Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 · 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals

From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, $R_e$, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase $R_e$ and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of $R_e$ when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl

Capsaicin-Loaded Chitosan Nanocapsules for wtCFTR-mRNA Delivery to a Cystic Fibrosis Cell Line

Cystic fibrosis (CF), a lethal hereditary disease caused by mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) gene coding for an epithelial chloride channel, is characterized by an imbalanced homeostasis of ion and water transports in secretory epithelia. As the disease is single-gene based, transcript therapy using therapeutic mRNA is a promising concept of treatment in order to correct many aspects of the fatal pathology on a cellular level. Hence, we developed chitosan nanocapsules surface-loaded with wtCFTR-mRNA to restore CFTR function. Furthermore, we loaded the nanocapsules with capsaicin, aiming to enhance the overall efficiency of transcript therapy by reducing sodium hyperabsorption by the epithelial sodium channel (ENaC). Dynamic light scattering with non-invasive back scattering (DLS-NIBS) revealed nanocapsules with an average hydrodynamic diameter of ~200 nm and a Zeta potential of ~+60 mV. The results of DLS-NIBS measurements were confirmed by asymmetric flow field-flow fractionation (AF4) with multidetection, while transmission electron microscopy (TEM) images confirmed the spherical morphology and size range. After stability measurements showed that the nanocapsules were highly stable in cell culture transfection medium, and cytotoxicity was ruled out, transfection experiments were performed with the CF cell line CFBE41o-. Finally, transepithelial measurements with a new state-of-the-art Ussing chamber confirmed successfully restored CFTR function in transfected cells. This study demonstrates that CS nanocapsules as a natural and non-toxic delivery system for mRNA to target cells could effectively replace risky vectors for gene delivery. The nanocapsules are not only suitable as a transcript therapy for treatment of CF, but open aspiring possibilities for safe gene delivery in general

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

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