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 emphasizes mainly on developing the probabilities of all possible epidemic chains with one introductory case for three, four and five member household. The key phenomenon towards developing this paper is to provide an alternative model of chain binomial model.
Highlights
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
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
A more detailed comparison of the fits provided by the two models namely, Reed-Frost chain binomial model and the stochastic version of the Kermack-McKendrick epidemic model, is not attempted by Becker for any epidemic chain model developed by assuming any other kind of Beta distribution for the probability of being infected by contacting with a given infective from the same household
Summary
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. 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. A more detailed comparison of the fits provided by the two models namely, Reed-Frost chain binomial model and the stochastic version of the Kermack-McKendrick epidemic model, is not attempted by Becker for any epidemic chain model developed by assuming any other kind of Beta distribution for the probability of being infected by contacting with a given infective from the same household. In order to make a more exhaustive comparison, we formulate a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contacting with a given infective from the same household
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