TY - JOUR A1 - Weiße, Andrea Y. A1 - Middleton, Richard H. A1 - Huisinga, Wilhelm T1 - Quantifying uncertainty, variability and likelihood for ordinary differential equation models N2 - Background: In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results: The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well- known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions: While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations. Y1 - 2010 UR - http://www.biomedcentral.com/1752-0509/ U6 - https://doi.org/10.1186/1752-0509-4-144 SN - 1752-0509 ER - TY - JOUR A1 - Pilari, Sabine A1 - Preusse, Cornelia A1 - Huisinga, Wilhelm T1 - Gestational influences on the pharmacokinetics of gestagenic drugs a combined in silico, in vitro and in vivo analysis JF - European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences, EUFEPS N2 - During preclinical development of a gestagenic drug, a significant increase of the total plasma concentration was observed after multiple dosing in pregnant rabbits, but not in (non-pregnant) rats or monkeys. We used a PBPK modeling approach in combination with in vitro and in vivo data to address the question to what extent the pharmacologically active free drug concentration is affected by pregnancy induced processes. In human, a significant increase in sex hormone binding globulin (SHBG), and an induction of hepatic CYP3A4 as well as plasma esterases is observed during pregnancy. We find that the observed increase in total plasma trough levels in rabbits can be explained as a combined result of (i) drug accumulation due to multiple dosing, (ii) increase of the binding protein SHBG, and (iii) clearance induction. For human, we predict that free drug concentrations in plasma would not increase during pregnancy above the steady state trough level for non-pregnant women. KW - PBPK KW - Pregnancy KW - Gestagenic drug KW - Protein binding KW - SHBG KW - Clearance induction Y1 - 2011 U6 - https://doi.org/10.1016/j.ejps.2010.12.003 SN - 0928-0987 VL - 42 IS - 4 SP - 318 EP - 331 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - von Kleist, Max A1 - Menz, Stephan A1 - Stocker, Hartmut A1 - Arasteh, Keikawus A1 - Schuette, Christof A1 - Huisinga, Wilhelm T1 - HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs JF - PLoS one N2 - The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at & 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial. Y1 - 2011 U6 - https://doi.org/10.1371/journal.pone.0018204 SN - 1932-6203 VL - 6 IS - 3 PB - PLoS CY - San Fransisco ER - TY - CHAP A1 - Steenholdt, Casper A1 - Edlund, Helena A1 - Ainsworth, Mark A. A1 - Brynskov, Jorn A1 - Thomsen, Ole Ostergaard A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Relationship between measures of infliximab exposure and clinical outcome of infliximab intensification at therapeutic failure in Crohn's disease T2 - JOURNAL OF CROHNS & COLITIS Y1 - 2015 SN - 1873-9946 SN - 1876-4479 VL - 9 SP - S330 EP - S330 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Menz, Stephan A1 - Latorre, Juan C. A1 - Schütte, Christof A1 - Huisinga, Wilhelm T1 - Hybrid stochastic-deterministic solution of the chemical master equation JF - Multiscale modeling & simulation : a SIAM interdisciplinary journal N2 - The chemical master equation (CME) is the fundamental evolution equation of the stochastic description of biochemical reaction kinetics. In most applications it is impossible to solve the CME directly due to its high dimensionality. Instead, indirect approaches based on realizations of the underlying Markov jump process are used, such as the stochastic simulation algorithm (SSA). In the SSA, however, every reaction event has to be resolved explicitly such that it becomes numerically inefficient when the system's dynamics include fast reaction processes or species with high population levels. In many hybrid approaches, such fast reactions are approximated as continuous processes or replaced by quasi-stationary distributions in either a stochastic or a deterministic context. Current hybrid approaches, however, almost exclusively rely on the computation of ensembles of stochastic realizations. We present a novel hybrid stochastic-deterministic approach to solve the CME directly. Our starting point is a partitioning of the molecular species into discrete and continuous species that induces a partitioning of the reactions into discrete-stochastic and continuous-deterministic processes. The approach is based on a WKB (Wentzel-Kramers-Brillouin) ansatz for the conditional probability distribution function (PDF) of the continuous species (given a discrete state) in combination with Laplace's method of integral approximation. The resulting hybrid stochastic-deterministic evolution equations comprise a CME with averaged propensities for the PDF of the discrete species that is coupled to an evolution equation of the related expected levels of the continuous species for each discrete state. In contrast to indirect hybrid methods, the impact of the evolution of discrete species on the dynamics of the continuous species has to be taken into account explicitly. The proposed approach is efficient whenever the number of discrete molecular species is small. We illustrate the performance of the new hybrid stochastic-deterministic approach in an application to model systems of biological interest. KW - chemical master equation KW - hybrid model KW - multiscale analysis KW - partial averaging KW - asymptotic approximation KW - WKB ansatz Y1 - 2012 U6 - https://doi.org/10.1137/110825716 SN - 1540-3459 VL - 10 IS - 4 SP - 1232 EP - 1262 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - CHAP A1 - Andersson, H. A1 - Keunecke, A. A1 - Eser, A. A1 - Huisinga, Wilhelm A1 - Reinisch, W. A1 - Kloft, Charlotte T1 - Pharmacokinetic considerations for optimising dosing regimens of a potsdam univ infliximab in patients with Crohn's disease T2 - JOURNAL OF CROHNS & COLITIS Y1 - 2014 U6 - https://doi.org/10.1016/S1873-9946(14)60086-6 SN - 1873-9946 SN - 1876-4479 VL - 8 SP - S44 EP - S44 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Engbert, Ralf A1 - Rabe, Maximilian Michael A1 - Kliegl, Reinhold A1 - Reich, Sebastian T1 - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics JF - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology N2 - Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach. KW - Stochastic epidemic model KW - Sequential data assimilation KW - Ensemble Kalman KW - filter KW - COVID-19 Y1 - 2020 U6 - https://doi.org/10.1007/s11538-020-00834-8 SN - 0092-8240 SN - 1522-9602 VL - 83 IS - 1 PB - Springer CY - New York ER - TY - JOUR A1 - Sharma, Shubham A1 - Hainzl, Sebastian A1 - Zöller, Gert T1 - Seismicity parameters dependence on main shock-induced co-seismic stress JF - Geophysical journal international N2 - The Gutenberg-Richter (GR) and the Omori-Utsu (OU) law describe the earthquakes' energy release and temporal clustering and are thus of great importance for seismic hazard assessment. Motivated by experimental results, which indicate stress-dependent parameters, we consider a combined global data set of 127 main shock-aftershock sequences and perform a systematic study of the relationship between main shock-induced stress changes and associated seismicity patterns. For this purpose, we calculate space-dependent Coulomb Stress (& UDelta;CFS) and alternative receiver-independent stress metrics in the surrounding of the main shocks. Our results indicate a clear positive correlation between the GR b-value and the induced stress, contrasting expectations from laboratory experiments and suggesting a crucial role of structural heterogeneity and strength variations. Furthermore, we demonstrate that the aftershock productivity increases nonlinearly with stress, while the OU parameters c and p systematically decrease for increasing stress changes. Our partly unexpected findings can have an important impact on future estimations of the aftershock hazard. KW - earthquake hazards KW - earthquake interaction KW - forecasting and prediction KW - statistical seismology KW - b-value Y1 - 2023 U6 - https://doi.org/10.1093/gji/ggad201 SN - 0956-540X SN - 1365-246X VL - 235 IS - 1 SP - 509 EP - 517 PB - Oxford Univ. Press CY - Oxford ER - TY - THES A1 - Sareeto, Apatsara T1 - Algebraic properties of a subsemigroup of the symmetric inverse semigroup Y1 - 2024 ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt A1 - Glück, Jochen T1 - On a convergence theorem for semigroups of positive integral operators JF - Comptes Rendus Mathematique N2 - We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result. Y1 - 2017 U6 - https://doi.org/10.1016/j.crma.2017.07.017 SN - 1631-073X SN - 1778-3569 VL - 355 SP - 973 EP - 976 PB - Elsevier CY - Paris ER -