Share This Article:

Memory and relaxation time of biological systems. an analysis of the effect of abortion legalization in italy

Full-Text HTML Download Download as PDF (Size:465KB) PP. 694-701
DOI: 10.4236/ns.2011.38093    5,430 Downloads   9,389 Views   Citations

ABSTRACT

When a population is affected by a new law there is a lag between the date of application of the law and the response of the population; moreover there is a relaxation time after which a steady state is reached. The time to maximum response and the relaxation time may be approximately estimated from the raw data but the mathematical modeling of the data allows a better estimate. The model, when tested on real data, may be used for future laws or, when appropriately adapted, for other biological systems also. In this note the memory based model is tested on the effects of the 1978 law which legalized the abortions in Italy finding the response and the relaxation time. It is shown that Italian population, after the abortion law, has required about 5 years to have the maximum effect and about 10 years to reach stability. The evolution of women life and the changes of the structure of society in Italy is also discussed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Caputo, M. and Gloria-Bottini, F. (2011) Memory and relaxation time of biological systems. an analysis of the effect of abortion legalization in italy. Natural Science, 3, 694-701. doi: 10.4236/ns.2011.38093.

References

[1] ISTAT. (1997) La fecondità nelle regioni italiane. Analisi per coorti, Anni 1952-1993, Collana Informazioni Noise Rating 35, Istat, Roma.
[2] ISTAT. (1998) La fecondità regionale nel 1994, Collana Informazioni Noise Rating 66, Istat, Roma.
[3] ISTAT. (1999) La fecondità regionale nel 1995, Collana Informazioni Noise Rating 97, Istat, Roma.
[4] ISTAT. (2000) La fecondità regionale nel 1996, Collana Informazioni Noise Rating 11, Istat, Roma.
[5] ISTAT. (2007) Le statistiche del genere, Approfondimenti, Istat, Roma.
[6] Caputo, M. and Kolari, J. (2001) An analytical model of the Fisher equation with memory function, Alternative Perspectives on Finance and Accounting, 1, 1-16.
[7] Smith, D.P. and Keyfitz, N. (1977) Mathematical demography: selected papers, Springer, Berlin.
[8] Keyfitz, N. and Flieger, W. (1990) World population growth and aging: demographic trends in the late twentieth century, the University of Chicago press, Chicago.
[9] Iannelli, M. (1995) Mathematical theory of age structured population dynamics, Giardini Editori e Stampatori, Pisa.
[10] Caputo, M. Nicotra, M. and Gloria-Bottini, F. (2008) Fertility transition: forecast for demography, Human Biology, 80, 359-376. doi.org/10.3378/1534-6617-80.4.359
[11] Caputo, M. (2003) Population self-growth with memory, Proceedings Meeting: Fenomeni di auto-organizzazione nei sistemi biologici, Atti convegni Lincei, Accademia Nazionale dei Lincei, 106, 113-128.
[12] Kiryakova, V. (1999) Generalized fractional calculus and applications, Pitman Research Notes in Mathematics, Longman, Harlow.
[13] Podlubny, I. Fractional differential equations, Academic Press, New York.
[14] Kilbas, A. and Srivastavam, H.M. and Trujillo, J.J. (2006) Theory and applications of fractional differential equations, North Holland Mathem, Studies, 204.
[15] Caputo M. and Plastino, (2004) W. Diffusion in porous layers with memory, Geophysics Journal of International, 158, 385-396. doi.org/10.1111/j.1365-246X.2004.02290.x
[16] Mainardi, F. (1996) Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos, Solitons and Fractals, 7, 1461-1477. doi.org/10.1016/0960-0779(95)00125-5
[17] Baleanu, D. and Agraval, O.P. Fractional, (2006) Hamilton formalism within Caputo’s derivative, Czechoslovak Journal of Physics, 56, 0-11.
[18] K?rnig, H. and Müller, G. (1989) Rheological model and interpretation of postglacial uplift, Geophysical Journal Royal Astronomical Society, 98, 245-253.
[19] Bonilla F.A. and Cushman, J.H. (2000) Role of boundary conditions on convergence and nlocality of solutions to stochastic flow problems in bounded domains, Water Resources Research, 36, 981-997.doi.org/10.1029/1999WR900279
[20] Iaffaldano, P. Caputo, M. and Martino, S. (2006) Experimental and theoretical memory diffusion of water in sand, Hydrology and Earth System Science, 10, 93-100.doi.org/10.5194/hess-10-93-2006
[21] Jacquelin, J. (1984) Use of fractional derivatives to express the properties of energy storage phenomena in electrical networks, Technical Report, Laboratoires Alcatel de Marcoussis.
[22] Le Mehaute, A. and Crépy, G. (1983) Introduction to transfer motion in fractal media: the geometry of kinetics, Solid State Ionic, 9&10, 17-30.
[23] Caputo, M. and Cametti, C. (2008) Diffusion with memory in two cases of biological interest, Journal of Theoretical Biology, 254, 697-703. doi.org/10.1016/j.jtbi.2008.06.021
[24] El Shaed, M.A. (2003) Fractional Calculus Model of Semilunar Heart Valve Vibrations, 2003 International Mathematica Symposium, Chicago.
[25] Naber, M. (2004) Time fractional Schr?dinger equation, Journal of mathematical Physik, 45, 83339-83352.
[26] Caputo, M. and Di Giorgio, G. (2006) Monetary Policy, Memory and Output Dynamics, In: Monetary Policy and Institutions, G. Di Giorgio and F. Neri eds., Essays in memory of M. Arcelli, Luiss University Press, Guido, 165-176.
[27] Cesarone, F. Caputo, M. and Cametti, C. (2005) Memory formalism in the passive diffusion across a biological membrane, Journal Membrane Science, 250, 79-84.doi.org/10.1016/j.memsci.2004.10.018

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.