On a Versatile Stochastic Growth Model

References

• R. M. Anderson and R. M. May , Infectious Diseases of Humans: Dynamics and Control , Oxford University Press , 1991
   Google Scholar
• S. Arif , PhD Thesis , Department of Computer Science, Old Dominion University , 2012 , http://www.cs.odu.edu/~sarif/
   Google Scholar
• N. T. J. Bailey , The Elements of Stochastic Processes with Applications to the Natural Sciences , John Wiley , New York , 1964
   Google Scholar
• Bass , F. M. 1969 . A new product growth for model consumer durables . Management Science , 15 ( 5 ) : 215 – 227 .
   Web of Science ®Google Scholar
• Bass , F. M. 2004 . A new product growth for model consumer durables . Management Science , 50 ( 12 ) : 1825 – 1832 .
   Google Scholar
• Bass , F. M. 2004 . Comments on “A New Product Growth for Model Consumer Durables” . Management Science , 50 ( 12 ) : 1833 – 1840 .
   Google Scholar
• D. Bernoulli , Essai dune nouvelle analyse de la mortalit cause par la petite vrole., Mm. Math. Phys. Acad. Roy. Sci., Paris, 1766. (Reprinted in: L.P. Bouckaert, B.L. van der Waerden (Eds.), Die Werke von Daniel Bernoulli, Bd. 2 Analysis und Wahrscheinlichkeitsrechnung, Birkhauser, Basel, 1982, p. 235. English translation entitled An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it in: L. Bradley, Smallpox Inoculation: An Eighteenth Century Mathematical Controversy, Adult Education Department, Nottingham, 1971, p. 21. Reprinted in: S. Haberman, T.A. Sibbett (Eds.) History of Actuarial Science, vol. VIII, Multiple Decrement and Multiple State Models , William Pickering , London , p. 1 . 2005
   Google Scholar
• Billings , L. and Schwartz , I. B. 2005 . A unified prediction of computer virus spread in connected networks . Physics Letters, A , 297 : 261 – 262 .
   Google Scholar
• Boland , P. J. and Singh , H. 2005 . A birth-process approach to Moranda's geometric software-reliability model . IEEE Transactions on Reliability , 22 ( 2 ) : 168 – 174 .
   Google Scholar
• Carlson , T. 1913 . Ueber Geschwindigkeit und Grsse der Hefevermehrung in Wrzei . Biochem. Z. , 57 : 313 – 334 .
   Google Scholar
• Daley , D. J. and Gani , J. 1999 . Epidemic Modelling: An Introduction , Cambridge : Cambridge University Press .
   Google Scholar
• J. Davidson , On the ecology of the growth of the sheep population in South Australia , Transactions of the Royal Society of Australia , 141 – 148 2005
   Google Scholar
• Doering , C. , Sargsyan , K. and Sander , L. 2005 . Extinction times for birth-death processes: exact results, continuum asymptotics and the failure of the Fokker-Planck approximation . Multiscale Modeling and Simulation , 39 ( 2 ) : 283 – 299 .
   Google Scholar
• Feller , W. 1939 . Die Grundlagen der Volterrashen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretiker Behandlung . Acta Biotheoretica , 5 : 11 – 40 .
   Google Scholar
• W. H. Furry , On fluctuation phenomena in the passage of high energy electrons through lead , The Physical Review , 52 , 569 – 581 .
   Google Scholar
• F. Galton , Natural Inheritance , MacMillan and Co. , London , 1889
   Google Scholar
• B. Gompertz , On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies , Philosophical Transactions of the Royal Society of London , 115 , 513 – 583 1825
   Google Scholar
• T. E. Harris , The Theory of Branching Processes , Springer-Verlag, Berlin , 1963
   Google Scholar
• Gamito , S. 1998 . Growth models and their use in ecological modelling: an application to a fish population . Ecological Modelling , 113 ( 1-3 ) : 83 – 94 .
   Web of Science ®Google Scholar
• Hethcote , H. W. 2000 . The mathematics of infectious diseases . SIAM Review , 42 ( 4 ) : 599 – 652 .
   Web of Science ®Google Scholar
• L'Homme , C. , Bizeau , C. , Arthaud , J. F. and Galzy , P. 1980 . Design of a growth model for yeast . PubMed , 25 ( 5 ) : 418 – 423 .
   Google Scholar
• M. Iosifescu and P. Tautu , Stochastic processes and applications in biology and medicine , 1 , Springer- Verlag, Berlin . 1973
   Google Scholar
• M. Iosifescu and P. Tautu , Stochastic processes and applications in biology and medicine , 2 , Springer- Verlag, Berlin . 1973
   Google Scholar
• A. J. Lotka , Theorie Analytique des Associations Biologiques , Actualities Scientifiques et Industrielles , Hermann , Paris , 1939
   Google Scholar
• Jonsson , H. and Levchenko , A. 2005 . An explicit spatial model of yeast microcolony . SIAM Society for Industrial and Applied Mathematics , 3 ( 2 ) : 346 – 361 .
   Google Scholar
• M. J. Keeling , Ecology, Genetics and Evolution , Elsevier , New York , 2004
   Google Scholar
• Kolmogorov , A. and Dimitriev , N. A. 1947 . Branching stochastic processes . Doklady Akademii Nauk SSSR , 56 : 5 – 8 .
   Google Scholar
• T. R. Malthus , An Essay on the Principle of Population, 1803; edited with an introduction by Geoffrey Gilbert . Oxford University Press 1993
   Google Scholar
• J. D. Murray , Mathematical Biology: I. An Introduction . Springer-Verlag , Berlin , 2003
   Google Scholar
• Nicholas , B. 2009 . Essential Mathematical Biology , 235 – 249 . Berlin : Springer-Verlag .
   Google Scholar
• Norton , L. A. 1988 . A Gompertzian model of human breast cancer growth . Cancer Research , 48 : 7067 – 7071 .
   PubMed Web of Science ®Google Scholar
• Obcemea , C. 2006 . Chaotic Dynamics of Tumor Growth and Regeneration , 349 – 354 . Berlin : Springer-Verlag .
   Google Scholar
• Okubo , A. 1980 . Diffusion and Ecological Problems: Mathematical Models , Berlin : Springer-Verlag .
   Google Scholar
• Olariu , S. and Nickerson , J. 2008 . A probabilistic model of integration . Decision Support Systems , 45 ( 4 ) : 746 – 763 .
   Web of Science ®Google Scholar
• E. Parzen , Stochastic Processes , Holden-Day, Inc. , San Francisco , 1962 .
   Google Scholar
• Pearl , R. 1927 . The growth of populations . Quarterly Review of Biology , 2 : 532 – 548 .
   Google Scholar
• Pfeifer , D. 1982 . The structure of elementary pure-birth processes . Journal of Applied Probability , 19 ( 3 ) : 664 – 667 .
   Web of Science ®Google Scholar
• E.P. Virene , Reliability growth and its upper limit , Proceedings of 1968 Annual Symposium on Reliability , 265 – 270 .
   Google Scholar
• Verhulst , P. F. 1838 . Notice sur la loi que la population poursuit dans son accroissement . Correspondance mathmatique et physique , 10 : 113 – 121 .
   Google Scholar
• A. Wood , Software Reliability Growth Models: Assumptions vs. Reality , Eighth International Symposium on Software Reliability Engineering , 1997
   Google Scholar
• Watson , H.W. and Galton , F. 1874 . On the probability of extinction of families . Journal of the Antrolological Institute of Great Britain and Ireland , 4 : 138 – 144 .
   Google Scholar
• A. Sharov , Quantitative population ecology online lecture notes, Department of Entomology, Virginia Tech, Blacksburg VA , http://home.comcast.net/~sharov/PopEcol/lec5/exp.html
   Google Scholar
• A. Wood , Software reliability growth models , Technical Report , 96.1, Tandem Computer Corporate Information Center , 1996
   Google Scholar
• Z. Yan , Prediction model based on Gompertz function , Proc. 2nd IEEE International Conference on Broadband Network & Multimedia Technology , 893-898, 18-20 Oct . 2009
   Google Scholar
• G. Yan , S. Rizvi and S. Olariu , A time-critical information diffusion model in vehicular ad-hoc networks , Proc. ACM MoMM'2010 , Paris , , France 2010 November
   Google Scholar
• Yule , G. U. 1924 . A mathematical theory of evolution, based on the theory of Dr. J. C. Willis . Philosophical Transactions of the Royal Society of London , 213 : 21 – 87 .
   Google Scholar