[Approximation to the dynamics of meningococcal meningitis through dynamic systems and time series]

Meningococcal meningitis is subjected to epidemiological surveillance due to its severity and the occasional presentation of epidemic outbreaks. This work analyses previous disease models, generate new ones and analyses monthly cases using ARIMA time series models. The results show that disease dynamics for closed populations is epidemic and the epidemic size is related to the proportion of carriers and the transmissiveness of the agent. In open populations, disease dynamics depends on the admission rate of susceptible and the relative admission of infected individuals. Our model considers a logistic populational growth and carrier admission proportional to populational size, generating an endemic dynamics. Considering a non-instantaneous system response, a greater realism is obtained establishing that the endemic situation may present a dynamics highly sensitive to initial conditions, depending on the transmissiveness and proportion of susceptible individuals in the population. Time series model showed an adequate predictive capacity in terms no longer than 10 months. The lack of long term predictability was attributed to local changes in the proportion of carriers or on transmissiveness that lead to chaotic dynamics over a seasonal pattern. Predictions for 1995 and 1996 were obtained.