluorescence uptake by NCI-H69-tumors in mice. Near-infrared imaging and dead cell staining on paraffin sections from resected tumors revealed that fluorescence uptake persisted in necrotic regions upon blocking with DOTA-TATE. This study shows that labeling peptides with cyanines can result in dead cell binding. This does not hamper the ultimate purpose of fluorescence-guided surgery, as necrotic tissue appears in most solid tumors. Hence, the necrosis binding can increase the overall tumor uptake. Moreover, necrotic tissue should be removed as much as possible: it cannot be salvaged, causes inflammation, and is tumorigenic. However, when performing binding experiments to cells with disrupted membrane integrity, which is routinely done with nuclear probes, this dead cell-binding can resemble non-specific binding. This study will benefit the development of fluorescent contrast agents

S. pneumoniae transmission according to inclusion in conjugate vaccines: Bayesian analysis of a longitudinal follow-up in schools

BACKGROUND: Recent trends of pneumococcal colonization in the United States, following the introduction of conjugate vaccination, indicate that non-vaccine serotypes tend to replace vaccine serotypes. The eventual extent of this replacement is however unknown and depends on serotype-specific carriage and transmission characteristics. METHODS: Here, some of these characteristics were estimated for vaccine and non-vaccine serotypes from the follow-up of 4,488 schoolchildren in France in 2000. A Bayesian approach using Markov chain Monte Carlo data augmentation techniques was used for estimation. RESULTS: Vaccine and non-vaccine serotypes were found to have similar characteristics: the mean duration of carriage was 23 days (95% credible interval (CI): 21, 25 days) for vaccine serotypes and 22 days (95% CI: 20, 24 days) for non-vaccine serotypes; within a school of size 100, the Secondary Attack Rate was 1.1% (95% CI: 1.0%, 1.2%) for both vaccine and non-vaccine serotypes. CONCLUSION: This study supports that, in 3–6 years old children, no competitive advantage exists for vaccine serotypes compared to non-vaccine serotypes. This is an argument in favour of important serotype replacement. It would be important to validate the result for infants, who are known to be the main reservoir in maintaining transmission. Overall reduction in pathogenicity should also be taken into account in forecasting the future burden of pneumococcal colonization in vaccinated populations

Trees Wanted—Dead or Alive! Host Selection and Population Dynamics in Tree-Killing Bark Beetles

Bark beetles (Coleoptera: Curculionidae, Scolytinae) feed and breed in dead or severely weakened host trees. When their population densities are high, some species aggregate on healthy host trees so that their defences may be exhausted and the inner bark successfully colonized, killing the tree in the process. Here we investigate under what conditions participating with unrelated conspecifics in risky mass attacks on living trees is an adaptive strategy, and what this can tell us about bark beetle outbreak dynamics. We find that the outcome of individual host selection may deviate from the ideal free distribution in a way that facilitates the emergence of tree-killing (aggressive) behavior, and that any heritability on traits governing aggressiveness seems likely to exist in a state of flux or cycles consistent with variability observed in natural populations. This may have implications for how economically and ecologically important species respond to environmental changes in climate and landscape (forest) structure. The population dynamics emerging from individual behavior are complex, capable of switching between “endemic” and “epidemic” regimes spontaneously or following changes in host availability or resistance. Model predictions are compared to empirical observations, and we identify some factors determining the occurrence and self-limitation of epidemics

Absolute quantitative total-body small-animal SPECT with focusing pinholes

Purpose: In pinhole SPECT, attenuation of the photon flux on trajectories between source and pinholes affects quantitative accuracy of reconstructed images. Previously we introduced iterative methods that compensate for image degrading effects of detector and pinhole blurring, pinhole sensitivity and scatter for multi-pinhole SPECT. The aim of this paper is (1) to investigate the accuracy of the Chang algorithm in rodents and (2) to present a practical Changbased method using body outline contours obtained with optical cameras. Methods: Here we develop and experimentally validate a practical method for attenuation correction based on a Chang first-order method. This approach has the advantage that it is employed after, and therefore independently from, iterative reconstruction. Therefore, no new system matrix has to be calculated for each specific animal. Experiments with phantoms and animals were performed with a highresolution focusing multi-pinhole SPECT system (USPECT-II, MILabs, The Netherlands). This SPECT system provides three additional optical camera images of the animal for each SPECT scan from which the animal contour can be estimated. Results: Phantom experiments demonstrated that an average quantification error of –18.7% was reduced to –1.7% when both window-based scatter correction and Chang correction based on the body outline from optical images were applied. Without scatter and attenuation correction, quantification errors in a sacrificed rat containing sources with known activity ranged from –23.6 to –9.3%. These errors were reduced to values between –6.3 and +4.3% (with an average magnitude of 2.1%) after applying scatter and Chang attenuation correction. Conclusion: We conclude that the modified Chang correction based on body contour combined with window-based scatter correction is a practical method for obtaining small-animal SPECT images with high quantitative accuracy.Radiation, Radionuclides and ReactorsApplied Science

Refractory periods and climate forcing in cholera dynamics

Outbreaks of many infectious diseases, including cholera, malaria and dengue, vary over characteristic periods longer than 1 year(1,2). Evidence that climate variability drives these interannual cycles has been highly controversial, chiefly because it is difficult to isolate the contribution of environmental forcing while taking into account nonlinear epidemiological dynamics generated by mechanisms such as host immunity(2-4). Here we show that a critical interplay of environmental forcing, specifically climate variability, and temporary immunity explains the interannual disease cycles present in a four-decade cholera time series from Matlab, Bangladesh. We reconstruct the transmission rate, the key epidemiological parameter affected by extrinsic forcing, over time for the predominant strain ( El Tor) with a nonlinear population model that permits a contributing effect of intrinsic immunity. Transmission shows clear interannual variability with a strong correspondence to climate patterns at long periods ( over 7 years, for monsoon rains and Brahmaputra river discharge) and at shorter periods ( under 7 years, for flood extent in Bangladesh, sea surface temperatures in the Bay of Bengal and the El Nino Southern Oscillation). The importance of the interplay between extrinsic and intrinsic factors in determining disease dynamics is illustrated during refractory periods, when population susceptibility levels are low as the result of immunity and the size of cholera outbreaks only weakly reflects climate forcing.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62876/1/nature03820.pd

Using Dynamic Stochastic Modelling to Estimate Population Risk Factors in Infectious Disease: The Example of FIV in 15 Cat Populations

BACKGROUND:In natural cat populations, Feline Immunodeficiency Virus (FIV) is transmitted through bites between individuals. Factors such as the density of cats within the population or the sex-ratio can have potentially strong effects on the frequency of fight between individuals and hence appear as important population risk factors for FIV. METHODOLOGY/PRINCIPAL FINDINGS:To study such population risk factors, we present data on FIV prevalence in 15 cat populations in northeastern France. We investigate five key social factors of cat populations; the density of cats, the sex-ratio, the number of males and the mean age of males and females within the population. We overcome the problem of dependence in the infective status data using sexually-structured dynamic stochastic models. Only the age of males and females had an effect (p = 0.043 and p = 0.02, respectively) on the male-to-female transmission rate. Due to multiple tests, it is even likely that these effects are, in reality, not significant. Finally we show that, in our study area, the data can be explained by a very simple model that does not invoke any risk factor. CONCLUSION:Our conclusion is that, in host-parasite systems in general, fluctuations due to stochasticity in the transmission process are naturally very large and may alone explain a larger part of the variability in observed disease prevalence between populations than previously expected. Finally, we determined confidence intervals for the simple model parameters that can be used to further aid in management of the disease

Evolutionary Trajectory of White Spot Syndrome Virus (WSSV) Genome Shrinkage during Spread in Asia

Background - White spot syndrome virus (WSSV) is the sole member of the novel Nimaviridae family, and the source of major economic problems in shrimp aquaculture. WSSV appears to have rapidly spread worldwide after the first reported outbreak in the early 1990s. Genomic deletions of various sizes occur at two loci in the WSSV genome, the ORF14/15 and ORF23/24 variable regions, and these have been used as molecular markers to study patterns of viral spread over space and time. We describe the dynamics underlying the process of WSSV genome shrinkage using empirical data and a simple mathematical model. Methodology/Principal Findings - We genotyped new WSSV isolates from five Asian countries, and analyzed this information together with published data. Genome size appears to stabilize over time, and deletion size in the ORF23/24 variable region was significantly related to the time of the first WSSV outbreak in a particular country. Parameter estimates derived from fitting a simple mathematical model of genome shrinkage to the data support a geometric progression (