  A compartmental deterministic model that allows (1) immunity from two stages
of infection and carriage, and (2) disease induced death, is used in studying
the dynamics of meningitis epidemic process in a closed population. It allows
for difference in the transmission rate of infection to a susceptible by a
carrier and an infective. It is generalized to allow a proportion ({\phi}) of
those susceptibles infected to progress directly to infectives in stage I. Both
models are used in this study. The threshold conditions for the spread of
carrier and infectives in stage I are derived for the two models. Sensitivity
analysis is performed on the reproductive number derived from the next
generation matrix. The case-carrier ratio profile for various parameters and
threshold values are shown. So also are the graphs of the total number ever
infected as influenced by {\epsilon} and {\phi}. The infection transmission
rate (\b{eta}), the odds in favor of a carrier, over an infective, in
transmitting an infection to a susceptible ({\epsilon}) and the carrier
conversion rate ({\phi}) to an infective in stage I, are identified as key
parameters that should be subject of attention for any control intervention
strategy. The case-carrier ratio profiles provide evidence of a critical
case-carrier ratio attained before the number of reported cases grows to an
epidemic level. They also provide visual evidence of epidemiological context,
in this case, epidemic incidence (in later part of dry season) and endemic
incidence (during rainy season). Results from total proportion ever infected
suggest that the model, in which {\phi}=0 obtained, can adequately represent,
in essence, the generalized model for this study.
