DOI QR코드

DOI QR Code

AN EXTENSION OF AN ANALYTIC FORMULA OF THE DETERMINISTIC EPIDEMICS MODEL PROBLEM THROUGH LIE GROUP OF OPERATORS

  • Kumar, Hemant ;
  • Kumari, Shilesh
  • Received : 2008.12.20
  • Published : 2010.11.30

Abstract

In the present paper, we evaluate an analytic formula as a solution of Susceptible Infective (SI) model problem for communicable disease in which the daily contact rate (C(N)) is supposed to be varied linearly with population size N(t) that is large so that it is considered as a continuous variable of time t. Again, we introduce some Lie group of operators to make an extension of above analytic formula of the determin-istic epidemics model problem. Finally, we discuss some of its particular cases.

Keywords

an analytic formula of the deterministic epidemics model problem;Kummer hypergeometric function $_1F_1({\cdot})$;Lie group of operators;extension formula

References

  1. H. W. Hethcote, The basic epidemiology models i and ii: expressions for $r_0$ parameter estimation, and applications, 2005.
  2. N. T. J. Baily, The Mathematical Theory of Epidemics, 1st Edition Griffin, London, 1957.
  3. D. J. Daley and J. Gani, Epidemic Modeling: An Introduction, Cambridge University Press, 1999.
  4. A. Erde'lyi et al., Higher Transcendental Functions, Vol. 1, McGraw Hill Book Co., INC, New York, 1953.
  5. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42 (2000), no. 4, 599-653. https://doi.org/10.1137/S0036144500371907
  6. D. C. Joshi, Solution of the deterministic epidemiological model problem in terms of the hypergeometric functions $_0F_1(.)$, Jnanabha 34 (2004), 55-58.
  7. J. N. Kapur, Mathematical Modeling, New International (P) Limited Publishers, New Delhi, 1998.
  8. W. O. Kermack and A. G. McKendrick, Introduction to the mathematical theory of epidemics, part I, Proc. Roy. Soc. Lond. A 115 (1927), 700-721. https://doi.org/10.1098/rspa.1927.0118
  9. W. O. Kermack and A. G. McKendrick, Introduction to the mathematical theory of epidemics, part I, Proc. Roy. Soc. Lond. A 138 (1927), 55-63.
  10. E. D. Rainville, Special Functions, Mac Millan, Chalsea Pub. Co. Bronx, New York, 1971.
  11. H. M. Srivastava and H. L. Manocha, A Treatise On Generating Functions, John Wiley and Sons, New York, 1984.