Designing Optimal Intervention Policies for Bacterial CNS Infection Dynamics With Encephalitic Progression: A Multicontrol Compartmental Model

Central nervous system infections resulting from invasive bacterial pathogens are associated with a significant neurological burden. The ability of organisms such as Neisseria meningitidis and Streptococcus pneumoniae to invade the blood–brain barrier is often associated with severe neurological outcomes, including encephalitic complications. The progression from bacterial CNS infection to encephalitic states remains insufficiently explored in mathematical epidemiology, particularly in the presence of latent infection, asymptomatic carriage, and waning immunity. We develop a deterministic compartmental model of bacterial CNS infection, with the potential for progression to encephalitic states. The population structure consists of susceptible, exposed, transitional, asymptomatic infectious, symptomatic infectious, and recovered groups and includes a mechanism to represent declining immunity over time. Through this formulation, both the latent phase of infection and the subsequent disease progression can be effectively represented. The next-generation matrix method is used to evaluate R0, while the global stability of the disease-free equilibrium is analyzed via a Lyapunov approach with LaSalle’s invariance principle. To determine the dominant factors in disease transmission, a sensitivity analysis is also undertaken. An optimal control framework incorporating treatment, vaccination, and isolation is also formulated. Numerical simulations demonstrate that optimal strategies significantly reduce infection prevalence and limit progression toward encephalitic states. Overall, this modeling approach offers a useful way to examine the dynamics of bacterial infections in the central nervous system and to explore potential strategies for their control.