A second-order high-resolution finite difference scheme for a size-structured model for the spread of Mycobacterium marinum

• Published in: Journal of biological dynamics Vol. 9; no. sup1; pp. 156 - 187
• Main Authors: Ackleh, Azmy S., Delcambre, Mark L., Sutton, Karyn L.
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 30.06.2015; Taylor & Francis Ltd
• Subjects: Animals; Aquatic environment; Computer applications; ecology and evolutionary biology; Fertility; Fish Diseases - microbiology; Fishes - microbiology; Linear Models; Mathematical models; Models, Biological; Mycobacterium marinum; Mycobacterium marinum - physiology; Nonlinear Dynamics; Numerical Analysis, Computer-Assisted; Population Dynamics; ecology and evolutionary biology; population dynamics
• ISSN: 1751-3758; 1751-3766; 1751-3766
• DOI: 10.1080/17513758.2014.962998

We present a second-order high-resolution finite difference scheme to approximate the solution of a mathematical model of the transmission dynamics of Mycobacterium marinum (Mm) in an aquatic environment. This work extends the numerical theory and continues the preliminary studies on the model first developed in Ackleh et al. [Structured models for the spread of Mycobacterium marinum: foundations for a numerical approximation scheme, Math. Biosci. Eng. 11 (2014), pp. 679-721]. Numerical simulations demonstrating the accuracy of the method are presented, and we compare this scheme to the first-order scheme developed in Ackleh et al. [Structured models for the spread of Mycobacterium marinum: foundations for a numerical approximation scheme, Math. Biosci. Eng. 11 (2014), pp. 679-721] to show that the first-order method requires significantly more computational time to provide solutions with a similar accuracy. We also demonstrated that the model can be a tool to understand surprising or nonintuitive phenomena regarding competitive advantage in the context of biologically realistic growth, birth and death rates.