Theoretical assessment of the impact of desert aerosols on the dynamical transmission of meningitidis serogroup A

Abstract

This paper has been motivated by the following biological question: how influential are desert aerosols in the transmission of meningitidis serogroup A (MenA)? A mathematical model for the dynamical transmission of MenA is considered, with the aim of investigating the impact of desert aerosols. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on meningitis outbreak. We derive the basic reproduction number [Formula: see text]. We prove that there exists a threshold parameter [Formula: see text] such that when [Formula: see text], the disease-free equilibrium is globally asymptotically stable (GAS). However, when [Formula: see text], the model exhibits the phenomenon of backward bifurcation. At the endemic level, we show that the number of infectious individuals in the presence of desert aerosols is larger than the corresponding number without the presence of desert aerosols. In conjunction with the inequality [Formula: see text] where [Formula: see text] is the basic reproduction number without desert aerosols, we found that the ingestion of aerosols by carriers will increase the endemic level, and the severity of the outbreak. This suggests that the control of MenA passes through a combination of a large coverage vaccination of young susceptible individuals and the production of a vaccine with a high level of efficacy as well as respecting the hygienic rules to avoid the inhalation of desert aerosols. Theoretical results are supported by numerical simulations.