The population deterministic model agrees with the expected value of the general
solution of the probability generating function of the birth-death process as it has been
developed successfully to model the behavior of stochastic populations. These models
describe population sizes and their dynamics through the birth-death formulation
assuming the net migration is zero. A representation for the partial differential
difference equation and the probability generating function of a birth-death process
with a polynomial transition rates are derived and can be used for transitional
probabilities of the population. The form of the mean or the expected value derived
for constant birth and death parameters was applied to the real data of the population
of Rwanda to generate the backward and onwards estimates. With the methods
employed, it has been shown that the first occupants of the current sized Rwanda
started in the 15th century with assumption of a constant population growth rate of 3%
and applied to the referenced population size reported in 1950 with another
assumption that, there was no catastrophic event with intension to extinguish the
population. The analysis is extended to include the onward estimates and the effect of
Genocide against Tutsi in 1994 was also highlighted to show the level of perturbation
on the population growth. With Genocide effect, the population of Rwanda presented
a decline rate of almost 0.4% (or population growth rate =-0.4%) in the beginning of
1995 by which the death rate reached a high pick of 363/1000 (
?
4/10) and birth rate
reduced considerably and reached to 6/1000 populations.