In Memory of Vladimir Gerdt

Center for Computational Methods in Applied Mathematics of RUDN, Professor V.P. Gerdt, whose passing was a great loss to the scientific center and the computer algebra community. The article provides biographical information about V.P. Gerdt, talks about his contribution to the development of computer algebra in Russia and the world. At the end there are the author’s personal memories of V.P. Gerdt.Настоящая статья - мемориальная, она посвящена памяти руководителя научного центра вычислительных методов в прикладной математике РУДН, профессора В.П. Гердта, чей уход стал невосполнимой потерей для научного центра и всего сообщества компьютерной алгебры. В статье приведены биографические сведения о В.П. Гердте, рассказано о его вкладе в развитие компьютерной алгебры в России и мире. В конце приведены личные воспоминания автора о В.П. Гердте

On identifiability of nonlinear ODE models and applications in viral dynamics

Ordinary differential equations (ODEs) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last two decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determining unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past couple of decades, including structural identifiability analysis, practical identifiability analysis, and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV and influenza viruses are given to illustrate how to apply these identifiability analysis methods in practice.NIAID/NIH research grants AI055290, AI50020, AI28433, AI078498, RR06555, the University of Rochester Provost Award, and the University of Rochester DCFAR (P30AI078498) Mentoring Award.http://www.siam.org/journals/sirev/53-1/75700.htmlai201

Structural identifiability of large systems biology models

A fundamental principle of systems biology is its perpetual need for new technologies that can solve challenging biological questions. This precept will continue to drive the development of novel analytical tools. The virtuous cycle of biological progress can therefore only exist when experts from different disciplines including biology, chemistry, computer science, engineering, mathematics, and medicine collaborate. General opinion is however that one of the challenges facing the systems biology community is the lag in the development of such technologies. The topic of structural identifiability in particular has been of interest to the systems biology community. This is because researchers in this field often face experimental limitations. These limitations, combined with the fact that systems biology models can contain vast numbers of unknown parameters, necessitate an identifiability analysis. In reality, analysing the structural identifiability of systems biology models, even when they contain only a few states and system parameters, may be challenging. As these models increase in size and complexity, this difficulty is exasperated, and one becomes limited to only a few methods capable of analysing large ordinary differential equation models. In this thesis I study the use of a computationally efficient algorithm, well suited to the analysis of large models, in the model development process. The three related objectives of this thesis are: 1) develop an accurate method to asses the structural identifiability of large possibly nonlinear ordinary differential models, 2) implement thismethod in the preliminary design of experiments, and 3) use the method to address the topic of structural unidentifiability. To improve the method’s accuracy, I systematically study the role of individual factors, such as the number of experimentally measured sensors, on the sharpness of results. Based on the findings, I propose measures that can improve numerical accuracy. To address the second objective, I introduce an iterative identifiability algorithm that can determine minimal sets of outputs that need to be measured to ensure a model’s local structural identifiability. I also illustrate how one could potentially reduce the computational demand of the algorithm, enabling a user to detect minimal output sets of large ordinary differential equation models within minutes. For the last objective, I investigate the role of initial conditions in a model’s structural unidentifiability. I show that the method can detect problematic values for large ordinary differential equation models. I illustrate its role in reinstating the local structural identifiability of a model by identifying problematic initial conditions. I also show that the method can provide theoretical suggestions for the reparameterization of structurally unidentifiable models. The novelty of this work is that the algorithm allows for unknown initial conditions to be parameterised and accordingly, repameterisations requiring the transformation of states, associated with unidentifiable initial conditions, can easily be obtained. The computational efficiency of the method allows for the reparameterisation of large ordinary differential equation models in particular. To conclude, in this thesis I introduce an method that can be used during the model development process in an array of useful applications. These include: 1) determining minimal output sets, 2) reparameterising structurally unidentifiable models and 3) detecting problematic initial conditions. Each of these application can be implemented before any experiments are conducted and can play a potential role in the optimisation of the modelling process