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Original Articles

Mathematical analysis of the dynamical transmission of Neisseria meningitidis serogroup A

, , &
Pages 2409-2434 | Received 08 Jan 2016, Accepted 06 Jul 2016, Published online: 08 Feb 2017
 

ABSTRACT

We formulate a deterministic mathematical model for the dynamical transmission of Neisseria meningitidis serogroup A (NmA) within a community. The model incorporates the key epidemiological and biological features of NmA such as the vaccine efficacy and the waning of both vaccine-induced and recovery-induced immunity . We provide a theoretical study of the model. We compute the disease-free equilibrium (DFE) and derive the basic reproduction number R0 that determines the extinction and the persistence of the disease. We compute equilibria and study their stability. More precisely, we show that there exists a threshold parameter ξ such that when R0ξ<1, the DFE is globally asymptotically stable while when ξR0<1, the model exhibits the phenomenon of backward bifurcation on a feasible region. We also investigate the impact of imperfect mass vaccination with waning immunity within a community. The theory is supported by numerical simulations, which further suggest that the control of the epidemic of NmA pass through a combination of a large coverage vaccination of young susceptible individuals and the production of a vaccine with a high level of efficacy. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on meningitis outbreak.

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Disclosure statement

No potential conflict of interest was reported by the author(s).

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