Open AccessThreshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures
Author(s) -
Toshikazu Kuniya,
Yoshiaki Muroya,
Yoichi Enatsu
Publication year - 2014
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2014.11.1375
Subject(s) - epidemic model , basic reproduction number , stability theory , lyapunov function , mathematics , per capita , perturbation (astronomy) , value (mathematics) , mathematical economics , statistical physics , statistics , demography , physics , population , quantum mechanics , nonlinear system , sociology
In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number R0, is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically stable. We also show that if the threshold value is greater than unity, then the model is uniformly persistent and has an endemic equilibrium. Moreover, using a Lyapunov functional technique, we obtain a sufficient condition under which the endemic equilibrium is globally asymptotically stable. The sufficient condition is satisfied if the transmission coefficients in the same groups are large or the per capita recovery rates are small.