The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.

The literature on the causation of multiple sclerosis (MS), both genetic and environmental, extends over hundreds of years, with no firm conclusions on the exact role of autoimmunity and lifestyle. The epidemiology of MS was the basis for this review, but with a new, extensive examination of genes pertaining to each disorder, and disease of first, and second, degree relatives of those with MS. The author’s motivation was to discover some relationship between MS, and notable familial conditions, as the heredity of MS is concluded to be 30%, and the disorders had a chronic and/or idiopathic nature. This investigation hoped to further understand the randomness of MS- who acquires it, and what symptoms develop- after the author’s decades of observing several incidences of multiple members developing MS in a single family. Online databases for the human genome were used to link genes to MS, and symptoms, including excessive depression, fatigue and suicide rates, in coordination with linking genes for specific familial conditions including seizures, stroke, mental illness, bowel disorders, and thyroid conditions. Interesting associations were found, notably a cluster of Th2 cytokines, known to cure the animal model of MS, important receptors for neurotransmitters and hormones, a gene specific to Epstein Barr Virus, and potential genes for mitochondrial dysfunction. The results surprised the author, showing polygenic regions of chromosome 2 and 5, especially a cluster at loci 5q31-q33, may be dysregulated. The conclusion agrees with past hypotheses MS results not from a single gene, but from various genes, including those expressed in glial cells. The individual theories to the causation of MS, starting with Charcot may be explained by multiple pathways converging into a single disease outcome. In coordination with a sunlight factor, chromosome 2 appears to mediate the immune system, and inflammation, through ultraviolet radiation producing vitamin D3 in the skin, but additionally through peptides formed in the melanocyte stimulating and concentrating hormone class. The impact of stress in MS could be primary, given the loci of several stress-related and stress-modulated genes on these chromosomes, and calls for more appreciation of, and greater care for, the MS patients’ state of mind.