  We present a class of SEIR Markov chain models for infectious diseases
observed over discrete time in a random human population living in a closed
environment. The population changes over time through random births, deaths,
and transitions between states of the population. The SEIR models consist of
random dynamical equations for each state (S, E, I and R) involving driving
events for the process. We characterize some special types of SEIR Markov chain
models in the class including: (1) when birth and death are zero or non-zero,
and (2) when the incubation and infectious periods are constant or random. A
detailed parameter estimation applying the maximum likelihood estimation
technique and expectation maximization algorithm are presented for this study.
Numerical simulation results are given to validate the epidemic models.
