Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents
In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (20...
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2018-01-01
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| author | Raimund BÜrger Gerardo Chowell Elvis GavilÁn Pep Mulet Luis M. Villada |
| author_facet | Raimund BÜrger Gerardo Chowell Elvis GavilÁn Pep Mulet Luis M. Villada |
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| description | In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511-524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369-400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2018-01-01 |
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| spelling | doaj-art-f7d924c651b64a0eb28f79d447043bc12025-01-24T02:40:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-01-011519512310.3934/mbe.2018004Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodentsRaimund BÜrger0Gerardo Chowell1Elvis GavilÁn2Pep Mulet3Luis M. Villada4CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, ChileSchool of Public Health, Georgia State University, Atlanta, Georgia, USACI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, ChileDepartament de Matemàtiques, Universitat de València, Av. Dr. Moliner 50, E-46100 Burjassot, SpainGIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Casilla 5-C, Concepción, ChileIn this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511-524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369-400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.https://www.aimspress.com/article/doi/10.3934/mbe.2018004spatial-temporal seir modelhantavirus infectiongender-structured modelconvection-diffusion-reaction systemimplicit-explicit runge-kutta schemeweighted essentially non-oscillatory reconstruction |
| spellingShingle | Raimund BÜrger Gerardo Chowell Elvis GavilÁn Pep Mulet Luis M. Villada Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents Mathematical Biosciences and Engineering spatial-temporal seir model hantavirus infection gender-structured model convection-diffusion-reaction system implicit-explicit runge-kutta scheme weighted essentially non-oscillatory reconstruction |
| title | Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents |
| title_full | Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents |
| title_fullStr | Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents |
| title_full_unstemmed | Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents |
| title_short | Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents |
| title_sort | numerical solution of a spatio temporal gender structured model for hantavirus infection in rodents |
| topic | spatial-temporal seir model hantavirus infection gender-structured model convection-diffusion-reaction system implicit-explicit runge-kutta scheme weighted essentially non-oscillatory reconstruction |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018004 |
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