TY - JOUR
T1 - FRONT PROPAGATION AND ARRIVAL TIMES IN NETWORKS WITH APPLICATION TO NEURODEGENERATIVE DISEASES
AU - Putra, Prama
AU - Oliveri, Hadrien
AU - Thompson, Travis
AU - Goriely, Alain
N1 - Publisher Copyright:
© 2023 Society for Industrial and Applied Mathematics.
PY - 2023
Y1 - 2023
N2 - Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying dynamical system; the Lambert time, obtained by considering the interaction of pairs of nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher-Kolmogorov-Petrovsky-Piskunov equation as a paradigm for the dynamics and show that each method provides different insights but consistent time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution, valid in the entire domain, and the correct ordering of arrival regions over large regions of parameters and initial conditions.
AB - Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying dynamical system; the Lambert time, obtained by considering the interaction of pairs of nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher-Kolmogorov-Petrovsky-Piskunov equation as a paradigm for the dynamics and show that each method provides different insights but consistent time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution, valid in the entire domain, and the correct ordering of arrival regions over large regions of parameters and initial conditions.
KW - connectome
KW - fronts
KW - networks
KW - neurodegenerative diseases
UR - http://www.scopus.com/inward/record.url?scp=85151275771&partnerID=8YFLogxK
U2 - 10.1137/21M1467547
DO - 10.1137/21M1467547
M3 - Article
AN - SCOPUS:85151275771
SN - 0036-1399
VL - 83
SP - 194
EP - 224
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 1
ER -