Time-scale separation and centre manifold analysis describing vector-borne disease dynamics

2013 ◽  
Vol 90 (10) ◽  
pp. 2105-2125 ◽  
Author(s):  
Filipe Rocha ◽  
Maíra Aguiar ◽  
Max Souza ◽  
Nico Stollenwerk
Keyword(s):  
Time Scale ◽  
Disease Dynamics ◽  
Centre Manifold ◽  
Scale Separation ◽  
Vector Borne Disease ◽  
Time Scale Separation ◽  
Vector Borne

scholarly journals Time scale separation in the vector borne disease model SIRUV via center manifold analysis

2021 ◽  
Author(s):  
Maíra Aguiar ◽  
Bob Kooi ◽  
Andrea Pugliese ◽  
Mattia Sensi ◽  
Nico Stollenwerk
Keyword(s):  
Small Parameter ◽  
Time Scale ◽  
Center Manifold ◽  
Jacobian Matrix ◽  
Disease Model ◽  
Model Parameters ◽  
Scale Separation ◽  
Vector Borne Disease ◽  
Time Scale Separation ◽  
Vector Borne

AbstractWe investigate time scale separation in the vector borne disease model SIRUV, as previously described in the literature [1], and recently reanalyzed with the singular perturbation technique [2]. We focus on the analysis with a single small parameter, the birth and death rate µ, whereas all other model parameters are much larger and describe fast transitions. The scaling of the endemic stationary state, the Jacobian matrix around it and its eigenvalues with this small parameter µ is calculated and the center manifold analysis performed with the method described in [3] which goes back to earlier work [4, 5], namely a transformation of the Jacobian matrix to block structure in zeroth order in the parameter µ is used and then a family of center manifolds with µ larger than zero is obtained.

Singular Perturbation Modeling of Nonlinear Processes with Non Explicit Time-Scale Separation

1996 ◽  
Vol 29 (1) ◽  
pp. 5799-5804 ◽  
Author(s):  
Aditya Kumar ◽  
Panagiotis D. Christofides ◽  
Prodromos Daoutidis
Keyword(s):  
Singular Perturbation ◽  
Time Scale ◽  
Nonlinear Processes ◽  
Scale Separation ◽  
Time Scale Separation

scholarly journals A Time Scale Separation Method for the Coordination of Voltage Controls for SVC and SVR

2004 ◽  
Vol 124 (7) ◽  
pp. 913-919 ◽  
Author(s):  
Naoto Yorino ◽  
Takahiro Miki ◽  
Yuuki Yamato ◽  
Yoshifumi Zoka ◽  
Hiroshi Sasaki
Keyword(s):  
Time Scale ◽  
Separation Method ◽  
Scale Separation ◽  
Time Scale Separation
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