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Bull. Korean Math. Soc. 2010; 47(6): 1131-1138

Printed November 1, 2010

https://doi.org/10.4134/BKMS.2010.47.6.1131

Copyright © The Korean Mathematical Society.

An extension of an analytic formula of the deterministic epidemics model problem through Lie group of operators

Hemant Kumar and Shilesh Kumari

D.A-V. P.G. College, D.A-V. P.G. College

Abstract

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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 deterministic 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

MSC numbers: 22E40, 33C05, 33C80, 33C90, 33C99

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