Non-Markov stochastic dynamics of real epidemic process of respiratory infections

Physica A: Statistical Mechanics and its Applications

Volumn 331, Issue 1-2, 2004, Pages 300-318

  Yulmetyev, Renat M ^a   Emelyanova, Natalya A ^a   Demin, Sergey A ^a   Gafarov, Fail M ^a   Hänggi, Peter ^b   Yulmetyeva, Dinara G ^c  

^a KAZAN FEDERAL UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF AUGSBURG   (Germany)

^c Republican Clinical Psychiatric Hospital   (Russian Federation)

Author keywords

Complex systems; Discrete non Markov processes; Grippe and Acute respiratory track infections; Stochastic processes; Time series analysis

Indexed keywords

CORRELATION METHODS; EPIDEMIOLOGY; KINETIC THEORY; LARGE SCALE SYSTEMS; MARKOV PROCESSES; RANDOM PROCESSES; TIME SERIES ANALYSIS; TOPOLOGY;

DEGREE OF RANDOMNESS; SOCIAL NETWORKS;

PULMONARY DISEASES;

EID: 0242607015     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2003.09.023     Document Type: Article

References (43)

1. Newman M.E. Spread of epidemic disease on networks. Phys. Rev. E. 66:2002;016 128.
2. Pastor-Satorras R., Vespignani A. Epidemic dynamics in finite size scale-free networks. Phys. Rev. E. 65:2002;035 108.
3. Grassberger P., Chate H., Rousseau G. Spreading in media with long-time memory. Phys. Rev. E. 55:1997;2488.
4. Ipsen M., Mikhailov A. Evolutionary reconstruction of networks. Phys. Rev. E. 66:2002;046 109.
5. Amaral L.A., Scala A., Barthelemy M., Stanley H.E. Classes of small-world networks. Proc. Natl. Acad. Sci. USA. 97:2000;11 149.
6. Barthelemy M., Amaral L.A.N. Small-world networks. evidence for a crossover picture Phys. Rev. Lett. 82:1999;3180.
7. Mossa S., Barthelemy M., Stanley H.E., Amaral L.A.N. Truncation of power law behavior in scale-free network models due to information filtering. Phys. Rev. Lett. 88:2002;138 701.
8. Camacho J., Guimera R., Amaral L.A.N. Analytical solution of a model for complex food webs. Phys. Rev. E. 65:2002;030901(R).
9. Burk R.F., Schaffner W., Koenig M.G. Severe influenza virus pneumonia in the pandemic of 1968-1969. Arch. Intern. Med. 127:1971;1122.
10. S.D. Collins, J. Lehman, Excess deaths from influenza and pneumonia and from important chronic diseases during epidemic periods 1918-1951, Public Health Monographs, Vol. 10, 1953, p. 1.
11. Schwarzmann S.W., Adler J.L., Sullivan R.J., Marine W.M. Bacterial pneumonia during the Hong Kong influenza epidemic of 1968-1969. Arch. Intern. Med. 127:1971;1037.
12. Stuart-Harris C.H. Virus of the 1968 Influenza pandemic. Nature. 225:1970;850.
13. Peng C.K., Buldyrev S.V., Goldberger A.L., Havlin S., Simons M., Stanley H.E. Finite size effects on long-range correlations. implications for analyzing DNA sequences Phys. Rev. E. 47:1993;3730.
14. Peng C.K., Havlin S., Stanley H.E., Goldberger A.L. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 6:1995;82.
15. Amaral L.A.N., Buldyrev S.V., Havlin S., Salinger M.A., Stanley H.E. Power law scaling for a system of interacting units with complex internal structure. Phys. Rev. Lett. 80:1998;1385.
16. Ashkenazy Y., Ivanov P.Ch., Havlin S., Peng C.K., Goldberger A.L., Stanley H.E. Magnitude and sign correlations in heartbeat fluctuation. Phys. Rev. Lett. 86:2001;1900.
17. Amaral L.A.N., Ivanov P.Ch., Aoyagi N., Hidaka I., Tomono S., Goldberger A.L., Stanley H.E., Yamamoto Y. Behavioral-independent features of complex heartbeat dynamics. Phys. Rev. Lett. 86:2001;6026.
18. Schulte-Frohlinde V., Ashkenazy Y., Ivanov P.Ch., Glass L., Goldberger A.L., Stanley H.E. Noise effects on the complex patterns of abnormal heartbeats. Phys. Rev. Lett. 87:2001;068 104.
19. Chen Z., Ivanov P.Ch., Hu K., Stanley H.E. Effect of nonstationarities on detrended fluctuation analysis. Phys. Rev. E. 65:2002;041 107.
20. Ivanov P.Ch., Amaral L.A.N., Goldberger A.L., Havlin S., Rosenblum M.G., Stanley H.E., Struzik Z.R. From. 1/f noise to multifractal cascades in heartbeat dynamics Chaos. 11:2001;641.
21. Webster R.G., Bean W.J., Gorman T.O. Evolution and ecology of influenza A viruses. Microbiology. 56:1992;159.
22. Scheiblauer H., Reinacher M., Tashiro M., Rott R. Interactions between bacteria and influenza A virus in the development of influenza pneumonia. J. Infect. Dis. 166:1992;783.
23. LaForce F.M., Nichol K.L., Cox N.J. Influenza. virology, epidemiology, disease, and prevention Am. J. Prev. Med. 10:1994;31.
24. Hokanen P.O., Keistinen T., Kivela S.-L. Factors associated with influenza coverage among elderly. role of health care personnel Public Health. 110:1996;163.
25. Ghendon Y. Influenza vaccines. a main problem in control of pandemics Eur. J. Epidemiol. 10:1994;485.
26. Snacken R., Manuguerra J.C., Taylor P. European influenza surveillance scheme on the internet. Method Inf. Med. 37:1998;266.
27. Kuperman M., Abramson G. Small world effect in an epidemiological model. Phys. Rev. Lett. 86:2001;2909.
28. Warren C.P., Sander L.M., Sokolov I.M. Firewalls, disorder, and percolation in epidemics. cond-mat/0106450. v1:2001;1.
29. Albert R., Barabasi A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74:2002;47.
30. Rozenfeld A.F., Cohen R., ben-Avraham D., Havlin S. Scale-free networks on lattices. Phys. Rev. Lett. 89:2002;218 701.
31. Zhu J.-Y., Zhu H. Introducing small-world network effects to critical dynamics. Phys. Rev. E. 67:2003;026 125.
32. Newman M.E. Mixing patterns in networks. Phys. Rev. E. 67:2003;026 126.
33. Newman M.E. Assortative mixing in networks. Phys. Rev. Lett. 89:2002;208 701.
34. Vazguez A., Weigt M. Computational complexity arising from degree correlations in networks. Phys. Rev. E. 67:2003;027 101.
35. Ravasz E., Barabasi A.-L. Hierarchical organization in complex networks. Phys. Rev. E. 67:2003;026 112.
36. Klemm K., Equiluz V.M., Toral R., Miguel M.S. Nonequilibrium transitions in complex networks. a model of social interaction Phys. Rev. E. 67:2003;026 120.
37. Filipe J.A.N., Gilligan C.A. Solution of epidemic models with quenched transients. Phys. Rev. E. 67:2003;021 906.
38. Yulmetyev R.M., Hänggi P., Gafarov F.M. Stochastic dynamics of time correlation in complex systems with discrete current time. Phys. Rev. E. 62:2000;6178.
39. Yulmetyev R.M., Gafarov F.M., Hänggi P., Nigmatullin R.R., Kayumov Sh. Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis. Phys. Rev. E. 64:2001;066 132.
40. Yulmetyev R.M., Hänggi P., Gafarov F. Quantification of heart rate variability by discrete nonstationary non-Markov stochastic processes. Phys. Rev. E. 65:2002;046 107.
41. Yulmetyev R.M., Gafarov F.M., Yulmetyeva D.G., Emelyanova N.A. Intensity approximation of random fluctuation in complex systems. Physica A. 303:2002;427.
42. Yulmetyev R., Emelyanova N., Hänggi P., Gafarov F., Prokhorov A. Long-range memory and non-Markov statistical effects in human sensorimotor coordination. Physica A. 316:2002;361.
43. Yulmetyev R., Demin S., Emelyanova N., Gafarov F., Hänggi P. Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients. Physica A. 319:2003;432.