in this paper at rst, a history of mathematical models is given.next, some basic information about random variables, stochastic processesand markov chains is introduced. as follows, the entropy for a discrete timemarkov process is mentioned. after that, the entropy for sis stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

In this paper at rst, a history of mathematical models is given.Next, some basic information about random variables, stochastic processesand Markov chains is introduced. As follows, the entropy for a discrete timeMarkov process is mentioned. After that, the entropy for SIS stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

Network security is very important when sending confidential data through the network. Cryptography is the science of hiding information, and a combination of cryptography solutions with cognitive science starts a new branch called cognitive cryptography that guarantee the confidentiality and integrity of the data. Brain signals as a biometric indicator can convert to a binary code which can be...

Let X be a discrete random variable with support S and f : S → S′ be a bijection. Then it is wellknown that the entropy of X is the same as the entropy of f(X). This entropy preservation property has been well-utilized to establish non-trivial properties of discrete stochastic processes, e.g. queuing process [1]. Entropy as well as entropy preservation is well-defined only in the context of pur...

Shannon entropy of a probability measure P , defined as − ∫ X dP dμ ln dP dμ dμ on a measure space (X,M, μ), is not a natural extension from the discrete case. However, maximum entropy (ME) prescriptions of Shannon entropy functional in the measure-theoretic case are consistent with those for the discrete case. Also it is well known that Kullback-Leibler relative entropy can be extended natural...