Non-linear age-dependent population dynamics

Gurtin, Morton E.; MacCamy, R. C.

doi:10.1007/bf00250793

Cited by 596 publications

(263 citation statements)

References 6 publications

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“…where ∆ h Z represents some (consistent) numerical operator for computing first order derivatives (see (9), for instance). Therefore, we have that…”

Section: Theoretical Results and Optimality Of The Assumptionsmentioning

confidence: 99%

“…The expression (3) is usually referred to as geometrical source term, that is motivated by the applications to the mathematical modeling for hydrogeology: in the Saint-Venant system for shallow waters, for instance, and the groundwater flows of an aquifer, the function Z(x) describes the bottom topography with respect to the spatial coordinates (see [5] and also [29]). Some models for nonlinear age-dependent population dynamics comprise source terms like (3) (refer to [9] for the original formulation of such problems), and various birth-death dynamical processes including the effects of competition for food are represented in [6] through equations for the probability density with that type of multiplicative noise. Furthermore, the influence of variable parameters as expressed via (3) characterizes many differential systems which are relevant to physical phenomena : relaxation inside chemical reactions, presence of external potentials in gas dynamics, material elasticity with memory, integro-differential models for granular flows in [11], simple optimization strategies for PDEs with non-conservative flux under hyperbolic constraints (see [15], for example), and besides basic quantitative models of multi-dimensional tomography for medical imaging to reconstruct the internal structure of solid objects from external measurements (refer to [7]).…”

Section: Introductionmentioning

confidence: 99%

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Three-points interfacial quadrature for geometrical source terms on nonuniform grids

Katsaounis

Simeoni

2011

Calcolo

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“…where ∆ h Z represents some (consistent) numerical operator for computing first order derivatives (see (9), for instance). Therefore, we have that…”

Section: Theoretical Results and Optimality Of The Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three-points interfacial quadrature for geometrical source terms on nonuniform grids

Katsaounis

Simeoni

2011

Calcolo

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“…Following the technique of the classical models introduced long ago, [58], it is possible to show existence and uniqueness results also for (4.9).…”

Section: Structured Modelsmentioning

confidence: 99%

Ecoepidemiology: a More Comprehensive View of Population Interactions

Venturino

2015

Math. Model. Nat. Phenom.

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Abstract. Models proposed for the description of population interactions with pathogenic agents are presented. We review some basic quadratic-interactions models, then move to more complex demographics, structured models, models involving several populations, delays, plankton dynamics, the Allee effect and group behavior. In most of these cases basic reproduction numbers are evaluated and commented.

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“…More recently, Gurtin and MacCamy [10] proved the existence of solutions of (2.1) for a class of models where the mortality modulus depends on the total population, µ ≡ µ(a, N (t)). However, due to the particular form of the boundary condition (2.2), no explicit solutions of the McKendrick equation have been found.…”

Section: ∂N(a T) ∂T + ∂N(a T) ∂A = −µ(A)n(a T) (21)mentioning

confidence: 99%

On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles

Dilão¹,

Lakmeche²

2006

Math. Model. Nat. Phenom.

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Abstract. We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time, the temporal evolution of the number of individuals of a population is always modulated by a time periodic function. The periodicity of the cycles is equal to the age of the reproductive age class, and a population retains the memory from the initial data through the amplitude of oscillations. For a population with a continuous distribution of reproductive age classes, the amplitude of oscillation is damped. The periodicity of the damped cycles is associated with the age of the first reproductive age class. Damping increases as the dispersion of the fertility function around the age class with maximal fertility increases. In general, the period of the demography cycles is associated with the time that a species takes to reach the reproductive maturity.

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Non-linear age-dependent population dynamics

Cited by 596 publications

References 6 publications

Three-points interfacial quadrature for geometrical source terms on nonuniform grids

Three-points interfacial quadrature for geometrical source terms on nonuniform grids

Ecoepidemiology: a More Comprehensive View of Population Interactions

On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles

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