Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Modeling Biological Systems: Principles and Applications
Modeling Biological Systems: Principles and Applications
Equivalent partial differential equations of a lattice Boltzmann scheme
Computers & Mathematics with Applications
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Computer simulations are increasingly used in biological fields. The amazing power, storage ability, and processing speeds available nowadays have enabled the implementation of computer individual-based models (IbMs) to simulate really complex biological populations. Computers can easily keep track of thousands of individuals (often called 'agents'), whose complex behaviours and large amounts of associated data were daunting only 20 years ago. As such, computer modelling has just entered a field where traditional PDE models used to reign alone. A study of the exchange and non-trivial relationship between these two fields, computer IbMs versus classic partial differential equations (PDEs), is appropriate. The aim of this paper is to compare both approaches through a relevant example, namely the evolution of a yeast population in a batch culture. Thus, this paper deals with the utilization of both classical mathematics and computer science in the solution of problems arising in microbiology. First, an IbM approach to study the evolution of a yeast batch culture is presented. Second, an equivalent PDE model is derived by using some techniques from the interacting particle systems field. Third, a comparison and discussion on the advantages and drawbacks of both modelling tools is given.