Parameter identifiability and model selection for partial differential equation models of cell invasion
Posted on: 09 Oct 2024
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In modeling phenomena, achieving a balance between the complexity of a model and its output is a key consideration. A model's parameters play a critical role in shaping its predictions. When phenomena are formulated using partial differential equations (PDES) or ordinary differential equations (ODES), accurate parameter estimation is essential to improve the precision of the solution. Additionally, when multiple models with different levels of complexity exist for a given phenomenon, parameter estimation helps in identifying the optimal model. In this presentation, we introduce the Fisher-KPP (developed by Ronald Fisher, Andrey Kolmogorov, Ivan Petrovsky,and Nikolai Piskunov) reaction-diffusion model and its various forms to study cell invasion. We also examine parameter estimation results using the profile likelihood method and discuss model selection based on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).