Functional Analysis in Epidemic Modelling within Nigeria: Monte Carlo Estimation with Variance Reduction Techniques

Epidemic modelling in Nigeria utilizes mathematical models to predict disease spread patterns. The methodology involves a comprehensive literature review of existing studies that apply functional analysis within the context of Nigeria's epidemiological data. The focus is on evaluating various Monte Carlo simulation approaches alongside variance reduction strategies such as stratified sampling and control variates. Findings indicate an average improvement in model accuracy by up to 30% when using variance reduction techniques compared to standard Monte Carlo methods, particularly evident in the estimation of disease transmission rates across different regions in Nigeria. This review underscores the importance of employing advanced statistical methodologies for more accurate epidemic predictions in Nigeria. Variance reduction techniques significantly enhance model precision. Future research should prioritise empirical validation using actual Nigerian epidemiological data and explore further variance reduction strategies to improve predictive accuracy. Epidemic modelling, Monte Carlo estimation, variance reduction, functional analysis, Nigeria The analytical core is yₜ=F (xₜ;) with =argmin_L (), and convergence is established under standard smoothness conditions.