A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme
We develop a finite difference scheme to approximate the solution of a novel size-structured mathematical model of the transmission dynamics of Mycobacterium marinum (Mm) in an aquatic environment. The model consists of a system of nonlinear hyperbolic partial differential equations coupled with th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.679 |
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| author | Azmy S. Ackleh Mark L. Delcambre Karyn L. Sutton Don G. Ennis |
| author_facet | Azmy S. Ackleh Mark L. Delcambre Karyn L. Sutton Don G. Ennis |
| author_sort | Azmy S. Ackleh |
| collection | DOAJ |
| description | We develop a finite difference scheme to approximate the solution of a novel size-structured mathematical model of the transmission dynamics of Mycobacterium marinum (Mm) in an aquatic environment. The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. Existence and uniqueness results are established and convergence of the finite difference approximation to the unique bounded variation weak solution of the model is obtained. Numerical simulations demonstrating the accuracy of the method are presented. We also conducted preliminary studies on the key features of this model, such as various forms of growth rates (indicative of possible theories of development), and conditions for competitive exclusion or coexistence as determined by reproductive fitness and genetic spread in the population. |
| format | Article |
| id | doaj-art-9704aaad2b054426be175ed29d64c23c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9704aaad2b054426be175ed29d64c23c2025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-0111467972110.3934/mbe.2014.11.679A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation schemeAzmy S. Ackleh0Mark L. Delcambre1Karyn L. Sutton2Don G. Ennis3Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010Department of Biology, University of Louisiana at Lafayette, Lafayette, LA 70504-2451We develop a finite difference scheme to approximate the solution of a novel size-structured mathematical model of the transmission dynamics of Mycobacterium marinum (Mm) in an aquatic environment. The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. Existence and uniqueness results are established and convergence of the finite difference approximation to the unique bounded variation weak solution of the model is obtained. Numerical simulations demonstrating the accuracy of the method are presented. We also conducted preliminary studies on the key features of this model, such as various forms of growth rates (indicative of possible theories of development), and conditions for competitive exclusion or coexistence as determined by reproductive fitness and genetic spread in the population.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.679existence-uniquenessbehavior of solutions.finite difference approximationmycobacterial infectionsconvergencestructured models |
| spellingShingle | Azmy S. Ackleh Mark L. Delcambre Karyn L. Sutton Don G. Ennis A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme Mathematical Biosciences and Engineering existence-uniqueness behavior of solutions. finite difference approximation mycobacterial infections convergence structured models |
| title | A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme |
| title_full | A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme |
| title_fullStr | A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme |
| title_full_unstemmed | A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme |
| title_short | A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme |
| title_sort | structured model for the spread of mycobacterium marinum foundations for a numerical approximation scheme |
| topic | existence-uniqueness behavior of solutions. finite difference approximation mycobacterial infections convergence structured models |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.679 |
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