Problems of Stability of Dynamic Macroeconomic Models

This paper deals with the problems of stabilizing economic growth using traditional macroeconomic strategies. The goal taken implies a large-scale use of the machinery of the qualitative theory of discrete economic dynamics. A set of economic and mathematical models that take into consideration the specifics of macroeconomic equilibrium in view of neo-Keynesian economics is proposed. It is essential to analyze the residual effect caused by the “dynamic memory” of all previous values in relation to the present moment in time in the investment policy and the consumption structure. When building dynamic models of economic growth of Gross Domestic Product, functional equations of a specific type, such as Volterra difference equations, were obtained. Accordingly, for each of the above functional equations studied, there received a number of inequalities that determine the domains of parametric stability of the equilibrium. Structural constraints of the basic parameters of the multiplier-accelerator model, which can have a significant impact on the distribution of consumption and investment to ensure sustainable growth of national income, are formulated in an explicit form. There indicated conditions for constraining such parameters as the accelerator capacity and marginal propensity to save, which should be taken into account when developing economic and mathematical models for the purposes of forecasting and managing national macroeconomic policies. Graphic illustrations of the obtained solutions to the corresponding difference equations of the national income behavior are presented

Innovation Development of an Enterprise: Modeling Dynamics

At the present stage of economic development, the leading role in ensuring the competitiveness of both an singular enterprise and the country as a whole, as well as in creating conditions for the transition to sustainable development, is played by the successful implementation of the latest scientific developments in production processes, comprehensive support for the strategy of innovative development. The development and implementation of innovations is a complex dynamic process that requires the use of special research methods. Such a method is system dynamics, which makes it possible to take into account the nonlinearity of the impact of innovation on the state of the economy. The paper considers the methodology for building a model for managing innovation processes, taking into account the self-organization of the logistic type. The main danger that can accompany the evolution of innovation processes is the emergence of unacceptable dynamic modes, so one of the tasks of the study was to determine the conditions capable of ensuring the stability of equilibrium states of a complex dynamic system according to the proposed models. The object of research is a complex dynamic system, between the elements of which there is both positive and negative feedback. To build a model of the dynamics of innovation processes, the mathematical apparatus of the theory of differential equations was applied, which made it possible to consider the development of the innovation process in continuous time. With the help of the instrumentarium of nonlinear dynamics, a study of the stability of diffusion of innovations depending on the parameters of the control influence was carried out. The conditions for the transition of the system to a critical state, which may be accompanied by the occurrence of bifurcations and chaos, have been determined. Particular attention was paid to determining the structural stability of the regulated innovation process in the case when both equilibrium positions are close in terms of parameter values. It is expedient to apply the proposed model to solve the problem of innovation management both at the State level and at the level of an individual industry or an individual enterprise. The obtained theoretical conclusions were confirmed through the use of simulation modeling

Key Points in Remote-Controlled Drug Delivery: From the Carrier Design to Clinical Trials

The increased research activity aiming at improved delivery of pharmaceutical molecules indicates the expansion of the field. An efficient therapeutic delivery approach is based on the optimal choice of drug-carrying vehicle, successful targeting, and payload release enabling the site-specific accumulation of the therapeutic molecules. However, designing the formulation endowed with the targeting properties in vitro does not guarantee its selective delivery in vivo. The various biological barriers that the carrier encounters upon intravascular administration should be adequately addressed in its overall design to reduce the off-target effects and unwanted toxicity in vivo and thereby enhance the therapeutic efficacy of the payload. Here, we discuss the main parameters of remote-controlled drug delivery systems: (i) key principles of the carrier selection; (ii) the most significant physiological barriers and limitations associated with the drug delivery; (iii) major concepts for its targeting and cargo release stimulation by external stimuli in vivo. The clinical translation for drug delivery systems is also described along with the main challenges, key parameters, and examples of successfully translated drug delivery platforms. The essential steps on the way from drug delivery system design to clinical trials are summarized, arranged, and discussed

Degradation of Hybrid Drug Delivery Carriers with a Mineral Core and a Protein–Tannin Shell under Proteolytic Hydrolases

Hybrid carriers with the mineral CaCO3/Fe3O4 core and the protein–tannin shell are attractive for drug delivery applications due to reliable coupling of anticancer drugs with protein–tannin complex and the possibility of remote control over drug localization and delivery by the external magnetic field. This study aims to elucidate the mechanisms of drug release via enzymatic degradation of a protein–tannin carrier shell triggered by proteolytic hydrolases trypsin and pepsin under physiological conditions. To do this, the carriers were incubated with the enzyme solutions in special buffers to maintain the enzyme activity. The time-lapse spectrophotometric and electron microscopy measurements were carried out to evaluate the degradation of the carriers. It was established that the protein–tannin complex demonstrates the different degradation behavior depending on the enzyme type and buffer medium. The incubation in trypsin solution mostly resulted in the protein shell degradation. The incubation in pepsin solution did not affect the protein component; however, the citric buffer stimulates the degradation of the mineral core. The presented results allow for predicting the degradation pathways of the carriers including the release profile of the loaded cargo under physiological conditions. The viability of 4T1 breast cancer cells with mineral magnetic carriers with protein–tannin shells was investigated, and their movement in the fields of action of the permanent magnet was shown

Time-Delayed Anticancer Effect of an Extremely Low Frequency Alternating Magnetic Field and Multimodal Protein–Tannin–Mitoxantrone Carriers with Brillouin Microspectroscopy Visualization In Vitro

The effect of an extremely low frequency alternating magnetic field (ELF AMF) at frequencies of 17, 48, and 95 Hz at 100 mT on free and internalized 4T1 breast cancer cell submicron magnetic mineral carriers with an anticancer drug, mitoxantrone, was shown. The alternating magnetic field (100 mT; 17, 48, 95 Hz; time of treatment—10.5 min with a 30 s delay) does not lead to the significant destruction of carrier shells and release of mitoxantrone or bovine serum albumin from them according to the data of spectrophotometry, or the heating of carriers in the process of exposure to magnetic fields. The most optimal set of factors that would lead to the suppression of proliferation and survival of cells with anticancer drug carriers on the third day (in comparison with the control and first day) is exposure to an alternating magnetic field of 100 mT in a pulsed mode with a frequency of 95 Hz. The presence of magnetic nanocarriers in cell lines was carried out by a direct label-free method, space-resolved Brillouin light scattering (BLS) spectrometry, which was realized for the first time. The analysis of the series of integrated BLS spectra showed an increase in the magnetic phase in cells with a growth in the number of particles per cell (from 10 to 100) after their internalization. The safety of magnetic carriers in the release of their constituent ions has been evaluated using atomic absorption spectrometry