A boundedness and monotonicity preserving method for a generalized population model

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.

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Stability and Periodic Solution to a Nonlinear Partial Differential Equation Population Model with Delay

Acta Analysis Functionalis Applicata ◽

10.3724/sp.j.1160.2010.00125 ◽

2010 ◽

Vol 12 (2) ◽

pp. 125-131

Author(s):

Wei XIAO ◽

Ping YAN ◽

Qirong SHENG

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Periodic Solution ◽

Population Model ◽

Nonlinear Partial Differential Equation ◽

Partial Differential

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Numerical solutions of a linear age-structured population model

10.1063/1.5097799 ◽

2019 ◽

Author(s):

Maan A. Rasheed ◽

Sean Laverty ◽

Brittany Bannish

Keyword(s):

Population Model ◽

Numerical Solutions ◽

Structured Population Model ◽

Structured Population ◽

Age Structured ◽

Age Structured Population

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

Advances in Applied Probability ◽

10.1017/apr.2020.35 ◽

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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