Mathematical analysis of the dynamical transmission of Neisseria meningitidis serogroup A

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 ${\mathcal{R}}_0$ 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 ${\mathcal{R}}_0\le \xi <1$, the DFE is globally asymptotically stable while when $\xi \le {\mathcal{R}}_0<1$, 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.

Keywords:

• Mathematical models
• dynamical systems
• Neisseria meningitidis serogroup A
• stability

AMS subject classifications:

• 34A34
• 34D23
• 34D40
• 92D30

Disclosure statement

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