Bernoulli, D. (1766) Essai d’une nouvelle analyse de la mortalite causee par la petite verole. Mem. Math. Phys. Acad. Roy. Sci., Paris (1766) 1. (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, 1995, p. 1.)

has been cited by the following article:

• TITLE: A Modified Epidemic Chain Binomial Model (MECBM) and Its 2,3-Introductory Probabilities

  AUTHORS: Dilip C. Nath, Kishore K. Das, Tandrima Chakraborty

  KEYWORDS: Beta Distribution, Infection, Susceptible

  JOURNAL NAME: Open Journal of Statistics, Vol.7 No.2, April 24, 2017

  ABSTRACT: Through the ages, human life and happiness are affected much by wide spread diseases, an unpredictable phenomenon. And infectious disease spread is one of the most unsolvable problems. How infection evolves, how it spreads from person to person and mainly which pattern it follows are some questions which are always unanswerable. Out of many techniques, discrete epidemic models like the chain binomial model are ones which 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 infection from the same household with closed population. This paper emphasized mainly on developing the probabilities of all possible epidemic chains with two introductory cases for three-, four- and five-member household and three introductory cases for four- and five-member household. The key phenomenon towards developing this paper was to provide an extension of the modified chain binomial model and its possible probabilities.