African Applied Mathematics (Pure Science) | 14 August 2011
Partial Differential Equations for Asymptotic Analysis and Identifiability in Nigerian Epidemic Spread Modelling
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Abstract
The study examines partial differential equations (PDEs) to model epidemic spread in Nigeria, focusing on asymptotic analysis and identifiability. The study employs a combination of theoretical analysis and numerical simulations to investigate the spread dynamics under various conditions. Asymptotic methods are applied to derive simplified models that capture long-term behaviour, while identifiability is assessed through sensitivity analysis on parameter estimates. A key finding is that the basic reproduction number R0 exhibits significant variability across different regions in Nigeria, highlighting regional differences in epidemic control strategies. The research provides a robust framework for understanding and predicting Nigerian epidemic spread using PDE models, with a focus on parameter identifiability. Further empirical studies are recommended to validate the model predictions and explore the impact of identified parameters on epidemic outcomes. epidemic modelling, partial differential equations, asymptotic analysis, identifiability, R0 Under standard regularity and boundary assumptions, the forecast state is modelled by $\partial<em>t u(t,x)=\kappa\,\partial</em>{xx}u(t,x)+f(t,x)$, and stability follows from bounded perturbations.