Backward bifurcation and sensitivity analysis for bacterial meningitis transmission dynamics with a nonlinear recovery rate

Bacterial meningitis is one of the major causes of death in sub-Saharan Africa and a medical emergency around the world. To increase the number of recoveries and/or reduce the number of sequelae, and deaths need effective antibiotics: and also the ability to identify influential state variables, parameters and threshold properties. Therefore, we propose a mathematical model for bacterial meningitis to include nonlinear recovery rate. The studies show instances for forward and backward bifurcation. We use Latin hypercube sampling to test for influential parameters in the basic reproduction number, R0. We use sensitivity heat map and parameter sensitivity spectrum to test for the group sensitivity of all the state variables and parameters. The sensitivity heat map shows that the most sensitive state variable to all parameters in the model during none seasonal transmission is the recovery class followed by the susceptible class; and that the most sensitive state variable during seasonal transmission is the susceptible class followed by the carrier-class. Meanwhile, we use optimal control theory to study the impact of inoculation in an endemic setting with limited number of antibiotics and hospital beds. The work provides a potential framework for the control of the disease spread in limited-resource settings. Potential extensions of the model are likewise examined.