A hybrid transmission model for Plasmodium vivax accounting for superinfection, immunity and the hypnozoite reservoir.

Malaria is a vector-borne disease that exacts a grave toll in the Global South. The epidemiology of Plasmodium vivax, the most geographically expansive agent of human malaria, is characterised by the accrual of a reservoir of dormant parasites known as hypnozoites. Relapses, arising from hypnozoite activation events, comprise the majority of the blood-stage infection burden, with implications for the acquisition of immunity and the distribution of superinfection. Here, we construct a novel model for the transmission of P. vivax that concurrently accounts for the accrual of the hypnozoite reservoir, (blood-stage) superinfection and the acquisition of immunity. We begin by using an infinite-server queueing network model to characterise the within-host dynamics as a function of mosquito-to-human transmission intensity, extending our previous model to capture a discretised immunity level. To model transmission-blocking and antidisease immunity, we allow for geometric decay in the respective probabilities of successful human-to-mosquito transmission and symptomatic blood-stage infection as a function of this immunity level. Under a hybrid approximation-whereby probabilistic within-host distributions are cast as expected population-level proportions-we couple host and vector dynamics to recover a deterministic compartmental model in line with Ross-Macdonald theory. We then perform a steady-state analysis for this compartmental model, informed by the (analytic) distributions derived at the within-host level. To characterise transient dynamics, we derive a reduced system of integrodifferential equations, likewise informed by our within-host queueing network, allowing us to recover population-level distributions for various quantities of epidemiological interest. In capturing the interplay between hypnozoite accrual, superinfection and acquired immunity-and providing, to the best of our knowledge, the most complete population-level distributions for a range of epidemiological values-our model provides insights into important, but poorly understood, epidemiological features of P. vivax.

Development of Improved Spectrophotometric Assays for Biocatalytic Silyl Ether Hydrolysis.

Reported herein is the development of assays for the spectrophotometric quantification of biocatalytic silicon-oxygen bond hydrolysis. Central to these assays are a series of chromogenic substrates that release highly absorbing phenoxy anions upon cleavage of the sessile bond. These substrates were tested with silicatein, an enzyme from a marine sponge that is known to catalyse the hydrolysis and condensation of silyl ethers. It was found that, of the substrates tested, tert-butyldimethyl(2-methyl-4-nitrophenoxy)silane provided the best assay performance, as evidenced by the highest ratio of enzyme catalysed reaction rate compared with the background (uncatalysed) reaction. These substrates were also found to be suitable for detailed enzyme kinetics measurements, as demonstrated by their use to determine the Michaelis-Menten kinetic parameters for silicatein.

Superinfection and the hypnozoite reservoir for Plasmodium vivax: a general framework.

A characteristic of malaria in all its forms is the potential for superinfection (that is, multiple concurrent blood-stage infections). An additional characteristic of Plasmodium vivax malaria is a reservoir of latent parasites (hypnozoites) within the host liver, which activate to cause (blood-stage) relapses. Here, we present a model of hypnozoite accrual and superinfection for P. vivax. To couple host and vector dynamics for a homogeneously-mixing population, we construct a density-dependent Markov population process with countably many types, for which disease extinction is shown to occur almost surely. We also establish a functional law of large numbers, taking the form of an infinite-dimensional system of ordinary differential equations that can also be recovered by coupling expected host and vector dynamics (i.e. a hybrid approximation) or through a standard compartment modelling approach. Recognising that the subset of these equations that model the infection status of the human hosts has precisely the same form as the Kolmogorov forward equations for a Markovian network of infinite server queues with an inhomogeneous batch arrival process, we use physical insight into the evolution of the latter process to write down a time-dependent multivariate generating function for the solution. We use this characterisation to collapse the infinite-compartment model into a single integrodifferential equation (IDE) governing the intensity of mosquito-to-human transmission. Through a steady state analysis, we recover a threshold phenomenon for this IDE in terms of a parameter [Formula: see text] expressible in terms of the primitives of the model, with the disease-free equilibrium shown to be uniformly asymptotically stable if [Formula: see text] and an endemic equilibrium solution emerging if [Formula: see text]. Our work provides a theoretical basis to explore the epidemiology of P. vivax, and introduces a strategy for constructing tractable population-level models of malarial superinfection that can be generalised to allow for greater biological realism in a number of directions.

How effective were Australian Quarantine Stations in mitigating transmission aboard ships during the influenza pandemic of 1918-19?

The influenza pandemic of 1918-19 was the most devastating pandemic of the 20th century. It killed an estimated 50-100 million people worldwide. In late 1918, when the severity of the disease was apparent, the Australian Quarantine Service was established. Vessels returning from overseas and inter-state were intercepted, and people were examined for signs of illness and quarantined. Some of these vessels carried the infection throughout their voyage and cases were prevalent by the time the ship arrived at a Quarantine Station. We study four outbreaks that took place on board the Medic, Boonah, Devon, and Manuka in late 1918. These ships had returned from overseas and some of them were carrying troops that served in the First World War. By analysing these outbreaks under a stochastic Bayesian hierarchical modeling framework, we estimate the transmission rates among crew and passengers aboard these ships. Furthermore, we ask whether the removal of infectious, convalescent, and healthy individuals after arriving at a Quarantine Station in Australia was an effective public health response.

Improving estimates of waning immunity rates in stochastic SIRS models with a hierarchical framework.

As most disease causing pathogens require transmission from an infectious individual to a susceptible individual, continued persistence of the pathogen within the population requires the replenishment of susceptibles through births, immigration, or waning immunity. Consider the introduction of an unknown infectious disease into a fully susceptible population where it is not known how long immunity is conferred once an individual recovers from infection. If, initially, the prevalence of disease increases (that is, the infection takes off), the number of infectives will usually decrease to a low level after the first major outbreak. During this post-outbreak period, the disease dynamics may be influenced by stochastic effects and there is a non-zero probability that the epidemic will die out. Die out in this period following the first major outbreak is known as an epidemic fade-out. If the disease does not die out, the susceptible population may be replenished by the waning of immunity, and a second wave may start. In this study, we investigate if the rate of waning immunity (and other epidemiological parameters) can be reliably estimated from multiple outbreak data, in which some outbreaks display epidemic fade-out and others do not. We generated synthetic outbreak data from independent simulations of stochastic SIRS models in multiple communities. Some outbreaks faded-out and some did not. We conducted Bayesian parameter estimation under two alternative approaches: independently on each outbreak and under a hierarchical framework. When conducting independent estimation, the waning immunity rate was poorly estimated and biased towards zero when an epidemic fade-out was observed. However, under a hierarchical approach, we obtained more accurate and precise posterior estimates for the rate of waning immunity and other epidemiological parameters. The greatest improvement in estimates was obtained for those communities in which epidemic fade-out was observed. Our findings demonstrate the feasibility and value of adopting a Bayesian hierarchical approach for parameter inference for stochastic epidemic models.

A Model for Cell Proliferation in a Developing Organism.

In mathematical biology, there is a great deal of interest in producing continuum models by scaling discrete agent-based models governed by local stochastic rules. We discuss a particular example of this approach: a model for the proliferation of neural crest cells that can help us understand the development of Hirschprung's disease, a potentially-fatal condition in which the enteric nervous system of a new-born child does not extend all the way through the intestine and colon. Our starting point is a discrete-state, continuous-time Markov chain model proposed by Hywood et al. (2013a) for the location of the neural crest cells that make up the enteric nervous system. Hywood et al. (2013a) scaled their model to derive an approximate second order partial differential equation describing how the limiting expected number of neural crest cells evolve in space and time. In contrast, we exploit the relationship between the above-mentioned Markov chain model and the well-known Yule-Furry process to derive the exact form of the scaled version of the process. Furthermore, we provide expressions for other features of the domain agent occupancy process, such as the variance of the marginal occupancy at a particular site, the distribution of the number of agents that are yet to reach a given site and a stochastic description of the process itself.

Estimation of the probability of epidemic fade-out from multiple outbreak data.

Deterministic epidemic models that allow for replenishment of susceptibles typically display damped oscillatory behaviour. If the population is initially fully susceptible, once an epidemic takes off a distinct trough will exist between the first and second waves of infection. Epidemic dynamics are, however, influenced by stochastic effects, particularly when the prevalence is low. At the beginning of an epidemic, stochastic die-out is possible and well characterised through use of a branching process approximation. Conditional on an epidemic taking off, stochastic extinction is highly unlikely during the first epidemic wave, but the probability of extinction increases again as the wave declines. Extinction during this period, prior to a potential second wave of infection, is defined as 'epidemic fade-out'. We consider a set of observed epidemics, each distinct and having evolved independently, in which some display fade-out and some do not. While fade-out is necessarily a stochastic phenomenon, the probability of fade-out will depend on the model parameters associated with each epidemic. Accordingly, we ask whether time-series data for the epidemics contain sufficient information to identify the key driver(s) of different outcomes-fade-out or otherwise-across the sub-populations supporting each epidemic. We apply a Bayesian hierarchical modelling framework to synthetic data from an SIRS model of epidemic dynamics and demonstrate that we can (1) identify when the sub-population specific model parameters supporting each epidemic have significant variability and (2) estimate the probability of epidemic fade-out for each sub-population. We demonstrate that a hierarchical analysis can provide precise estimates of the probability of fade-out than is possible if considering each epidemic in isolation. Our methods may be applied to both epidemiological and other biological data to identify where differences in outcome-fade-out or recurrent infection/waves are purely due to chance or driven by underlying changes in the parameters driving the dynamics.

Emulation of epidemics via Bluetooth-based virtual safe virus spread: Experimental setup, software, and data.

We describe an experimental setup and a currently running experiment for evaluating how physical interactions over time and between individuals affect the spread of epidemics. Our experiment involves the voluntary use of the Safe Blues Android app by participants at The University of Auckland (UoA) City Campus in New Zealand. The app spreads multiple virtual safe virus strands via Bluetooth depending on the physical proximity of the subjects. The evolution of the virtual epidemics is recorded as they spread through the population. The data is presented as a real-time (and historical) dashboard. A simulation model is applied to calibrate strand parameters. Participants' locations are not recorded, but participants are rewarded based on the duration of participation within a geofenced area, and aggregate participation numbers serve as part of the data. The 2021 experimental data is available as an open-source anonymized dataset, and once the experiment is complete, the remaining data will be made available. This paper outlines the experimental setup, software, subject-recruitment practices, ethical considerations, and dataset description. The paper also highlights current experimental results in view of the lockdown that started in New Zealand at 23:59 on August 17, 2021. The experiment was initially planned in the New Zealand environment, expected to be free of COVID and lockdowns after 2020. However, a COVID Delta strain lockdown shuffled the cards and the experiment is currently extended into 2022.

Safe Blues: The case for virtual safe virus spread in the long-term fight against epidemics.

Viral spread is a complicated function of biological properties, the environment, preventative measures such as sanitation and masks, and the rate at which individuals come within physical proximity. It is these last two elements that governments can control through social-distancing directives. However, infection measurements are almost always delayed, making real-time estimation nearly impossible. Safe Blues is one way of addressing the problem caused by this time lag via online measurements combined with machine learning methods that exploit the relationship between counts of multiple forms of the Safe Blues strands and the progress of the actual epidemic. The Safe Blues protocols and techniques have been developed together with an experimental minimal viable product, presented as an app on Android devices with a server backend. Following initial exploration via simulation experiments, we are now preparing for a university-wide experiment of Safe Blues.

Antibody Dynamics for Plasmodium vivax Malaria: A Mathematical Model.

Malaria is a mosquito-borne disease that, despite intensive control and mitigation initiatives, continues to pose an enormous public health burden. Plasmodium vivax is one of the principal causes of malaria in humans. Antibodies, which play a fundamental role in the host response to P. vivax, are acquired through exposure to the parasite. Here, we introduce a stochastic, within-host model of antibody responses to P. vivax for an individual in a general transmission setting. We begin by developing an epidemiological framework accounting for P. vivax infections resulting from new mosquito bites (primary infections), as well as the activation of dormant-liver stages known as hypnozoites (relapses). By constructing an infinite server queue, we obtain analytic results for the distribution of relapses in a general transmission setting. We then consider a simple model of antibody kinetics, whereby antibodies are boosted with each infection, but are subject to decay over time. By embedding this model for antibody kinetics in the epidemiological framework using a generalised shot noise process, we derive analytic expressions governing the distribution of antibody levels for a single individual in a general transmission setting. Our work provides a means to explore exposure-dependent antibody dynamics for P. vivax, with the potential to address key questions in the context of serological surveillance and acquired immunity.

Synthesis of Organosilicon Ligands for Europium (III) and Gadolinium (III) as Potential Imaging Agents.

The relaxivity of MRI contrast agents can be increased by increasing the size of the contrast agent and by increasing concentration of the bound gadolinium. Large multi-site ligands able to coordinate several metal centres show increased relaxivity as a result. In this paper, an "aza-type Michael" reaction is used to prepare cyclen derivatives that can be attached to organosilicon frameworks via hydrosilylation reactions. A range of organosilicon frameworks were tested including silsesquioxane cages and dimethylsilylbenzene derivatives. Michael donors with strong electron withdrawing groups could be used to alkylate cyclen on three amine centres in a single step. Hydrosilylation successfully attached these to mono-, di-, and tri-dimethylsilyl-substituted benzene derivatives. The europium and gadolinium complexes were formed and studied using luminescence spectroscopy and relaxometry. This showed the complexes to contain two bound water moles per lanthanide centre and T1 relaxation time measurements demonstrated an increase in relaxivity had been achieved, in particular for the trisubstituted scaffold 1,3,5-tris((pentane-sDO3A)dimethylsilyl)benzene-Gd3. This showed a marked increase in the relaxivity (13.1 r1p/mM-1s-1).

An Activation-Clearance Model for Plasmodium vivax Malaria.

Malaria is an infectious disease with an immense global health burden. Plasmodium vivax is the most geographically widespread species of malaria. Relapsing infections, caused by the activation of liver-stage parasites known as hypnozoites, are a critical feature of the epidemiology of Plasmodium vivax. Hypnozoites remain dormant in the liver for weeks or months after inoculation, but cause relapsing infections upon activation. Here, we introduce a dynamic probability model of the activation-clearance process governing both potential relapses and the size of the hypnozoite reservoir. We begin by modelling activation-clearance dynamics for a single hypnozoite using a continuous-time Markov chain. We then extend our analysis to consider activation-clearance dynamics for a single mosquito bite, which can simultaneously establish multiple hypnozoites, under the assumption of independent hypnozoite behaviour. We derive analytic expressions for the time to first relapse and the time to hypnozoite clearance for mosquito bites establishing variable numbers of hypnozoites, both of which are quantities of epidemiological significance. Our results extend those in the literature, which were limited due to an assumption of collective dormancy. Our within-host model can be embedded readily in multiscale models and epidemiological frameworks, with analytic solutions increasing the tractability of statistical inference and analysis. Our work therefore provides a foundation for further work on immune development and epidemiological-scale analysis, both of which are important for achieving the goal of malaria elimination.

Influence of the initial chemical conditions on the rational design of silica particles.

The influence of the water content in the initial composition on the size of silica particles produced using the Stöber process is well known. We have shown that there are three morphological regimes defined by compositional boundaries. At low water levels (below stoichiometric ratio of water:tetraethoxysilane), very high surface area and aggregated structures are formed; at high water content (>40 wt%) similar structures are also seen. Between these two boundary conditions, discrete particles are formed whose size are dictated by the water content. Within the compositional regime that enables the classical Stöber silica, the structural evolution shows a more rapid attainment of final particle size than the rate of formation of silica supporting the monomer addition hypothesis. The clearer understanding of the role of the initial composition on the output of this synthesis method will be of considerable use for the establishment of reliable reproducible silica production for future industrial adoption.

Enhancing in vitro selection techniques to assist the discovery, understanding and use of inorganic binding peptides.

Reflecting the increasing interest in combinatorial approaches, peptide phage display has seen an unprecedented expansion in a wide range of research areas. Its application to the discovery and analysis of metal binding peptides has opened up new research directions and largely contributed to the nanotechnology field. The rationale behind the need to identify such peptides varies depending on the final aim of the research and its application. Therefore, the possibility to modify the selection technique according to the different requirements would allow for a more systematic approach to be adopted and would ultimately provide substantial benefits. Although the standard panning method can be virtually applied to any target, its use for the identification of metal binding peptides does not provide the characteristics and the flexibility required for an efficient and tailored selection. Here we report on the development of a new panning method that can contribute to a faster, versatile and more informative analysis. Through the use of rolling-circle amplification, polymerase reaction and wild type phage, we have converted the standard selection technique into a more dynamic process in which adjustments can be evaluated and made consistently with the need of the experiment. The successfulness of the improved method is demonstrated in a number of panning experiments with different inorganic targets. The modifications applied to each selection are described and comparisons between the results obtained are made in order to extensively assess and evaluate the impact of the new process. The importance of tailoring the screening method to the specific objectives of a study is also considered. New binder sequences for the materials included in the investigation are identified; their sequences and distinctive characteristics are reported and their ability to act as templates for the nucleation of inorganic material is demonstrated and discussed.

Properties and self-assembled packing morphology of long alkyl-chained substituted polyhedral oligomeric silsesquioxanes (POSS) cages.

Polyhedral oligomeric silsesquioxane (POSS) cubic cage systems (octa-n-octadecyloctasilsesquioxane, (T8C18) and octakis(n-octadecyldimethylsiloxy)octasilsesquioxane, (Q8C18)) were synthesised with eight long n-alkyl chain (R = C18H37) substituent arms, as model nano-functionalized compounds. The crystalline packing morphology of the cages was studied using time-resolved Small- and Wide-angle X-ray scattering (SAXS/WAXS), thermal and optical techniques. From thermal analysis the melting and crystallization temperatures of the Q8 cage were significantly less than those for the T8 cage. X-ray scattering showed that both cage systems have long-range crystalline ordering where the alkyl chains align in a parallel axial disposition from the POSS core giving a 'rod-like' self-assembled packing morphology. The packing length-scale can be directly related to the overall dimensions of the POSS molecules. Compared to the T8 cages, the Q8 cages pack more efficiently allowing the interdigitation of the alkyl chain arms. Different packing modes and thermal behaviour observed for the T8 and Q8 cages is directly attributed to their structural chemistry. For the Q8 cage, the presence of the OSiMe2 spacer groups which tether the alkyl chain arms to the cage (absent in the T8 cages) allows greater flexibility of the arms letting them interdigitate with each other when packing which is not observed for the analogous T8 cages.

Cationic complexes of silicon and germanium with (O,S)-chelate ligands.

Synthesis and X-ray diffraction study of cationic bischelates MeSi(SCH(2)CONMe(2))(2)(+)Cl(-) and MeGe(SCH(2)CONMe(2))(2)(+)Br(-) are reported. According to X-ray data, the Si and Ge atoms in these compounds have distorted TBP environments with two coordinating oxygen atoms in axial positions.

Further studies of fluoride ion entrapment in octasilsesquioxane cages; X-ray crystal structure studies and factors that affect their formation.

A range of fluoride-encapsulated octasilsesquioxane cage compounds have been prepared using the TBAF route. Our studies suggest that whilst it is relatively straightforward to prepare fluoride-encapsulated octasilsesquioxane cage compounds with adjacent sp(2) carbons, leading to a range of aryl and vinyl substituted compounds, the corresponding sp(3) carbon derivatives are more capricious, requiring an electron withdrawing group that can stabilize the cage whilst not acting as a leaving group. Analysis by X-ray crystallography and solution (19)F/(29)Si NMR spectroscopy of R(8)T(8)@F(-) reveal very similar environments for the encapsulated fluoride octasilsesquioxane cages. Migration of a fluoride ion from inside the cage to outside the cage without breaking the T(8) framework and the possibility of encapsulating other anions within silsesquioxane cages have been also investigated.

A large scale enzyme screen in the search for new methods of silicon-oxygen bond formation.

Biotransformations make use of biological systems to catalyze or promote specific chemical reactions. Transformations that utilize enzymes as "greener" and milder catalysts compared to traditional reaction conditions are of particular interest. Recently, organosilicon compounds have begun to be explored as non-natural enzymatic substrates for biotransformations. The aims of this study were to screen readily available (approximately eighty) enzymes for their ability to catalyze in vitro siloxane bond formation under mild reaction conditions using a model monoalkoxysilane as the substrate and to make a preliminary evaluation of potential factors that might lead to activity or inactivity of a particular enzyme. Several new hydrolase enzymes were observed to catalyze the formation of the condensation product when compared to peptide controls, or buffer solutions at the same pH, as judged from quantitative analyses by gas chromatography. Aspergillus ficuum phytase, Aspergillus niger phytase, chicken egg white lysozyme, porcine gastric mucosa pepsin, and Rhizopus oryzae lipase all catalyzed the condensation of silanols in aqueous media. Factors involved in determining the activity of an enzyme towards silanol condensation appear to include: the presence of imidazole and hydroxyl functions in the active site; solvent; the presence of water; the surface properties of the enzyme; possible covalent inhibition; and steric factors in the substrate.

Enzyme mediated silicon-oxygen bond formation; the use of Rhizopus oryzae lipase, lysozyme and phytase under mild conditions.

The potential for expanding the variety of enzymic methods for siloxane bond formation is explored. Three enzymes, Rhizopus oryzae lipase (ROL), lysozyme and phytase are reported to catalyse the condensation of the model compound, trimethylsilanol, formed in situ from trimethylethoxysilane, to produce hexamethyldisiloxane in aqueous media at 25 °C and pH 7. Thermal denaturation and reactant inhibition experiments were conducted to better understand the catalytic role of these enzyme candidates. It was found that enzyme activities were significantly reduced following thermal treatment, suggesting a potential key-role of the enzyme active sites in the catalysis. Similarly, residue-specific modification of the key-amino acids believed to participate in the ROL catalysis also had a significant effect on the silicon bio-catalysis, indicating that the catalytic triad of the lipase may be involved during the enzyme-mediated formation of the silicon-oxygen bond. E. coli phytase was found to be particularly effective at catalysing the condensation of trimethylsilanol in a predominantly organic medium consisting of 95% acetonitrile and 5% water. Whereas the use of enzymes in silicon chemistry is still very much a developing and frontier activity, the results presented herein give some grounds for optimism that the variety of enzyme mediated reactions will continue to increase and may one day become a routine element in the portfolio of the synthetic silicon chemist.

Four independent structures of a pentacoordinate silicon species at different points on the Berry pseudorotation pathway.

A new pentacoordinate silicon species containing two chelating ligands has been synthesized. The structures of four independent cations of the same compound correspond to different points on the Berry pseudorotation pathway. The percentage of square planar character varies between 19% and 40%.