Optimal control of the spread of meningitis: in the presence of behaviour change of the society and information dependent vaccination

Abstract

A mathematical model of meningococcal meningitis with incidence dependent self-protection measure and vaccination is formulated and analysed. The vaccination considered is assumed to be given to everyone and is information dependent. It is shown that the disease free equilibrium is globally asymptotically stable, which implies that if the disease reproduction number R0 can be reduced to a value less than unity then it is possible to eradicate the meningococcal meningitis. In addition, the behaviour modification parameters are found to have significant impact on the dynamics of the disease. Moreover, an optimal control theory is applied to propose the optimal combination of efforts in controlling the disease. It is shown that the optimal use of controls, such as preventive education, vaccination and treatment reduces the incidence of the disease. It is also indicated that, incidence dependent self-protection measure and vaccination are important in controlling meningitis, and the cost-effectiveness analysis reveals that combining education with vaccination is the most cost-effective strategy in the setting of the model.