Abstract
<jats:p>Epidemic meningococcal meningitis in the African meningitis belt recurs on two superimposed timescales: a sharp annual dry-season peak and irregular multi-annual epidemics separated by five to twelve years. Because invasive disease is a rare, epidemiologically dead-end outcome of asymptomatic nasopharyngeal carriage, transmission models built on the standard susceptible-infectious template misrepresent the driving process. We formulate a deterministic carriage-structured model in which only carriers transmit, immunity against carriage re-acquisition is leaky, and a conjugate vaccine protects imperfectly and wanes. We show analytically that the basic reproduction number \( R_0 \) is a property of carriage transmission and is decoupled, to first order, from disease incidence, so that reproduction numbers inferred from case notifications estimate the wrong quantity. Using the Castillo-Chavez-Song centre manifold method, we derive, in closed form, the condition for backward bifurcation and prove that it is governed by a threshold \( \varepsilon^\ast \) on carriage-blocking immunity, not by vaccine leakiness or by case-management capacity: the invasive-disease compartment is provably absent from the bifurcation condition. Under seasonal forcing we characterize, through Floquet analysis and two-parameter continuation, the region of immunity-waning and seasonal-amplitude space in which multi-annual recurrence arises, confirming that annual forcing alone cannot generate it. A scenario analysis calibrated to published belt parameter ranges quantifies the burden averted by routine infant immunisation, catch-up campaigns, and improved carriage efficacy, and shows that whether sustained immunisation eliminates epidemics or merely postpones them depends on the same carriage-efficacy threshold that governs bistability.</jats:p>