TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Weiser, Martin A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Optimal control for a tuberculosis model with undetected cases in Cameroon N2 - This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years T3 - ZIB-Report - 13-73 KW - Tuberculosis KW - Optimal control KW - Nonlinear dynamical systems Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43142 SN - 1438-0064 ER - TY - JOUR A1 - Heller, Markus O. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Schell, H. A1 - Seebeck, P. A1 - Taylor, William R. T1 - Muskuloskeletale Belastungen im Schafshinterlauf JF - Materialwissenschaft und Werkstofftechnik Y1 - 2005 IS - 36 SP - 775 EP - 780 ER - TY - CHAP A1 - Heller, Markus O. A1 - Duda, G. A1 - König, Christian A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Hinterwimmer, S. A1 - Graichen, H. T1 - Validation of a New Model of Human Knee Kinematics against in Vivo Data under Physiologic Neuromuscular Activation Patterns T2 - Proceedings of the 51th Annual Meeting of the Orthopedic Society Y1 - 2005 CY - Washington ER - TY - JOUR A1 - Heller, Markus O. A1 - Kratzenstein, Stefan A1 - Ehrig, Rainald A1 - Wassilew, Georgi A1 - Duda, Georg A1 - Taylor, William R. T1 - The weighted optimal common shape technique improves identification of the hip joint centre of rotation in vivo JF - Journal of Orthopedic Research Y1 - 2011 VL - 29 SP - 1470 EP - 5 ER - TY - JOUR A1 - Heller, Markus O. A1 - König, Christian A1 - Graichen, F. A1 - Hinterwimmer, S. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Taylor, William R. T1 - A new model to predict in vivo human knee kinematics under physiological-like muscle activation JF - Journal of Biomechanics Y1 - 2007 SP - 45 EP - 53 ER - TY - JOUR A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Kratzenstein, Stefan A1 - Duda, Georg A1 - Trepczynski, Adam A1 - Taylor, William R. T1 - The SCoRE residual: A quality index to assess the accuracy of joint estimations JF - Journal of Biomechanics Y1 - 2011 U6 - https://doi.org/10.1016/j.jbiomech.2010.12.009 VL - 44 IS - 7 SP - 1400 EP - 1404 ER - TY - JOUR A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, G. A1 - Heller, Markus O. T1 - A Survey for Formal Methods for Determining the Centre of Ball Joints JF - Journal of Biomechanics Y1 - 2006 IS - 39 SP - 2798 EP - 2809 ER - TY - CHAP A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, G. A1 - Heller, Markus O. T1 - A New Approach for the Determination of Joint Axes T2 - Proceedings of the 52th Annual Meeting of the Orthopedic Society Y1 - 2006 CY - Chicago ER - TY - JOUR A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, Georg A1 - Heller, Markus O. T1 - A Survey for Formal Methods for Determining Functional Joint Axes JF - Journal of Biomechanics Y1 - 2007 SP - 2150 EP - 2157 ER - TY - CHAP A1 - Kornaropoulos, Evgenios I. A1 - Taylor, William R. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Matziolis, Georg A1 - Müller, Michael A1 - Wassilew, Georgi A1 - Asbach, Patrick A1 - Perka, Carsten A1 - Heller, Markus O. T1 - An imageless method to quantify the mechanical femoral-tibial angle based on the functional determination of joint centers and axes T2 - Annual meeting of the ESMAC 2009 Y1 - 2009 CY - London ER - TY - JOUR A1 - Kornaropoulos, Evgenios I. A1 - Taylor, William R. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Matziolis, Georg A1 - Müller, Michael A1 - Wassilew, Georgi A1 - Asbach, Patrick A1 - Perka, Carsten A1 - Heller, Markus O. T1 - Frontal plane alignment: An imageless method to predict the mechanical femoral–tibial angle (mFTA) based on functional determination of joint centres and axes JF - Gait & Posture Y1 - 2010 U6 - https://doi.org/10.1016/j.gaitpost.2009.10.006 VL - 31 IS - 2 SP - 204 EP - 208 ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. T1 - Reduction of the influence of skin marker artefacts using the optimal common shape technique T2 - Annual meeting of the ESMAC 2009 Y1 - 2009 CY - London ER - TY - CHAP A1 - Kassi, J.-P. A1 - Taylor, William R. A1 - Schwarzkopf, J. A1 - Schell, H. A1 - Duda, G. A1 - Ehrig, Rainald T1 - Wie sind Osteosynthesesysteme und Defektzonen in vivo belastet? T2 - 68. Jahrestagung der Deutschen Gesellschaft für Unfallchirurgie in Verbindung mit dem Deutschen Orthopädenkongress Y1 - 2004 CY - Berlin ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Duda, Georg A1 - Taylor, William R. T1 - A Quantification of Accuracy in Estimating Joint Centers T2 - 17th Congress of the European Society of Biomechanics Y1 - 2010 CY - Edinburgh ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Schröder, Jörg H. A1 - Taylor, William R. T1 - Die Bestimmung der Genauigkeit nicht-invasiver Techniken zur Ermittlung der Hüftgelenksposition in-vivo T2 - 6th annual meeting of the German Society for Biomechanics (DGfB) Y1 - 2009 CY - Münster ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Schröder, Jörg H. A1 - Taylor, William R. T1 - Der Vergleich von nicht-invasiven Techniken zur Bestimmung der Hüftgelenksposition T2 - Annual meeting of the German Society of Orthopaedics and Trauma Surgery Y1 - 2009 CY - Berlin ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Taylor, William R. T1 - The Residual: A Reliable Measure of Accuracy in the Determination of Joint Centers T2 - Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society Y1 - 2010 CY - New Orleans ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Taylor, William R. T1 - The Hip Joint Centre can be determined to within 3 mm T2 - 17th Congress of the European Society of Biomechanics Y1 - 2010 CY - Edinburgh ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Wassilew, Georgi A1 - Duda, Georg A1 - Taylor, William R. T1 - A new approach for optimally reducing skin marker artifact allows determination of the hip joint center within 3mm T2 - Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society Y1 - 2010 CY - New Orleans ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - The determination of joint axes T2 - 5. World Congress of Biomechanics, Munich, Journal of Biomechanics Y1 - 2006 IS - 39, Suppl. 1 SP - S571 EP - S572 ER -