Open AccessDisease dynamics for the hometown of migrant workers
Author(s) -
Ram P. Sigdel,
C. Connell McCluskey
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.2014.11.1175
Subject(s) - dynamics (music) , constant (computer programming) , population , stability theory , work (physics) , differential equation , mathematics , disease , mathematical analysis , demography , computer science , physics , nonlinear system , sociology , medicine , thermodynamics , programming language , pathology , quantum mechanics , acoustics
A recent paper by L. Wang, X. Wang J. Theoret. Biol. 300:100--109 (2012) formulated and studied a delay differential equation model for disease dynamics in a region where a portion of the population leaves to work in a different region for an extended fixed period. Upon return, a fraction of the migrant workers have become infected with the disease. The global dynamics were not fully resolved in that paper, but are resolved here. We show that for all parameter values and all delays, the unique equilibrium is globally asymptotically stable, implying that the disease will eventually reach a constant positive level in the population.