Bifurcation analysis in a serogroup a meningococcal infection model

Abstract

A mathematical model is formulated that enables the understanding of the dynamics of the transmission of serogroup A meningococcal (MenA) infection. We provide the theoretical analysis of the model. We compute the basic reproduction number R0 and shows that the outcome of the disease depends on a threshold parameter ξ. More precisely, we show that when R0 ≤ ξ, the disease-free equilibrium is globally asymptotically stable, while when ξ ≤ R0 ≤ 1, the model exhibits the phenomenon of backward bifurcation, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibria. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on meningitis outbreak. Random perturbation of the vaccine efficacy was performed to gain insight into the role of the vaccine efficacy on the stability of the disease-free equilibrium. Theoretical results are supported by numerical simulations, which further suggest that the control of the epidemic of MenA 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.