Stability and persistence in ODE models for populations with many stages
From MaRDI portal
Publication:888643
DOI10.3934/mbe.2015.12.661zbMath1369.92095OpenAlexW2318388350WikidataQ41231204 ScholiaQ41231204MaRDI QIDQ888643
Yijun Lou, Guihong Fan, Jianhong Wu, Horst R. Thieme
Publication date: 2 November 2015
Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/mbe.2015.12.661
stabilityexistenceuniquenessboundednesspersistenceextinctionLyapunov functionsbasic reproduction numberequilibria
Population dynamics (general) (92D25) Stability of solutions to ordinary differential equations (34D20) Global stability of solutions to ordinary differential equations (34D23)
Related Items
Modeling co-infection of \textit{ixodes} tick-borne pathogens ⋮ Delay differential systems for tick population dynamics ⋮ Modelling physiologically structured populations: renewal equations and partial differential equations ⋮ The dynamics of delayed models for interactive wild and sterile mosquito populations ⋮ Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes ⋮ Are host control strategies effective to eradicate tick-borne diseases (TBD)? ⋮ How ticks keep ticking in the adversity of host immune reactions ⋮ Basic reproduction ratios for periodic abstract functional differential equations (with application to a spatial model for Lyme disease) ⋮ Long-term transmission dynamics of tick-borne diseases involving seasonal variation and co-feeding transmission
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hopf bifurcation for a size-structured model with resting phase
- Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example
- Well-posedness of physiologically structured population models for Daphnia magna. How biological concepts can benefit by abstract mathematical analysis
- Delay differential systems for tick population dynamics
- Structured population models in biology and epidemiology.
- Hopf bifurcation in a size-structured population dynamic model with random growth
- Fluctuation periodicity, generation separation, and the expression of larval competition
- Some theoretical and numerical aspects of modelling dispersion in the development of ectotherms
- The differential infectivity and staged progression models for the transmission of HIV
- Developing a temperature-driven map of the basic reproductive number of the emerging tick vector of lyme disease \textit{Ixodes scapularis} in Canada
- Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
- Physiologically structured populations with diffusion and dynamic boundary conditions
- A nonlinear age and maturity structured model of population dynamics. II: Chaos
- Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation
- Measure-valued solutions for a hierarchically size-structured population
- Effects of tick population dynamics and host densities on the persistence of tick-borne infections
- A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes
- The Theory of the Chemostat
- Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior
- A Nonlinear Model of Population Dynamics Containing an Arbitrary Number of Continuous Structure Variables
- Reproduction Numbers and the Stability of Equilibria of SI Models for Heterogeneous Populations
- Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity
- Ticks and tick-borne diseases: a vector-host interaction model for the brown ear tick (Rhipicephalus appendiculatus)
- Multiparametric Bifurcation Analysis of a Basic Two-Stage Population Model
- Global Attractors and Steady States for Uniformly Persistent Dynamical Systems
- An Introduction to Delay Differential Equations with Applications to the Life Sciences
