Open AccessStability and persistence in ODE modelsfor populations with many stages
Author(s) -
Guihong Fan,
Yijun Lou,
Horst R. Thieme,
Jianhong Wu
Publication year - 2015
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.2015.12.661
Subject(s) - persistence (discontinuity) , ode , uniqueness , ordinary differential equation , mathematics , stability (learning theory) , extinction (optical mineralogy) , population , basic reproduction number , mathematical economics , differential equation , mathematical analysis , biology , computer science , demography , paleontology , geotechnical engineering , machine learning , sociology , engineering
A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.