A study of a deterministic model for meningitis epidemic

Abstract

Abstract Objectives A compartmental deterministic model that allows immunity from two stages of infection and carriage, and 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 of those susceptible infected to progress directly to infectives in stage I. Methods Two models are used in this study; the generalized model when these proportions are greater than zero (called model 1) and a special case when the proportion is zero (called model 2). The threshold conditions for the spread of carrier and infectives in stage I are derived for both 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 the odds in favor of a carrier over an infective, in transmitting an infection to a susceptible, and the proportion of those susceptible that can progress directly to the infected stage. Results The infection transmission rate, these odds in favor of a carrier, and the carrier conversion rate 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 grow 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). Conclusions Results from the total proportion ever infected suggest that the special case (model 2) can adequately represent, in essence, the generalized model (model 1) for this study.