https://pubs.aip.org/aip/acp/article-abstract/3489/1/020003/3389001/Differential-equations-in-pharmacodynamic-data?redirectedFrom=fulltext
Differential equations in pharmacodynamic data analysis. A challenge to numerical analysts
Differential equations with memory terms (delays) are commonly used by pharmaceutical companies to perform phar-macokinetic and pharmacodynamic (PKPD) data analysis. Recently, new models which make use of distributed delays have been proposed. However, their numerical integration is quite a challenging task. There exist efficient codes for the numerical treatment of stiff and differential-algebraic problems (e.g., Radau5), as well as in the case where these equations present discrete delays (e.g., Radar5), but such codes are not able to treat distributed delays. This article aims to present a method that permits a direct application of the mentioned codes to a class of problems having a right-hand side with distributed delay terms (a special kind of integro differential equations). An illustrative example of a model from pharmacometric is considered.
https://pubs.aip.org/aip/acp/article-abstract/3489/1/020003/3389001/Differential-equations-in-pharmacodynamic-data?redirectedFrom=fulltext