  In Part 1, we introduced a stochastic model of an infectious disease, based
on the BDI (birth and death with immigration) process. We showed that random
processes defined by this model can capture the essence of the stochastic,
often erratic, behavior of the infection process. The most significant finding
was that it is negative binomial distributed with small r, hence it is
geometrically distributed with an exceedingly long tail. This leads to a much
larger disparity in the epidemic patterns than has been known to the modeling
community. In Part 2 we conduct simulation experiments by implementing an
event-driven simulator. Several independent runs are presented to verify the
findings reported in Part 1. The enormous variations among the sample paths
obtained from several consecutive and independent runs with statistically
identical conditions confirm our analysis. Note that the epidemic pattern that
we observe is merely one sample path taken out of infinitely many paths. Thus,
one such path cannot represent the ensemble of the underlying random process.
By plotting the simulation runs in the semi-log scale, we can see that the
probabilistic chances in the early phase of the infection process determine the
behavior of the process. Once the process has reached a considerable number,
the weak law of large numbers sets in, and the process behaves less erratically
than in the early phase. One important implication of our findings is that it
would be a futile effort to attempt to identify all plausible causes of the
epidemic patterns. Mere luck may play a more significant role than most people
believe. It would be worth remarking that the BDI process might be applicable
to explain the disparity in wealth among individuals of similar earning power,
expenditure, and investment portfolio.
