The lorenz attractor and a related population model

1979 ◽  
pp. 169-187 ◽  
Author(s):  
William Parry
Keyword(s):  
Population Model ◽  
Lorenz Attractor ◽  
Related Population

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

scholarly journals Ten-year trends in epidemiology and outcomes of pediatric kidney replacement therapy in Europe: data from the ESPN/ERA-EDTA Registry

2021 ◽  
Author(s):  
Marjolein Bonthuis ◽  
Enrico Vidal ◽  
Anna Bjerre ◽  
Özlem Aydoğ ◽  
Sergey Baiko ◽  
...  
Keyword(s):  
Replacement Therapy ◽  
Cox Regression ◽  
Patient Survival ◽  
Healthcare Providers ◽  
Resource Planning ◽  
Policy Makers ◽  
Age Related ◽  
Kidney Replacement Therapy ◽  
Over Time ◽  
Related Population

Abstract Background For 10 consecutive years, the ESPN/ERA-EDTA Registry has included data on children with stage 5 chronic kidney disease (CKD 5) receiving kidney replacement therapy (KRT) in Europe. We examined trends in incidence and prevalence of KRT and patient survival. Methods We included all children aged <15 years starting KRT 2007–2016 in 22 European countries participating in the ESPN/ERA-EDTA Registry since 2007. General population statistics were derived from Eurostat. Incidence and prevalence were expressed per million age-related population (pmarp) and time trends studied with JoinPoint regression. We analyzed survival trends using Cox regression. Results Incidence of children commencing KRT <15 years remained stable over the study period, varying between 5.5 and 6.6 pmarp. Incidence by treatment modality was unchanged over time: 2.0 for hemodialysis (HD) and peritoneal dialysis (PD) and 1.0 for transplantation. Prevalence increased in all age categories and overall rose 2% annually from 26.4 pmarp in 2007 to 32.1 pmarp in 2016. Kidney transplantation prevalence increased 5.1% annually 2007–2009, followed by 1.5% increase/year until 2016. Prevalence of PD steadily increased 1.4% per year over the entire period, and HD prevalence started increasing 6.1% per year from 2011 onwards. Five-year unadjusted patient survival on KRT was around 94% and similar for those initiating KRT 2007–2009 or 2010–2012 (adjusted HR: 0.98, 95% CI:0.71–1.35). Conclusions We found a stable incidence and increasing prevalence of European children on KRT 2007–2016. Five-year patient survival was good and was unchanged over time. These data can inform patients and healthcare providers and aid health policy makers on future resource planning of pediatric KRT in Europe.

scholarly journals Limit theorems for multi-type general branching processes with population dependence

2020 ◽  
Vol 52 (4) ◽  
pp. 1127-1163
Author(s):  
Jie Yen Fan ◽  
Kais Hamza ◽  
Peter Jagers ◽  
Fima C. Klebaner
Keyword(s):  
Carrying Capacity ◽  
Population Model ◽  
General Framework ◽  
Limit Theorems ◽  
Mating Systems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Special Section ◽  
Large Numbers ◽  
Type Population

AbstractA general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population as a measure-valued process and obtain its asymptotics as the population grows with the environmental carrying capacity. Thus, a deterministic approximation is given, in the form of a law of large numbers, as well as a central limit theorem. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.

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