A Carriage-Structured Model of Meningococcal Meningitis: Backward Bifurcation, Seasonal Recurrence, and the Reach of Conjugate-Vaccine Strategies in the African Meningitis Belt

Background: Epidemic meningococcal meningitis in the African meningitis belt recurs on two timescales: a sharp annual dry-season peak and irregular multi-annual epidemics five to twelve years apart, whose mechanistic origin remains unsettled. Invasive disease is a rare, dead-end outcome of asymptomatic nasopharyngeal carriage, so susceptible–infectious templates misrepresent community transmission. We ask how carriage structure shapes bifurcation, seasonal recurrence, and the reach of conjugate-vaccine strategies. Methods: We formulate a deterministic carriage-structured model in which only carriers transmit, immunity against re-acquisition is leaky, and a conjugate vaccine is imperfect and wanes. We use the Castillo-Chavez–Song centre manifold method, numerical continuation, Floquet and eigenvalue analysis, and scenario simulations of abstract rate- and pulse-type interventions parameterised from published belt ranges. Results: The basic reproduction number R0 is a property of carriage transmission, decoupled to first order from disease incidence. Backward bifurcation at R0=1 is governed by a threshold ε∗ on carriage-blocking immunity; only the untreated fatality hazard and treatment capacity are absent from the local condition. It is impossible without vaccination and, with any positive routine coverage, persists across the plausible coverage range, giving vaccine-induced bistability. Continuation confirms a fold at R0,c≈0.946 (φ=0.12yr−1, weak carriage immunity), but not at baseline immunity. Under seasonal forcing, dynamics converge to a simple annual cycle throughout the region searched; we found no multi-annual recurrence, although damped eigenmodes of the unforced system have periods overlapping the observed interval. Conclusions: Within this deterministic, single-strain model, irregular recurrence likely requires additional structure, with stochastic amplification of damped cycles a natural next step. Whether sustained immunisation eliminates epidemics or merely postpones them may depend on the same carriage-efficacy threshold that governs the bistability result.