Open Journal of Statistics, 2016, 6, 1-6 Published Online February 2016 in SciRes. http://www.scirp.org/journal/ojs http://dx.doi.org/10.4236/ojs.2016.61001 How to cite this paper: Nath, D.C., Das, K.K. and Chakraborty, T. (2016) A Modified Epidemic Chain Binomial Model. Open Journal of Statistics, 6, 1-6. http://dx.doi.org/10.4236/ojs.2016.61001 A Modified Epidemic Chain Binomial Model Dilip C. Nath, Kishore K. Das, Tandrima Chakraborty Department of Statistics, Gauhati University, Guwahati, India Received 11 December 2015; accepted 31 January 2016; published 3 February 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract Discrete epidemic models are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contact with a given infective from the same household with closed population. This paper em- phasizes mainly on developing the probabilities of all possible epidemic chains with one intro- ductory case for three, four and five member household. The key phenomenon towards develop- ing this paper is to provide an alternative model of chain binomial model. Keywords Beta Distribution, Infection, Susceptible 1. Introduction The chain binomial models (Bailey, 1975) [1] have met with reasonable accomplishment, when fitted to data on communicable diseases for households, for example diseases like common cold or influenza. Also, Heasman and Reid (1961) [2] have demonstrated that the Reed-Frost chain binomial model can provide an adequate fit to data on outbreaks of the common cold in households of size five. And, by comparing the observed frequencies with the expected frequencies for the total number of cases, they also demonstrate that the stochastic version of the Kermack-McKendrick epidemic model (Bailey, 1975) [1] may provide an even better fit. In the later stage, a detailed comparison of the fits provided by these two models is attempted by Becker(1980) [3] by formulating an epidemic chain model, that is developed by assuming a beta distribution of first kind, for the probability of being infected by contact with a given infective from the same household. This model includes, as a particular case, the epidemic chain model corresponding to the stochastic version of the Kermack-McKendrick epidemic model (Bailey, 1975) [1] and, as a limiting case, the Reed-Frost chain binomial model. The advantages of the more general model are also illustrated with an application to household data for the common cold. Also the as- sumptions made were similar in many ways to those used by Ludwig (1975) [4] in his derivations of the final