Background: Socioeconomic transformation in China at the beginning of the twenty-first century has led to rapid urbanization and accelerated rural–urban migration. As a result, the concerns about public health problems triggered by increasing internal population mobility have been more widely studied in recent years. Sources of data: Published data in Chinese and English on health of migrants and their families in mainland China from 2000 to 2012. Areas of agreement: The shifting patterns of disease distribution due to rural– urban migration, health equity and health reform strategies that cater for this specific yet substantial subpopulation are outstanding concerns. Infectious diseases, mental health, occupational health and women’s health are emerging public health priorities related to migration. Areas of controversy: The high mobility and large numbers of Chinese rural–urban migrants pose challenges to research methods and the reliability of evidence gained. Growing points: While the theme of working migrants is common in the literature, there have also been some studies of health of those left behind but who often remain unregistered. Migration within China is not a single entity and understanding the dynamics of new and emerging societies will need further study.

Health of China's rural–urban migrants and their families: a review of literature from 2000 to 2012

I. Preliminaries.- 1. Liapunov Functions.- 2. Almost Periodic Functions.- 3. Asymptotically Almost Periodic Functions.- 4. Quasi-Periodic Functions.- 5. Boundary Value Problem.- II. Stability and Boundedness.- 6. Stability of a Solution.- 7. Asymptotic Stability of a Solution.- 8. Boundedness of Solutions.- 9. Asymptotic Stability in the Large.- 10. Asymptotic Behavior of Solutions.- 11. Converse Theorems.- 12. Total Stability.- 13. Inherited Properties in Almost Periodic Systems.- 14. Uniformly Asymptotic Stability in Almost Periodic Systems.- III. Existence Theorems for Periodic Solutions and Almost Periodic Solutions.- 15. Existence Theorems for Periodic Solutions.- 16. Existence Theorems for Almost Periodic Solutions.- 17. Separation Condition in Almost Periodic Systems.- 18. Uniform Stability and Existence of Almost Periodic Solutions.- 19. Existence of Almost Periodic Solutions by Liapunov Functions.- References.

Stability theory and the existence of periodic solutions and almost periodic solutions

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.

/pdf/existence-and-exponential-stability-of-positive-almost-ewg3vgn4i3.pdf

Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

Global stability for an SEI model of infectious disease with immigration

Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.

Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith

In this paper, we discuss the following reaction–diffusion model which is a general form of many population models (∗) ∂ u ( t , x ) ∂ t = △ u ( t , x ) − δ u ( t , x ) + f ( u ( t − τ , x ) ) . We study the oscillatory behavior of solutions about the positive equilibrium K of system (∗) with Neumann boundary conditions. Sufficient and necessary conditions are obtained for global attractivity of the zero solution and acceptable conditions are established for the global attractivity of K . These results improve and complement existing results for system (∗) without diffusion. Moreover, when these results are applied to the diffusive Nicholson’s blowflies model and the diffusive model of Hematopoiesis, some new results are obtained for the latter.

Dynamics for a type of general reaction–diffusion model

Since it is very difficult to obtain the compactness of an almost periodic function set, many classical methods controlled by compact conditions such as Schauder’s fixed point theorem and the coincidence degree cannot be applied to solve almost periodic cases. Therefore, it becomes more complicated to investigate the existence, nonexistence and uniqueness of positive almost periodic solution for a certain model by the traditional methods. In this paper, the authors establish a new fixed point theorem without the compact conditions. As its application, some sufficient conditions of the existence, nonexistence and uniqueness of positive almost periodic solution for a model of Hematopoiesis are obtained. Also, the technique used here is different from the usual methods employed to solve almost periodic cases such as the contraction mapping principle and the Lyapunov functional.

Xiao Wang

Papers

Dynamics for a type of general reaction–diffusion model

A new approach to the existence, nonexistence and uniqueness of positive almost periodic solution for a model of Hematopoiesis

Influence of temporary migration on the transmission of infectious diseases in a migrants' home village.

Dynamics for a class of general hematopoiesis model with periodic coefficients

Existence of positive periodic solutions for neutral functional differential equations.