TY - JOUR
T1 - A geometric analysis of the SIRS epidemiological model on a homogeneous network
AU - Jardon Kojakhmetov, Hildeberto
AU - Kuehn, Christian
AU - Pugliese, Andrea
AU - Sensi, Mattia
PY - 2021/10
Y1 - 2021/10
N2 - We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
AB - We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
UR - http://dx.doi.org/10.1007/s00285-021-01664-5
U2 - 10.1007/s00285-021-01664-5
DO - 10.1007/s00285-021-01664-5
M3 - Article
SN - 0303-6812
VL - 83
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
M1 - 37
ER -