Mathematical analysis of HIV-1 dynamics in vivo. Zbl 1078.92502
Perelson, Alan S.; Nelson, Patrick W. |
|
1999
|
Mathematical analysis of delay differential equation models of HIV-1 infection. Zbl 0992.92035
Nelson, Patrick W.; Perelson, Alan S. |
|
2002
|
A model of HIV-1 pathogenesis that includes an intracellular delay. Zbl 0942.92017
Nelson, Patrick W.; Murray, James D.; Perelson, Alan S. |
|
2000
|
An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Zbl 1060.92038
Nelson, Patrick W.; Gilchrist, Michael A.; Coombs, Daniel; Hyman, James M.; Perelson, Alan S. |
|
2004
|
Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models. Zbl 1086.92022
Ciupe, M. S.; Bivort, B. L.; Bortz, D. M.; Nelson, P. W. |
|
2006
|
Modeling the mechanisms of acute hepatitis B virus infection. Zbl 1455.92022
Ciupe, Stanca M.; Ribeiro, Ruy M.; Nelson, Patrick W.; Perelson, Alan S. |
|
2007
|
Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics. Zbl 1334.92225
Bortz, D. M.; Nelson, P. W. |
|
2004
|
Eigenvalue assignment via the Lambert W function for control of time-delay systems. Zbl 1269.93036
Yi, S.; Nelson, P. W.; Ulsoy, A. G. |
|
2010
|
Controllability and observability of systems of linear delay differential equations via the matrix Lambert \(W\) function. Zbl 1367.93084
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2008
|
Time-delay systems. Analysis and control using the Lambert W function. Zbl 1209.93002
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2010
|
Applications of Sturm sequences to bifurcation analysis of delay differential equation models. Zbl 1257.34050
Forde, Jonathan; Nelson, Patrick |
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2004
|
Design of observer-based feedback control for time-delay systems with application to automotive powertrain control. Zbl 1298.93173
Yi, Sun; Ulsoy, A. Galip; Nelson, Patrick W. |
|
2010
|
Traveling-wave solutions of the diffusively corrected kinematic-wave model. Zbl 0994.90031
Nelson, P. |
|
2002
|
Model selection and mixed-effects modeling of HIV infection dynamics. Zbl 1296.92123
Bortz, D. M.; Nelson, P. W. |
|
2006
|
Delay differential equations via the matrix Lambert \(W\) function and bifurcation analysis: application to machine tool chatter. Zbl 1131.34056
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2007
|
Modeling viral infections. Zbl 1025.92010
Perelson, Alan S.; Nelson, Patrick W. |
|
2002
|
Modeling dynamic changes in type 1 diabetes progression: quantifying \(\beta\)-cell variation after the appearance of islet-specific autoimmune responses. Zbl 1190.53052
Nelson, Patrick; Smith, Noah; Ciupe, Stanca; Zou, Weiping; Omenn, Gilbert S.; Pietropaolo, Massimo |
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2009
|
Existence and uniqueness of an inverse problem for a hyperbolic system of lidar probing. Zbl 0766.35074
Dat Duc Bui; Nelson, P. |
|
1992
|
Semi-regular graphs of minimum independence number. Zbl 1030.05059
Nelson, P.; Radcliffe, A. J. |
|
2004
|
A data-validated temporary immunity model of COVID-19 spread in Michigan. Zbl 1508.92290
Pell, Bruce; Johnston, Matthew D.; Nelson, Patrick |
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2022
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Analysis and control of time delay systems using the LambertWDDE Toolbox. Zbl 1275.93034
Yi, Sun; Duan, Shiming; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2014
|
Limit cycle-strange attractor competition. Zbl 1141.34323
Criminale, W. O.; Jackson, T. L.; Nelson, P. W. |
|
2004
|
A data-validated temporary immunity model of COVID-19 spread in Michigan. Zbl 1508.92290
Pell, Bruce; Johnston, Matthew D.; Nelson, Patrick |
|
2022
|
Analysis and control of time delay systems using the LambertWDDE Toolbox. Zbl 1275.93034
Yi, Sun; Duan, Shiming; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2014
|
Eigenvalue assignment via the Lambert W function for control of time-delay systems. Zbl 1269.93036
Yi, S.; Nelson, P. W.; Ulsoy, A. G. |
|
2010
|
Time-delay systems. Analysis and control using the Lambert W function. Zbl 1209.93002
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2010
|
Design of observer-based feedback control for time-delay systems with application to automotive powertrain control. Zbl 1298.93173
Yi, Sun; Ulsoy, A. Galip; Nelson, Patrick W. |
|
2010
|
Modeling dynamic changes in type 1 diabetes progression: quantifying \(\beta\)-cell variation after the appearance of islet-specific autoimmune responses. Zbl 1190.53052
Nelson, Patrick; Smith, Noah; Ciupe, Stanca; Zou, Weiping; Omenn, Gilbert S.; Pietropaolo, Massimo |
|
2009
|
Controllability and observability of systems of linear delay differential equations via the matrix Lambert \(W\) function. Zbl 1367.93084
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2008
|
Modeling the mechanisms of acute hepatitis B virus infection. Zbl 1455.92022
Ciupe, Stanca M.; Ribeiro, Ruy M.; Nelson, Patrick W.; Perelson, Alan S. |
|
2007
|
Delay differential equations via the matrix Lambert \(W\) function and bifurcation analysis: application to machine tool chatter. Zbl 1131.34056
Yi, Sun; Nelson, Patrick W.; Ulsoy, A. Galip |
|
2007
|
Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models. Zbl 1086.92022
Ciupe, M. S.; Bivort, B. L.; Bortz, D. M.; Nelson, P. W. |
|
2006
|
Model selection and mixed-effects modeling of HIV infection dynamics. Zbl 1296.92123
Bortz, D. M.; Nelson, P. W. |
|
2006
|
An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Zbl 1060.92038
Nelson, Patrick W.; Gilchrist, Michael A.; Coombs, Daniel; Hyman, James M.; Perelson, Alan S. |
|
2004
|
Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics. Zbl 1334.92225
Bortz, D. M.; Nelson, P. W. |
|
2004
|
Applications of Sturm sequences to bifurcation analysis of delay differential equation models. Zbl 1257.34050
Forde, Jonathan; Nelson, Patrick |
|
2004
|
Semi-regular graphs of minimum independence number. Zbl 1030.05059
Nelson, P.; Radcliffe, A. J. |
|
2004
|
Limit cycle-strange attractor competition. Zbl 1141.34323
Criminale, W. O.; Jackson, T. L.; Nelson, P. W. |
|
2004
|
Mathematical analysis of delay differential equation models of HIV-1 infection. Zbl 0992.92035
Nelson, Patrick W.; Perelson, Alan S. |
|
2002
|
Traveling-wave solutions of the diffusively corrected kinematic-wave model. Zbl 0994.90031
Nelson, P. |
|
2002
|
Modeling viral infections. Zbl 1025.92010
Perelson, Alan S.; Nelson, Patrick W. |
|
2002
|
A model of HIV-1 pathogenesis that includes an intracellular delay. Zbl 0942.92017
Nelson, Patrick W.; Murray, James D.; Perelson, Alan S. |
|
2000
|
Mathematical analysis of HIV-1 dynamics in vivo. Zbl 1078.92502
Perelson, Alan S.; Nelson, Patrick W. |
|
1999
|
Existence and uniqueness of an inverse problem for a hyperbolic system of lidar probing. Zbl 0766.35074
Dat Duc Bui; Nelson, P. |
|
1992
|