Stability Analysis of a Bacterial Meningitis Model with Saturated Incidence and Treatment Default

Bacterial meningitis is a severe type of disease that can lead to disability or sometimes death worldwide. A bacterial meningitis model incorporating carriers and treatment default is presented and analyzed. The model formulated Beddington–De Angelis incidence function to capture the crowding effect of infected individuals. Mathematical analysis presented establishes the basic reproduction number \({{\mathcal{R}}_{0}}\), and the global asymptotic stability of the equilibrium points for the model. Bifurcation analysis is carried out using the center manifold theory and it is found that a forward bifurcation occurs provided certain conditions are adhered to. Numerical simulations for the dynamics of bacterial meningitis in the presence of a default in treatment are presented. It is established that adherence to antibiotic treatment reduces the number of cases of bacterial meningitis while default will increase the reproduction number and drives the model to an endemic equilibrium state. To contain bacterial meningitis, there is need to ensure that there is regular contact tracing in areas that are prone to bacterial meningitis and patients need to be educated on the importance of adherence to treatment.