A numerical scheme to the McKendrick–von Foerster equation with diffusion in age

Kakumani, Bhargav Kumar; Tumuluri, Suman Kumar

doi:10.1002/num.22280

Cited by 8 publications

(3 citation statements)

References 27 publications

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“…In [8], the authors considered the M-V-D with nonliner nonlocal Robin boundary condition and studied the existence and uniqueness of the solution. The authors of [10] proposed a convergent numerical scheme to the M-V-D. On the other hand, the existence of a global solution to the M-V-D in a bounded domain with nonliner nonlocal Robin boundary condition was proved when d = d(x) in [9]. Recently in [4], an implicit finite difference scheme has been introduced to approximate the solution to the M-V-D in a bounded domain with nonliner nonlocal Robin boundary condition at both the boundary points.…”

Section: Introductionmentioning

confidence: 99%

A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition

Halder¹,

Tumuluri²

2022

Preprint

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In this article, a numerical scheme to find approximate solutions to the McKendrick-Von Foerster equation with diffusion (M-V-D) is presented. The main difficulty in employing the standard analysis to study the properties of this scheme is due to presence of nonlinear and nonlocal term in the Robin boundary condition in the M-V-D. To overcome this, we use the abstract theory of discretizations based on the notion of stability threshold to analyze the scheme. Stability, and convergence of the proposed numerical scheme are established.

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Section: Introductionmentioning

confidence: 99%

A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition

Halder¹,

Tumuluri²

2022

Preprint

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“…Moreover, the authors studied the asymptotic behavior of the solution towards its steady state using the notion of the General Relative Entropy. There is a lot of literature available in the numerical study of McKendrick-von Foerster equation (MV) with Dirichlet boundary data and there are very few papers available related to MV-D with Robin boundary data ( [26]). In [31,32], the authors developed the concept of stability to certain class of nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

A convergent numerical scheme to a parabolic equation with a nonlocal boundary condition

Kakumani¹,

Tumuluri²

2022

Preprint

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In this paper, a numerical scheme for a nonlinear McKendrickvon Foerster equation with diffusion in age (MV-D) with the Dirichlet boundary condition is proposed. The main idea to derive the scheme is to use the discretization based on the method of characteristics to the convection part, and the finite difference method to the rest of the terms. The nonlocal terms are dealt with the quadrature methods. As a result, an implicit scheme is obtained for the boundary value problem under consideration. The consistency, and the convergence of the proposed numerical scheme is established. Moreover, numerical simulations are presented to validate the theoretical results.

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“…(For a thorough description of the generic singleand multi-stage age-structured system used for insects, see [4].) Model behavior has been studied numerically [14][15][16][17]31] and analytically [4,6,13,14,16], and models have been calibrated to numerous pests, including the grape berry moth [10], apple snail [11], and codling moth [31]. PDE model analysis and calibration has yet to be conducted on the spotted lanternfly, despite significant interest in this pest.…”

Section: Introductionmentioning

confidence: 99%

Temperature sensitivity of pest reproductive numbers in age-structured PDE models, with a focus on the invasive spotted lanternfly

Lewkiewicz¹,

Bona²,

Helmus³

et al. 2021

Preprint

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Invasive pest establishment is a pervasive threat to global ecosystems, agriculture, and public health. The recent establishment of the invasive spotted lanternfly in the northeastern United States has proven devastating to farms and vineyards, necessitating urgent development of population dynamical models and effective control practices. In this paper, we propose a stage-and age-structured system of PDEs to model insect pest populations, in which underlying dynamics are dictated by ambient temperature through rates of development, fecundity, and mortality. The model incorporates diapause and non-diapause pathways, and is calibrated to experimental and field data on the spotted lanternfly. We develop a novel moving mesh method for capturing age-advection accurately, even for coarse discretization parameters. We define a oneyear reproductive number (R 0 ) from the spectrum of a one-year solution operator, and study its sensitivity to variations in the mean and amplitude of the annual temperature profile. We quantify assumptions sufficient to give rise to the low-rank structure of the solution operator characteristic of part of the parameter domain. We discuss establishment potential as it results from the pairing of a favorable R 0 value and transient population survival, and address implications for pest control strategies.

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A numerical scheme to the McKendrick–von Foerster equation with diffusion in age

Cited by 8 publications

References 27 publications

A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition

A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition

A convergent numerical scheme to a parabolic equation with a nonlocal boundary condition

Temperature sensitivity of pest reproductive numbers in age-structured PDE models, with a focus on the invasive spotted lanternfly

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