Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses.

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?

The COVID-19 pandemic has devastated lives and economies around the world. Initially a primary response was locking down parts of the economy to reduce social interactions and, hence, the virus' spread. After vaccines have been developed and produced in sufficient quantity, they can largely replace broad lock downs. This paper explores how lockdown policies should be varied during the year or so gap between when a vaccine is approved and when all who wish have been vaccinated. Are vaccines and lockdowns substitutes during that crucial time, in the sense that lockdowns should be reduced as vaccination rates rise? Or might they be complementary with the prospect of imminent vaccination increasing the value of stricter lockdowns, since hospitalization and death averted then may be permanently prevented, not just delayed? We investigate this question with a simple dynamic optimization model that captures both epidemiological and economic considerations. In this model, increasing the rate of vaccine deployment may increase or reduce the optimal total lockdown intensity and duration, depending on the values of other model parameters. That vaccines and lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns.

Bioactive molecules for regenerative pulp capping.

Since the discovery of bioactive molecules sequestered in dentine, researchers have been exploring ways to harness their activities for dental regeneration. One specific area, discussed in this review, is that of dental-pulp capping. Dental-pulp caps are placed when the dental pulp is exposed due to decay or trauma in an attempt to enhance tertiary dentine deposition. Several materials are used for dental-pulp capping; however, natural biomimetic scaffolds may offer advantages over manufactured materials such as improved aesthetic, biocompatibility and success rate. The present review discusses and appraises the current evidence surrounding biomimetic dental-pulp capping, with a focus on bioactive molecules sequestered in dentine. Molecules covered most extensively in the literature include transforming growth factors (TGF-ßs, specifically TGF-ß1) and bone morphogenetic proteins (BMPs, specifically BMP-2 and BMP-7). Further studies would need to explore the synergistic use of multiple peptides together with the development of a tailored scaffold carrier. The roles of some of the molecules identified in dentine need to be explored before they can be considered as potential bioactive molecules in a biomimetic scaffold for dental-pulp capping. Future in vivo work needs to consider the inflammatory environment of the dental pulp in pulpal exposures and compare pulp-capping materials.

Improved osteogenic vector for non-viral gene therapy.

Therapeutic compensation of deficient bone regeneration is a challenging task and a topic of on-going search for novel treatment strategies. One promising approach for improvement involves non-viral gene delivery using the bone morphogenetic protein-2 (BMP-2) gene to provide transient, local and sustained expression of the growth factor. However, since efficiency of non-viral gene delivery is low, this study focused on the improvement of a BMP-2 gene expression system, aiming for compensation of poor transfection efficiency. First, the native BMP-2 gene sequence was modified by codon optimisation and altered by inserting a highly truncated artificial intron (96 bp). Transfection of multiple cell lines and rat adipose-derived mesenchymal stem cells with plasmids harbouring the improved BMP-2 sequence led to a several fold increased expression rate and subsequent osteogenic differentiation. Additionally, comparing expression kinetics of elongation factor 1 alpha (EF1α) promoter with a state of the art CMV promoter revealed significantly higher BMP-2 expression when under the influence of the EF1α promoter. Results obtained by quantification of bone markers as well as osteogenic assays showed reduced sensitivity to promoter silencing effects of the EF1α promoter in rat adipose-derived mesenchymal stem cells. Finally, screening of several protein secretion signals using either luciferase or BMP-2 as reporter protein revealed no superior candidates for potential replacement of the native BMP-2 secretion signal. Taken together, by enhancing the exogenous BMP-2 expression system, low transfection efficiencies in therapeutic applications can be compensated, making safe non-viral systems even more suitable for tissue regeneration approaches.

Constitutive and inducible co-expression systems for non-viral osteoinductive gene therapy.

Tissue regenerative gene therapy requires expression strategies that deliver therapeutic effective amounts of transgenes. As physiological expression patterns are more complex than high-level expression of a singular therapeutic gene, we aimed at constitutive or inducible co-expression of 2 transgenes simultaneously. Co-expression of human bone morphogenetic protein 2 and 7 (BMP2/7) from constitutively expressing and doxycycline inducible plasmids was evaluated in vitro in C2C12 cells with osteocalcin reporter gene assays and standard assays for osteogenic differentiation. The constitutive systems were additionally tested in an in vivo pilot for ectopic bone formation after repeated naked DNA injection to murine muscle tissue. Inductor controlled differentiation was demonstrated in vitro for inducible co-expression. Both co-expression systems, inducible and constitutive, achieved significantly better osteogenic differentiation than single factor expression. The potency of the constitutive co-expression systems was dependent on relative expression cassette topology. In vivo, ectopic bone formation was demonstrated in 6/13 animals (46% bone formation efficacy) at days 14 and 28 in hind limb muscles as proven by in vivo µCT and histological evaluation. In vitro findings demonstrated that the devised single vector BMP2/7 co-expression strategy mediates superior osteoinduction, can be applied in an inductor controlled fashion and that its efficiency is dependent on expression cassette topology. In vivo results indicatethatco-expression of BMP2/7 applied by non-viral naked DNA gene transfer effectively mediates bone formation without the application of biomaterials, cells or recombinant growth factors, offering a promising alternative to current treatment strategies with potential for clinical translation in the future.

Minimizing the dependency ratio in a population with below-replacement fertility through immigration.

Many industrialized countries face fertility rates below replacement level, combined with declining mortality especially in older ages. Consequently, the populations of these countries have started to age. One important indicator of age structures is the dependency ratio which is the ratio of the nonworking age population to the working age population. In this work we find the age-specific immigration profile that minimizes the dependency ratio in a stationary population with below-replacement fertility. It is assumed that the number of immigrants per age is limited. We consider two alternative policies. In the first one, we fix the total number of people who annually immigrate to a country. In the second one, we prescribe the size of the receiving country's population. For both cases we provide numerical results for the optimal immigration profile, for the resulting age structure of the population, as well as for the dependency ratio.

Starch-poly-epsilon-caprolactone microparticles reduce the needed amount of BMP-2.

BMP-2 is currently administered clinically using collagen matrices often requiring large amounts of BMP-2 due to burst release over a short period of time. We developed and tested a novel injectable drug delivery system consisting of starch-poly-epsilon-caprolactone microparticles for inducing osteogenesis and requiring smaller amounts of BMP-2. We evaluated BMP-2 encapsulation efficiency and the in vitro release profile by enzyme-linked immunosorbent assay. BMP-2 was rapidly released during the first 12 hours, followed by sustained release for up to 10 days. We then evaluated the osteogenic potential of dexamethasone (standard osteogenic induction agent) and BMP-2 after incorporation and during release using an osteo/myoblast cell line (C2C12). Alkaline phosphatase activity was increased by released BMP-2. Mineralization occurred after stimulation with BMP-2-loaded microparticles. A luciferase assay for osteocalcin promoter activity showed high levels of activity upon treatment with BMP-2-loaded microparticles. In contrast, no osteogenesis occurred in C2C12 cells using dexamethasone-loaded microparticles. However, human adipose stem cells exposed to the microparticles produced high amounts of alkaline phosphatase. The data suggest starch-poly-epsilon-caprolactone microparticles are suitable carriers for the incorporation and controlled release of glucocorticoids and growth factors. Specifically, they reduce the amount of BMP-2 needed and allow more sustained osteogenic effects.

Ultrasound-responsive gene-activated matrices for osteogenic gene therapy using matrix-assisted sonoporation.

Gene-activated matrix (GAM)-based therapeutics for tissue regeneration are limited by efficacy, the lack of spatiotemporal control and availability of target cells, all of which impact negatively on their translation to the clinic. Here, an advanced ultrasound-responsive GAM is described containing target cells that facilitates matrix-assisted sonoporation (MAS) to induce osteogenic differentiation. Ultrasound-responsive GAMs consisting of fibrin/collagen hybrid-matrices containing microbubbles, bone morphogenetic protein BMP2/7 coexpression plasmids together with C2C12 cells were treated with ultrasound either in vitro or following parenteral intramuscular implantation in vivo. Using direct measurement for alkaline phosphatase activity, von Kossa staining and immunohistochemical analysis for osteocalcin expression, MAS-stimulated osteogenic differentiation was confirmed in the GAMs in vitro 7 days after treatment with ultrasound. At day 30 post-treatment with ultrasound, ectopic osteogenic differentiation was confirmed in vivo using X-ray microcomputed tomography and histological analysis. Osteogenic differentiation was indicated by the presence of ectopic bone structures in all animals treated with MAS. In addition, bone volumes in this group were statistically greater than those in the control groups. This novel approach of incorporating a MAS capability into GAMs could be exploited to facilitate ex vivo gene transfer with subsequent surgical implantation or alternatively provide a minimally invasive means of stimulating in situ transgene delivery for osteoinductive gene-based therapies. Copyright © 2017 John Wiley & Sons, Ltd.

A dynamic model of drug initiation: implications for treatment and drug control.

We set up a time-continuous version of the first-order difference equation model of cocaine use introduced by Everingham and Rydell [S.S. Everingham, C.P. Rydell, Modeling the Demand for Cocaine, MR-332-ONDCP/A/DPRC, RAND, Santa Monica, CA, 1994] and extend it by making initiation an endogenous function of prevalence. This function reflects both the epidemic spread of drug use as users 'infect' non-users and Musto's [D.F. Musto, The American Disease: Origins of Narcotic Control, Oxford University, New York, 1987] hypothesis that drug epidemics die out when a new generation is deterred from initiating drug use by observing the ill effects manifest among heavy users. Analyzing the model's dynamics suggests that drug prevention can temper drug prevalence and consumption, but that drug treatment's effectiveness depends critically on the stage in the epidemic in which it is employed. Reducing the number of heavy users in the early stages of an epidemic can be counter-productive if it masks the risks of drug use and, thereby, removes a disincentive to initiation. This strong dependence of an intervention's effectiveness on the state of the dynamic system illustrates the pitfalls of applying a static control policy in a dynamic context.

Capital accumulation, aspiration adjustment, and population growth: limit cycles in an Easterlin-type model.

"One of the recent interesting hypotheses of population growth is due to Easterlin who suggests the possibility of self-generating fluctuations in birth numbers. The present paper tries to answer the question whether feedback mechanisms produce persistent oscillations in population growth. A system of two nonlinear differential equations for the per capita capital stock and the aspiration level is studied by a phase portrait analysis. Using the Poincare-Bendixson theorem we derive sufficient conditions for the existence of a stable limit cycle." (SUMMARY IN FRE)

How stock dependent flow rates may imply chaos in educational planning.

"The aim of the present paper is to illustrate how extremely complex patterns may be generated in a simple model of educational planning. In particular, we will show that certain dependencies of the flow rates on the teacher/student ratio imply nonlinearities which are substantial enough to generate erratic behaviour of the time paths. The main message is that chaos in educational planning may result from assumptions which are indeed qualitatively realistic but which are quantitatively exaggerated." (SUMMARY IN FRE)

Endogenous population growth and the exploitation of renewable resources.

The authors consider a demo-economic model where the economy consists of two sectors ("hunting and farming" and "industry"), and both sectors depend directly or indirectly on the explanation of a renewable resource. The primary sector harvests a renewable resource (fish, corn, or wood) which is used as the input into industrial production, the secondary sector of our economy. Labor is divided up between these two sectors under the assumption of competitive labor markets. A system of two nonlinear differential equations for the resources and the population is studied by phase space analysis. Using the Hopf bifurcation theorem, the authors obtain two different routes to limit cycles and prove numerically the existence of a stable Malthusian limit cycle.

Auricular cartilage repair using cryogel scaffolds loaded with BMP-7-expressing primary chondrocytes.

The loss of cartilage tissue due to trauma, tumour surgery or congenital defects, such as microtia and anotia, is one of the major concerns in head and neck surgery. Recently tissue-engineering approaches, including gene delivery, have been proposed for the regeneration of cartilage tissue. In this study, primary chondrocytes were genetically modified with plasmid-encoding bone morphogenetic protein-7 (BMP-7) via the commercially available non-viral Turbofect vector, with the aim of bringing ex vivo transfected chondrocytes to resynthesize BMP-7 in vitro as they would in vivo. Genetically modified cells were implanted into gelatin-oxidized dextran scaffolds and cartilage tissue formation was investigated in 15 × 15 mm auricular cartilage defects in vivo in 48 New Zealand (NZ) white rabbits for 4 months. The results were evaluated via histology and early gene expression. Early gene expression results indicated a strong effect of exogenous BMP-7 on matrix synthesis and chondrocyte growth. In addition, histological analysis results exhibited significantly better cartilage healing with BMP-7-modified (transfected) cells than in the non-modified (non-transfected) group and as well as the control.

Endogenous population growth may imply chaos.

The authors consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, they obtain numerical results on the qualitative behavior of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies--assumed to be characterized by low and high savings rate respectively--are characterized by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.

Self-generated fertility waves in a non-linear continuous overlapping generations model.

In this paper, Samuelson's simplified version of the Easterlin theory is extended to a continuous-time model with 3 age groups. This approach enables one to apply the qualitative theory of nonlinear differential equations to show the existence of Easterlin-type cycles. In contrast to the discrete time model we obtain information about the period length of the cycle.

A model on the escape from the Malthusian trap.

"We propose a model to capture the escape from the Malthusian trap in the longrun. Our aim is to emphasize the key role of endogenous technological progress--as initiated by population growth and education--for longrun economic development. In addition we stress the importance to consider the level of fertility and mortality as the determinants of economic development and not only the rate of population growth. In particular, we may observe different economic growth rates in countries with the same rate of population growth, but differing levels of birth and death rates."

Capital accumulation, endogenous population growth, and Easterlin cycles.

"In this paper we attempt to explain the occurrence of population cycles in industrialised economies where the birth rate depends on the difference between the actual and the expected consumption rate. This model of an endogenously growing population brings together Easterlin's idea of an adapting aspiration level with the neoclassical optimal growth paradigm. It is shown that in this highly aggregated demo-economic system (i.e., without inclusion of the age structure of a population) swings both in the economic and demographic variables may exist. The reason behind this 'strange' optimal behaviour is identified to be an intertemporal substitution effect between current and future levels of consumption."

[Conservative and semiconservative treatment of calcaneus fractures]. / Die konservative und semikonservative Behandlung der Kalkaneusfraktur.

The functional closed and percutaneous techniques for the treatment of fractures of the os calcis are described. We compare the different classifications, reduction techniques, advantages and disadvantages, as well as the results, after open reduction and internal fixation in an attempt to determine the special indications.

Endogenous growth of population and income depending on resource and knowledge.

PIP: This study focuses on the dynamic, endogenous, nonlinear interactions between the economy, population growth and the environment. Literature on endogenous growth theory was reviewed and the 3-sector demoeconomic model was provided as the analytical framework for the study of sustainable development through the integration of population growth, resource use and economic growth. The model is described in such a way that the labor force is considered as a free migrating variable among three different kinds of employment: the primary sector, which harvests a renewable resource, the secondary or industrial sector, and the tertiary sector, which is responsible for the accumulation of the stock that represents a public good for all three sectors. Presented in this paper is a nontechnical outline of the model that describes the economic, demographic, and environmental interactions considered. Also given are dynamics, market equilibrium and dynamic feedback rules. Furthermore, numerical analysis of the model quantifying the resulting time paths of the variables involved is included. The dynamics are simply the outcome of the nonlinear interactions of the demographic, economic and environmental modules. Numerical studies have also shown that the system variables move with different velocity. Technology and population can generally be regarded as slow moving variables by comparison with resources.^ieng