Mathematical Study of Infectious Disease Dynamics: SIR Modelling of Meningitis in Zamfara State

This study employs the classical susceptible-infectious-recovered epidemiological modelling framework to analyse the dynamics of cerebrospinal meningitis transmission in Zamfara State, North West Nigeria, a region that lies within the sub-Saharan African meningitis belt and has experienced repeated seasonal meningitis epidemics. Meningococcal meningitis imposes severe public health and economic costs in northern Nigeria, with outbreaks concentrated in the dry season months between November and May. State-level disease incidence data sourced from the Nigeria Centre for Disease Control's annual disease surveillance reports for the years 2019 to 2023 are used to estimate model parameters including transmission rate, recovery rate, and the basic reproduction number. The SIR differential equation system is solved numerically using the fourth-order Runge-Kutta method, and sensitivity analysis of the basic reproduction number with respect to each model parameter is conducted to identify the most impactful intervention targets. The effects of vaccination coverage as an additional model compartment are simulated under the susceptible-vaccinated-infectious-recovered framework to project epidemic trajectories under varying vaccine deployment scenarios. Results indicate that achieving a vaccination coverage rate of 72 percent among the susceptible population in Zamfara would be sufficient to prevent epidemic amplification based on estimated transmission parameters. The study recommends pre-epidemic mass vaccination campaigns timed to the October-November pre-season window. Keywords: SIR model, meningitis, epidemiological modelling, basic reproduction number, Zamfara State