Abstract:
This research presents two compartmental models on the transmission dynamics of
Bacterial Meningitis, which best describes the scenario in real life. The first model
is made up of seven (7) mutually exclusive epidemiological compartments. The
quantitative analysis of the model is conducted and the criteria for local and global
stabilities of the disease-free equilibrium is established. The simulation results show
that getting people vaccinated is crucial to the control of the disease. This leads to
the novel two-strain vaccination control model denoted by nine (9) mutually exclusive
epidemiological compartments. The model is used to analyze the impact of vaccination
and early treatment on the population, especially on the recovered populations. It is
ascertained that Bacterial Meningitis will not spread in the population if 25% of the
population is immune to the disease. Numerical simulations of the model are carried
out by implementing the MATLAB ODE45 algorithm to visualize the effects of the
various model parameters on each compartment of the developed model. The two strain model is then extended to include control by the introduction of five control
mechanisms; effective human personal protection (such as wearing face or surgical
masks), vaccination for strains 1 and 2, timely and delayed diagnosis treatments of the
infection. An optimal control problem is formulated and the existence of its solution is
established. The characterization of the controls is performed using the Pontryagin’s
Maximum Principle. The Forward Backward Sweep (FBS) method is implemented and
used to solve the optimal control problem and its corresponding adjoint equations. In
order to determine the impact of combination of the control strategies on the different
model compartments, numerical simulations of the model are performed using real
life data from Ghana Center for Disease Control. It was established that the most
efficient and cost-effective control strategy is the strategy involving all the five control
variables. This is followed by Strategy C which is only the effective human personal
protection (such as face or surgical masks) control, uP (t). Based on the findings of
this research, necessary recommendations are made for the applications of the model
to an endemic area.
