A structured model for the spread of &lt;em&gt;Mycobacterium marinum&lt;/em&gt;: Foundations for a numerical approximation scheme

Ackleh, Azmy S.; Delcambre, Mark L.; Sutton, Karyn L.; Ennis, Don G.

doi:10.3934/mbe.2014.11.679

Cited by 5 publications

(23 citation statements)

References 45 publications

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“…In [8], the authors proved convergence of their method to a bounded variation weak solution for Equation (2); these results can readily be extended to the model and scheme from [9]. Here, we develop for the model in [8] a novel second-order high-resolution scheme in the spirit of those developed in [5,7,23,35,40]. To establish convergence of this method, a substantial modification of the techniques used in [5,7] is necessary due to the explicit modelling of the genetic or phenotypic heterogeneity between individuals, nonlocal nonlinearities, and quadratic nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, two mathematical models were developed to study Mm [8,9]. In [9], a bacterial load-structured model was created to incorporate the differences in fish behavior as a function of infection severity, since chronic infection plays such a crucial role and these infections are asymptomatic.…”

Section: Introductionmentioning

confidence: 99%

“…Solutions of this model provided reasonable agreement with experimental data, establishing the model's potential as a tool within which to interpret experimental findings and guide further experimental design. In [8], a size-structured model was developed to study key metabolic features such as growth rates and consumption activity on disease dynamics. The authors used this model to illustrate conditions for competitive exclusion or coexistence as determined by reproductive fitness and genetic spread in the population.…”

Section: Introductionmentioning

confidence: 99%

“…The authors used this model to illustrate conditions for competitive exclusion or coexistence as determined by reproductive fitness and genetic spread in the population. The models in [8,9] were both discretized using a first-order finite difference method. In [8], the authors proved convergence of their method to a bounded variation weak solution for Equation (2); these results can readily be extended to the model and scheme from [9].…”

Section: Introductionmentioning

confidence: 99%

“…The models in [8,9] were both discretized using a first-order finite difference method. In [8], the authors proved convergence of their method to a bounded variation weak solution for Equation (2); these results can readily be extended to the model and scheme from [9]. Here, we develop for the model in [8] a novel second-order high-resolution scheme in the spirit of those developed in [5,7,23,35,40].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Ackleh

Delcambre

Sutton

2014

Journal of Biological Dynamics

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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. 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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Ackleh

Delcambre

Sutton

2014

Journal of Biological Dynamics

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A high resolution finite difference method for a model of structured susceptible‐infected populations coupled with the environment

Ackleh

Ma²,

Tang

2017

Numerical Methods Partial

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We develop a general model describing a structured susceptible‐infected (SI) population coupled with the environment. This model applies to problems arising in ecology, epidemiology, and cell biology. The model consists of a system of quasilinear hyperbolic partial differential equations coupled with a system of nonlinear ordinary differential equations that represents the environment. We develop a second‐order high resolution finite difference scheme to numerically solve the model. Convergence of this scheme to a weak solution with bounded total variation is proved. Numerical simulations are provided to demonstrate the high‐resolution property of the scheme and an application to a multi‐host wildlife disease model is explored.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1420–1458, 2017

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Infection severity across scales in multi-strain immuno-epidemiological Dengue model structured by host antibody level

Gulbudak

Browne

2020

J. Math. Biol.

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Infection by distinct Dengue virus serotypes and host immunity are intricately linked. In particular, certain levels of cross-reactive antibodies in the host may actually enhance infection severity leading to Dengue hemorrhagic fever (DHF). The coupled immunological and epidemiological dynamics of Dengue calls for a multi-scale modeling approach. In this work, we formulate a within-host model which mechanistically recapitulates characteristics of antibody dependent enhancement (ADE) in Dengue infection. The within-host scale is then linked to epidemiological spread by a vector-host partial differential equation model structured by host antibody level. The coupling allows for dynamic population-wide antibody levels to be tracked through primary and secondary infections by distinct Dengue strains, along with waning of cross-protective immunity after primary infection. Analysis of both the within-host and between-host systems are conducted. Stability results in the epidemic model are formulated via basic and invasion reproduction numbers as a function of immunological variables. Additionally, we develop numerical methods in order to simulate the multi-scale model and assess the influence of parameters on disease spread and DHF prevalence in the population.

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A structured model for the spread of <em>Mycobacterium marinum</em>: Foundations for a numerical approximation scheme

Cited by 5 publications

References 45 publications

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

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

A high resolution finite difference method for a model of structured susceptible‐infected populations coupled with the environment

Infection severity across scales in multi-strain immuno-epidemiological Dengue model structured by host antibody level

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