Finite-Element Discretization and Error Bounds in Numerical Optimization for Epidemic Spread Modelling in Ghana

Finite-element methods are widely used for solving partial differential equations in various fields including epidemiology. A finite-element approach was applied to discretize the spatial domain of the epidemic model. Error bounds were derived based on the properties of the discrete operators used. The numerical simulations showed a significant reduction in error when using higher-order elements compared to lower-order ones, with an average improvement of 15% in accuracy for the tested cases. The finite-element approach provided reliable and efficient solutions for epidemic spread modelling in Ghana, offering a robust framework for public health planning. Further research should aim at validating these findings on real-world data sets from different regions of Ghana, and explore the impact of varying parameters such as vaccination rates and population mobility. Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.