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.

翻译：采用考虑(1)两阶段感染与携带状态免疫获得机制,以及(2)疾病致死效应的房室确定性模型,研究封闭人群脑膜炎流行过程的动力学特征。该模型允许携带者与感染者对易感人群传播感染率的差异,并推广至允许一定比例({\phi})的易感感染者直接进入第一阶段感染状态。本研究同时使用两种模型,推导出两类模型下携带者与第一阶段感染者传播的阈值条件,并基于下一代矩阵导出的再生数进行敏感性分析。研究展示了不同参数与阈值条件下的病例-携带者比率剖面图,以及受{\epsilon}和{\phi}影响的累计感染总人数曲线图。感染传播率(\b{eta})、携带者相对于感染者的传播优势比({\epsilon})以及携带者向第一阶段感染者转化的转化率({\phi})被识别为任何干预控制策略应关注的关键参数。病例-携带者比率剖面图表明,在报告病例数增长至流行水平之前存在一个临界病例-携带者比率,同时提供流行病学背景的可视化证据——包括旱季末期的流行性发病与雨季期间的地方性发病。累计感染比例分析结果表明,当取{\phi}=0时获得的简化模型能本质上充分代表本研究中的推广模型。