Numerical solution of a spatio-temporal predator-prey model with infected prey

Bürger, Raimund; Chowell, Gerardo; Gavilán, Elvis; Mulet, Pep; Villada, Luis Miguel

doi:10.3934/mbe.2019021

Cited by 15 publications

(16 citation statements)

References 33 publications

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“…• Computational biology. A spatio-temporal predator-prey model with infected prey was simulated in Burger et al (2019). Tumour growth and calcification were studied in Chen and Lowengrub (2019).…”

Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

118

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Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

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Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

118

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“…Clearly, Theorem 1 applies to ( 9)-( 2)-( 10)-( 12) and the cost (11) fits into (8). First, as a reference case, we integrate ( 9)-( 2)-( 10)- (12) with 𝑞 ≡ 0. The results are displayed in Figure 1.…”

Section: Optimized Timing Of Parasitoids' Releasesmentioning

confidence: 99%

Well‐posedness and control in a hyperbolic–parabolic parasitoid–parasite system

Colombo

Rossi

2021

Stud Appl Math

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We develop a time and space‐dependent predator—prey model. The predators' equation is a nonlocal hyperbolic balance law, while the diffusion of prey obeys a parabolic equation, so that predators “hunt” for prey, while prey diffuse. A control term allows to describe the use of predators as parasitoids to limit the growth of prey–parasites. The general well‐posedness and stability results here obtained ensure the existence of optimal pest control strategies, as discussed through some numerical integrations. The specific example we have in mind is that of Trichopria drosophilæ used to fight against the spreading of Drosophila suzukii.

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“…Explicit numerical schemes for (1) on a uniform Cartesian grid of meshwidth ∆x and time step ∆t are easy to implement but are associated with a Courant-Friedrichs-Lewy (CFL) stability condition [2] that imposes the proportionality ∆t ≈ ∆x 2 [3][4][5][6][7][8][9][10][11][12][13]. This restriction makes long-term simulations of ( 1)-( 3) on a uniform grid unacceptably slow.…”

Section: Scopementioning

confidence: 99%

Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires

et al. 2020

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Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-explicit Runge–Kutta (IMEX-RK) methods and Strang-type splitting technique to adequately handle the non-linear parabolic term and the stiffness in the reactive part. Weighted essentially non-oscillatory (WENO) reconstructions are applied to the discretization of the nonlinear convection term. Examples are focused on the applicative problem of determining the width of a firebreak to prevent the propagation of forest fires. Results illustrate that the model and numerical scheme provide an effective tool for defining that width and the parameters for control strategies of wildland fires.

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Numerical solution of a spatio-temporal predator-prey model with infected prey

Cited by 15 publications

References 33 publications

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Well‐posedness and control in a hyperbolic–parabolic parasitoid–parasite system

Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires

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