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A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence
On deriving lumped models for blood flow and pressure in the systemic arteries
1.  Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States 
2.  Keck Graduate Institute, 535 Watson Drive, Claremont, CA 91711, United States 
[1] 
Panagiotes A. Voltairas, Antonios Charalambopoulos, Dimitrios I. Fotiadis, Lambros K. Michalis. A quasilumped model for the peripheral distortion of the arterial pulse. Mathematical Biosciences & Engineering, 2012, 9 (1) : 175198. doi: 10.3934/mbe.2012.9.175 
[2] 
H. Thomas Banks, Shuhua Hu, Zackary R. Kenz, Carola Kruse, Simon Shaw, John Whiteman, Mark P. Brewin, Stephen E. Greenwald, Malcolm J. Birch. Model validation for a noninvasive arterial stenosis detection problem. Mathematical Biosciences & Engineering, 2014, 11 (3) : 427448. doi: 10.3934/mbe.2014.11.427 
[3] 
Alexandre Cornet. Mathematical modelling of cardiac pulse wave reflections due to arterial irregularities. Mathematical Biosciences & Engineering, 2018, 15 (5) : 10551076. doi: 10.3934/mbe.2018047 
[4] 
Ciro D'Apice, Olha P. Kupenko, Rosanna Manzo. On boundary optimal control problem for an arterial system: Firstorder optimality conditions. Networks & Heterogeneous Media, 2018, 13 (4) : 585607. doi: 10.3934/nhm.2018027 
[5] 
Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete & Continuous Dynamical Systems  B, 2013, 18 (2) : 417435. doi: 10.3934/dcdsb.2013.18.417 
[6] 
Larbi Berrahmoune. Constrained controllability for lumped linear systems. Evolution Equations & Control Theory, 2015, 4 (2) : 159175. doi: 10.3934/eect.2015.4.159 
[7] 
Scott R. Pope, Laura M. Ellwein, Cheryl L. Zapata, Vera Novak, C. T. Kelley, Mette S. Olufsen. Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences & Engineering, 2009, 6 (1) : 93115. doi: 10.3934/mbe.2009.6.93 
[8] 
John A. Adam. Inside mathematical modeling: building models in the context of wound healing in bone. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 124. doi: 10.3934/dcdsb.2004.4.1 
[9] 
W. Y. Tan, L.J. Zhang, C.W. Chen. Stochastic modeling of carcinogenesis: State space models and estimation of parameters. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 297322. doi: 10.3934/dcdsb.2004.4.297 
[10] 
H. W. Broer, Renato Vitolo. Dynamical systems modeling of lowfrequency variability in loworder atmospheric models. Discrete & Continuous Dynamical Systems  B, 2008, 10 (2&3, September) : 401419. doi: 10.3934/dcdsb.2008.10.401 
[11] 
Wouter Huberts, E. Marielle H. Bosboom, Frans N. van de Vosse. A lumped model for blood flow and pressure in the systemic arteries based on an approximate velocity profile function. Mathematical Biosciences & Engineering, 2009, 6 (1) : 2740. doi: 10.3934/mbe.2009.6.27 
[12] 
Shun Li, PengFei Yao. Modeling of a nonlinear plate. Evolution Equations & Control Theory, 2012, 1 (1) : 155169. doi: 10.3934/eect.2012.1.155 
[13] 
Avner Friedman, Wenrui Hao. Mathematical modeling of liver fibrosis. Mathematical Biosciences & Engineering, 2017, 14 (1) : 143164. doi: 10.3934/mbe.2017010 
[14] 
Luc Bergé, Stefan Skupin. Modeling ultrashort filaments of light. Discrete & Continuous Dynamical Systems  A, 2009, 23 (4) : 10991139. doi: 10.3934/dcds.2009.23.1099 
[15] 
Ka Kit Tung. Simple climate modeling. Discrete & Continuous Dynamical Systems  B, 2007, 7 (3) : 651660. doi: 10.3934/dcdsb.2007.7.651 
[16] 
Azmy S. Ackleh, Rinaldo M. Colombo, Sander C. Hille, Adrian Muntean. Preface to ``Modeling with Measures". Mathematical Biosciences & Engineering, 2015, 12 (2) : iii. doi: 10.3934/mbe.2015.12.2i 
[17] 
Cristina Anton, Jian Deng, Yau Shu Wong, Yile Zhang, Weiping Zhang, Stephan Gabos, Dorothy Yu Huang, Can Jin. Modeling and simulation for toxicity assessment. Mathematical Biosciences & Engineering, 2017, 14 (3) : 581606. doi: 10.3934/mbe.2017034 
[18] 
P. van den Driessche, Lin Wang, Xingfu Zou. Modeling diseases with latency and relapse. Mathematical Biosciences & Engineering, 2007, 4 (2) : 205219. doi: 10.3934/mbe.2007.4.205 
[19] 
Inez Fung. Challenges of climate modeling. Discrete & Continuous Dynamical Systems  B, 2007, 7 (3) : 543551. doi: 10.3934/dcdsb.2007.7.543 
[20] 
Ying Ji, Shaojian Qu, Fuxing Chen. Environmental game modeling with uncertainties. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 9891003. doi: 10.3934/dcdss.2019067 
2018 Impact Factor: 1.313
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