'Systems pharmacology' denotes the application of systems biology approaches to research questions arising in pharmacology. The aim is to understand the interaction of drugs with com- plex biological networks and to use this knowledge to develop- and improve medical therapy. Within the proposed project we will address unsolved mathematical challenges arising from this novel, interdisciplinary approach. We will integrate knowledge and data from three subtopics in order to study the mechanisms of drug resistance development in HIV-1, as a model system. In close cooperation with experts from the respective fields, the systems' response to drug interference, in terms of 'evolutionary dynamics' will be assessed alongside with the temporal resolution of drug interference ('drug action and pharmacokinetics') and their implications for the 'optimal use of therapy'. The proposed research program is expected to provide methodologi- cal advance that allows projecting these interrelations into measurable clinical outcomes, while addressing a relevant medical problem at the same time.
Development and spread of drug resistant microorganisms is a major health issue which, accompanied by an attrition in drug development, is expected to worsen in the near future. The source of drug resistance development is the inadequate use of antimicrobials: Inadequate therapies insufficiently suppress susceptible strains, which may give rise to a drug resistant type. At the same time, inadequate therapy exerts enough selective pressure to provide the newly emerged resistant strain with a selective advantage that allows it to become fixed in the population. In recent years, we have elaborated the idea, that an optimal switching between existing antimicrobial drugs may mitigate drug resistance development in the individual. Drug resistance development is an intrinsically stochastic process. This process can be accurately described by the chemical master equation (CME). A major mathematical drawback is the fact that the CME cannot be solved directly due to its numerical complexity. Therefore, computation of an optimal control/therapy based on a direct numerical solution of the CME is usually not feasible. The aim of the proposed project is to mathematically characterize and develop optimal control policies derived from approximations of the CME, and to use the developed methods to suggest drug mitigating therapies to clinical partners in the field of HIV-1 and antibiotic resistance.
For many chronic conditions, the optimal choice of therapies, dose-adjustment and an optimal schedule for monitoring the state of the disease is of great concern. The goal of this project is to combine mathematical modelling with control theoretic approaches in order to elaborate optimal therapeutic strategies for chronic conditions such as stroke prevention, diabetes treatment and HIV-1 infection, which require monitoring and therapy adjustment to avoid life-threatening over- or under medication. In this project we want to elaborate methods for stochastic feedback control, in particular Markov decision processes (MDP). MDPs are particularly suited to compute an optimal control strategy for processes that can continuously- or frequently be observed. If state observation is costly, and therefore rare, they may not be applicable. We want to develop a novel framework that considers the cost of state observation in its optimality function. This refinement of established theory will make optimal stochastic feedback control more valuable for clinical decision making, where an attending physician is confronted not only with determining the optimal medication, but also the time of the next examination.
My research interests include applications of mathematics to epidemiological control, treatment optimization, pharmacology and the control of pathogen evolution, particularly HIV. To achieve these goals, novel methods for PK/PD modeling, optimal control and model reduction are developed. For simulation purposes I use various modeling technologies for deterministic, stochastic and hybrid systems.
Currently, I am studying stochastic effects of high- and low-dose antivirals on viral growth. I am also currently working on unravelling resistance pathways and mechanisms in HIV. Together with the Robert Koch Institute, methods are being developed to anticipate the epidemiological consequences of "treatment as prevention" for HIV. Together with virologists at the CNRS Strasbourg we use mathematical modeling to predict the effectiveness and mechanisms of drug resistance development for the class of nucleoside analogous (used in Hepatitis B & C, Herpes and HIV treatment). Furthermore, I work with physicians and clinical pharmacologists at Charité Berlin and Augusta-Victoria hospital and FU-Berlin to optimize treatment for HIV, bacterial infections and pandemic influenza.