AN EXTENSION OF AN ANALYTIC FORMULA OF THE DETERMINISTIC EPIDEMICS MODEL PROBLEM THROUGH LIE GROUP OF OPERATORS
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
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.
참고문헌 (11)
- N. T. J. Baily, "The Mathematical Theory of Epidemics, 1st Edition" (1957), Griffin
- D. J. Daley, "Epidemic Modeling: An Introduction" (1999), Cambridge University Press
- A. Erde'lyi, "Higher Transcendental Functions, Vol. 1" (1953), McGraw Hill Book Co., INC
- H. W. Hethcote, "The mathematics of infectious diseases", SIAM Rev., 42(4), pp.599~653 (2000)
- H. W. Hethcote, "The basic epidemiology models i and ii: expressions for r0 parameter estima-tion, and applications", ~ (2005)
- D. C. Joshi, "Solution of the deterministic epidemiological model problem in terms of the hypergeometric functions 0F1(·)", Jňaňabha, 34, pp.55~58 (2004)
- J. N. Kapur, "Mathematical Modeling" (1998), New International (P) Limited Publishers
- W. O. Kermack, "Introduction to the mathematical theory of epidemics, part I", Proc. Roy. Soc. Lond. A, 115, pp.700~721 (1927)
- W. O. Kermack, "Introduction to the mathematical theory of epidemics, part I", Proc. Roy. Soc. Lond. A, 138, pp.55~63 (1927)
- E. D. Rainville, "Special Functions" (1971), Mac Millan, Chalsea Pub. Co.
- H. M. Srivastava, "A Treatise On Generating Functions" (1984), John Wiley and Sons