Identification of parameters of evolutionary model of monocyclic cells aggregation with the hop plants example

Akimenko, V. V.; Zahorodnii, Yu. V.; Boyko, A. L.

doi:10.1016/j.camwa.2013.02.023

Cited by 7 publications

(16 citation statements)

References 7 publications

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“…The setting where the global minimum can be the best discriminated from the other minima provides an inverse problem that is well-conditioned and thus provides the most robust solution to the parameter identification problem. Note that, once a "good" setting of trap is identified, other methods, such as random search methods, could be interesting alternatives to finding the global minimum of the objective function [30], [6], [1].…”

Section: Discussionmentioning

confidence: 99%

Parameter Identification in Population Models for Insects Using Trap Data

Dufourd¹,

Weldon²,

Anguelov³

et al. 2013

BIOMATH

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BIOMATH h t t p : / / w w w. b i o m a t h f o r u m . o r g / b i o m a t h / i n d e x . p h p / b i o m a t h /Abstract-Traps are used commonly to establish the presence and population density of pest insects. Deriving estimates of population density from trap data typically requires knowledge of the properties of the trap (e.g. active area, strength of attraction) as well as some properties of the population (e.g. diffusion rate). These parameters are seldom exactly known, and also tend to vary in time, (e.g. as a result of changing weather conditions, insect physiological condition). We propose using a set of traps in such a configuration that they trap insects at different rates. The properties of the traps and the characteristics of the population, including its density, are simultaneously estimated from the insects captured in these traps. The basic model is an advection-diffusion equation where the traps are represented via a suitable advection term defined by the active area of the traps. The values of the unknown parameters of the model are derived by solving an optimization problem. Numerical simulations demonstrate the accuracy and the robustness of this method of parameter identification.

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Section: Discussionmentioning

confidence: 99%

Parameter Identification in Population Models for Insects Using Trap Data

Dufourd¹,

Weldon²,

Anguelov³

et al. 2013

BIOMATH

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“…The practical efficiency of the monocyclic age-structured model of population dynamics as applied to identification of biological parameters of hop plant during several seasons is shown in [22]. Since we consider a more general polycyclic age-structured model in the present paper, the result application domain is expanded for a wider class of biological objects and hence the mathematical tools for applied scientific studies are enhanced.…”

Section: Introductionmentioning

confidence: 97%

“…The studies [21][22][23] consider modeling, parameter estimation, and optimal control for idealized monocyclic age-structured models of cell population on the example of cyclic (seasonal) growth of three-year plants. The relevant studies can also be applied to model developing biological systems at cellular level.…”

Section: Introductionmentioning

confidence: 99%

“…In the special case of linear system, analytical solution for the distribution of cell's density is obtained as a superposition of reflected and direct waves [21]. It was used to analyze the principal patterns of the behavior of biological macroparameters of hop plant [21], to solve identification problems for its biological parameters [22] and optimal control of growth [23], and to obtain explicit solutions for specific cases of applied systems.…”

Section: Introductionmentioning

confidence: 99%

“…This class of functions is defined on the compact set and is a formalization of expert estimates that describe the main plant behavior patterns at the qualitative level. We will also consider the identification of biological parameters of hop plant for the parameterized class of algebraic functions as a problem of searching for the global minimum on the compact set for deviations of the simulated function of the cell biomass on the observed experimental data (dried cellular biomass of hop plant collected at different periods during the life cycle of the plant, i.e., three years (seasons) [22]). Since we consider the optimization problem on a large set of parameters (14 parameters), the systems approach is used to construct the numerical algorithm of minimization [25] and the adaptive stochastic optimization method is applied [23,26] for the solution of the respective variational problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling the Dynamics of Age-Structured Polycyclic Population of Biological Cells on the Parameterized Set of Algebraic Functions

Akimenko

Zahorodnii

2014

Cybern Syst Anal

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We use the analytical approach and numerical modeling to analyze the dynamics of the population of biological cells based on the polycyclic age-structured model. We reduce the initial-boundary-value problem for transport equation to the Volterra integral equation of the second kind and solve it by infinite convergent series. For the initial-boundary-value problem for transport equation, we obtain an explicit two-layer numerical difference scheme of the second order of approximation with respect to time and the first one with respect to age with explicit recurrent formula for the integral boundary condition. We consider the set of main biological parameters of the system as a set of parameterized algebraic functions with compact domain of definition. The parameter identification problem is solved for approximate analytical solutions for the data of dried biomass of hop plant observed for 3 years. Since the maximum relative error of deviation of the simulated curves from the points of experimental data is less than 11%, we conclude that polycyclic age-structured cell population model is efficient to solve applied problems in biological systems.

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Two‐compartment age‐structured model of solitarious and gregarious locust population dynamics

Akimenko

Piou

2018

Math Methods in App Sciences

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Communicated by: R Anguelov MSC Classification: 92D25, 35L04, 37C75We study a nonlinear age-structured model of locust population dynamics with variable time of egg incubation that describes the phase shifting and behavior of desert locust, Schistocerca gregaria. The model is based on the 2compartment system of transport equations with nonlinear density-dependent fertility rates with time delay in boundary conditions. It describes the dynamics of the density of 2 phases of locust's population-solitarious and gregarious.Such system is studied both theoretically and numerically. The analysis of asymptotical stability of the trivial and nontrivial equilibria of the autonomous system allows to understand the conditions and the particularities of bidirectional phase shifts between solitarious and gregarious S gregaria. We found that the parameter of maturation age was very important in the 2-phase dynamics.We extrapolate that a rapid change in environmental conditions that may trigger the maturation process of dormant solitarious population may also decrease, overall, the maturation age and hence destabilize the solitarious subpopulation from a near zero population size towards much larger populations and hence initiate quickly good conditions for gregarization. We also observed that the most realistic population dynamics of locusts was when the attraction point of a stable solitarious population size was above the gregarization threshold. This means that solitarious populations may last through time only near a zero size, but as soon as environmental conditions become favorable to population increase, the gregarization may happen. This outlines the intrinsic character of outbreaking dynamics that a species such as desert locust displays.

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Identification of parameters of evolutionary model of monocyclic cells aggregation with the hop plants example

Cited by 7 publications

References 7 publications

Parameter Identification in Population Models for Insects Using Trap Data

Parameter Identification in Population Models for Insects Using Trap Data

Modeling the Dynamics of Age-Structured Polycyclic Population of Biological Cells on the Parameterized Set of Algebraic Functions

Two‐compartment age‐structured model of solitarious and gregarious locust population dynamics

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