期刊
MATHEMATICAL BIOSCIENCES AND ENGINEERING
卷 11, 期 4, 页码 679-721出版社
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/mbe.2014.11.679
关键词
Structured models; finite difference approximation; existence-uniqueness; convergence; mycobacterial infections; behavior of solutions
资金
- National Science Foundation [DMS-1312963]
- Louisiana Board of Regents [LEQSF(2012-15)-RD-A-30]
- NIH [5R21AI055964-01]
- NIEHS through Oregon State [P30 E503850]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1312963] Funding Source: National Science Foundation
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.
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