@ARTICLE{Allen2008,
author = {L. Allen and P. van den Driessche},
title = {The basic reproduction number in some discrete-time epidemic models},
journal = {Journal of Difference Equations and Applications},
volume = {14},
year = {2008},
pages = {1127--1147},
issue = {10},
doi = {10.1080/10236190802332308},
masid = {16314418}
}

@article{vanden2002,
author = {P. van den Driessche and J. Watmough},
title = {Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission},
journal = {Mathematical Biosciences},
volume = {180},
number = {1-2},
pages = {29 - 48},
year = {2002},
note = {},
issn = {0025-5564},
doi = {10.1016/S0025-5564(02)00108-6},
url = {http://www.sciencedirect.com/science/article/pii/S0025556402001086},
keywords = {Basic reproduction number},
keywords = {Sub-threshold equilibrium},
keywords = {Disease transmission model},
keywords = {Disease control}
}

@article {Bailey1980,
author = {N.T.J. Bailey and J. Duppenthaler},
title = {Sensitivity analysis in the modelling of infectious disease dynamics},
journal = {Journal of Mathematical Biology},
publisher = {Springer Berlin / Heidelberg},
issn = {0303-6812},
keyword = {Mathematics and Statistics},
pages = {113-131},
volume = {10},
issue = {2},
url = {http://dx.doi.org/10.1007/BF00275837},
note = {10.1007/BF00275837},
year = {1980}
}

@book{Berman1994,
author = {A. Berman and R. J. Plemmons},
title = {Nonnegative Matrices in the Mathematical Sciences},
publisher = {Society for Industrial and Applied Mathematics},
address = {Philadephia, PA},
year = {1994},
doi = {DOI:10.1137/1.9781611971262},
isbn = {9781611971262},
keywords = {semiconvergent; Leontief input-output model; Markov chains; inverse eigenvalue problem; cones; },
url = {http://dx.doi.org/10.1137/1.9781611971262},
}

@book{Bailey1975,
title={The mathematical theory of infectious diseases and its applications},
author={N.T.J. Bailey},
isbn={9780852642313},
lccn={76675653},
series={Mathematics in Medicine Series},
url={http://books.google.com/books?id=IXtrQgAACAAJ},
year={1975},
publisher={Griffin}
}


@article{Garba200811,
author = "S.M. Garba and A.B. Gumel and M.R. Abu Bakar",
title = "Backward bifurcations in dengue transmission dynamics",
journal = "Mathematical Biosciences",
volume = "215",
number = "1",
pages = "11 - 25",
year = "2008",
note = "",
issn = "0025-5564",
doi = "10.1016/j.mbs.2008.05.002",
url = "http://www.sciencedirect.com/science/article/pii/S0025556408000734",
keywords = "Dengue",
keywords = "Mosquitoes",
keywords = "Equilibria",
keywords = "Stability",
keywords = "Bifurcation",
keywords = "Vaccine"
}


@article{Meyers2003,
author = {L.A. Meyers and B.R. Levin and A.R. Richardson and I. Stojiljkovic},
jstor_articletype = {research-article},
title = {Epidemiology, Hypermutation, Within-Host Evolution and the Virulence of Neisseria meningitidis},
journal = {Proceedings: Biological Sciences},
jstor_issuetitle = {},
volume = {270},
number = {1525},
jstor_formatteddate = {Aug. 22, 2003},
pages = {pp. 1667-1677},
url = {http://www.jstor.org/stable/3592229},
ISSN = {09628452},
abstract = {Many so-called pathogenic bacteria such as Neisseria meningitidis, Haemophilus influenzae, Staphylococcus aureus and Streptococcus pneumoniae are far more likely to colonize and maintain populations in healthy individuals asymptomatically than to cause disease. Disease is a dead-end for these bacteria: virulence shortens the window of time during which transmission to new hosts can occur and the subpopulations of bacteria actually responsible for disease, like those in the blood or cerebral spinal fluid, are rarely transmitted to new hosts. Hence, the virulence factors underlying their occasional pathogenicity must evolve in response to selection for something other than making their hosts sick. What are those selective pressures? We address this general question of the evolution of virulence in the context of phase shifting in N. meningitidis, a mutational process that turns specific genes on and off, and, in particular, contingency loci that code for virulence determinants such as pili, lipopolysaccharides, capsular polysaccharides and outer membrane proteins. We use mathematical models of the epidemiology and the within-host infection dynamics of N. meningitidis to make the case that rapid phase shifting evolves as an adaptation for colonization of diverse hosts and that the virulence of this bacterium is an inadvertent consequence of short-sighted within-host evolution, which is exasperated by the increased mutation rates associated with phase shifting. We present evidence for and suggest experimental and retrospective tests of these hypotheses.},
language = {English},
year = {2003},
publisher = {The Royal Society},
copyright = {Copyright � 2003 The Royal Society},
}


@article{Estep2009,
location = {http://www.scientificcommons.org/52074666},
title = {\emph{A posteriori} analysis of a multirate numerical method for ordinary differential equations},
author = {D. Estep and V. Ginting and S.J. Tavener},
year = {2009},
keywords = {Key words. adjoint operator, a posteriori estimates, discontinuous Galerkin method, iterative method, multirate},
abstract = {Abstract. In this paper, we analyze a multirate time integration method for systems of ordinary differential equations that present significantly different scales within the components of the model. We interpret the multirate method as a multiscale operator decomposition method and use this formulation to conduct both an a priori error analysis and a hybrid a priori – a posteriori error analysis. The hybrid analysis has the form of a computable a posteriori leading order expression and a provably-higher order a priori expression. Both analyses distinguish the effects of the discretization of each component from the effects of multirate solution. The effects on stability arising from the multirate solution are reflected in perturbations to certain associated adjoint operators.},
url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.797},
institution = {CiteSeerX - Scientific Literature Digital Library and Search Engine [http://citeseerx.ist.psu.edu/oai2] (United States)},
}


@article{Macdonald1952,
title={The analysis of equilibrium in malaria.},
volume={49},
url={http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=12995455},
number={9},
journal={Tropical diseases bulletin},
author={Macdonald, G.},
year={1952},
pages={813--829}
}

@article{Li2011,
title={The Failure of ${R}_0$.},
volume={2011},
author={Jing Li and Daniel Blakeley and Robert J. Smith?},
journal={Computational and Mathematical Methods in Medicine},
year={2011},
doi={10.1155/2011/527610}
id={Article ID 527610}
pages={17 pages}
}

@article{Field2012,
title={Demographic projection of high-elevation white pines infected with white pine blister rust: a nonlinear disease model},
author={Field, S. G. and Schoettle, A. W. and Klutsch, J. G. and Tavener, S. J. and Antolin, M. F.},
doi={10.1890/11-0470.1},
journal={Ecological Applications},
volume={22},
issue={1},
url={http://dx.doi.org/10.1890/11-0470.1},
publisher={Ecological Society of America},
year={2012},
pages={166--183}
}

@article{Miller2006,
title={DYNAMICS OF PRION DISEASE TRANSMISSION IN MULE DEER},
author={Miller, Michael W. and Hobbs, N. Thompson and Tavener, Simon J.},
year = {2006},
journal={Ecological Applications},
pages={2208--2214},
volume={16},
issue={6},
doi={10.1890/1051-0761(2006)016[2208:DOPDTI]2.0.CO;2},
publisher={Ecological Society of America},
url={http://dx.doi.org/10.1890/1051-0761(2006)016[2208:DOPDTI]2.0.CO;2},
}

@article{Li2002,
   author = {Li, Chi-Kwong and Schneider, Hans},
   affiliation = {Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, USA. e-mail: ckli@math.wm.edu US US},
   title = {Applications of Perron�Frobenius theory to population dynamics},
   journal = {Journal of Mathematical Biology},
   publisher = {Springer Berlin / Heidelberg},
   issn = {0303-6812},
   keyword = {Mathematics and Statistics},
   pages = {450-462},
   volume = {44},
   issue = {5},
   url = {http://dx.doi.org/10.1007/s002850100132},
   note = {10.1007/s002850100132},
   year = {2002}
}

@book{horn1990,
  title={Matrix Analysis},
  address = {Cambridge},
  author={Horn, Roger A. and Johnson, Charles R.},
  isbn={9780521386326},
  lccn={lc85007736},
  url={http://books.google.com/books?id=PlYQN0ypTwEC},
  year={1990},
  publisher={Cambridge University Press}
}

@book{horn1991,
    address = {Cambridge},
    author = {Horn, Roger A. and Johnson, Charles R.},
    citeulike-article-id = {4211317},
    keywords = {file-import-09-03-23},
    mrnumber = {MR1091716 (92e:15003)},
    posted-at = {2009-03-23 20:43:08},
    priority = {2},
    publisher = {Cambridge University Press},
    title = {Topics in matrix analysis},
    year = {1991}
}


@book{Zhang2011,
  title={Matrix Theory: Basic Results and Techniques},
  author={Zhang, F.},
  isbn={9781461410980},
  series={Universitext Series},
  url={http://books.google.com/books?id=iWMYmL801vQC},
  year={2011},
  publisher={Springer}
}

@article{Caswell2008,
author = {Caswell, H.},
title={{Perturbation analysis of nonlinear matrix population models}},
journal = {Demographic Research},
volume = {18},
number = {3},
pages = {59-116},
doi = {10.4054/DemRes.2008.18.3},
year = {2008},
abstract = {Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models), feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios), age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.},
URL = {http://www.demographic-research.org/volumes/vol18/3/},
eprint = {http://www.demographic-research.org/volumes/vol18/3/18-3.pdf}
}

@article {Tavener2011,
author = {S.J. Tavener and M. Mikucki and S.G. Field  and M.F. Antolin},
title = {Transient sensitivity analysis for nonlinear population models},
journal = {Methods in Ecology and Evolution},
volume = {2},
number = {5},
publisher = {Blackwell Publishing Ltd},
issn = {2041-210X},
url = {http://dx.doi.org/10.1111/j.2041-210X.2011.00108.x},
doi = {10.1111/j.2041-210X.2011.00108.x},
pages = {560--575},
keywords = {elasticity, matrix population models, partial dominance, sensitivity, single-locus genetics, SIR model, transience},
year = {2011},
}

@MastersThesis{Mikucki2012,
author =     {M. Mikucki},
title  =     {{Sensitivity Analysis of the Basic Reproduction Number and other Quantities for Infectious Disease Models}},
school =     {Colorado State University},
year   =     {2012},
}

@article{Buzby2008,
author = {M. Buzby and D. Neckels and M.F. Antolin and D. Estep},
title = {Analysis of the sensitivity properties of a model of vector-borne bubonic plague},
volume = {5},
number = {26},
pages = {1099-1107},
year = {2008},
doi = {10.1098/rsif.2007.1339},
abstract ={Model sensitivity is a key to evaluation of mathematical models in ecology and evolution, especially in complex models with numerous parameters. In this paper, we use some recently developed methods for sensitivity analysis to study the parameter sensitivity of a model of vector-borne bubonic plague in a rodent population proposed by Keeling & Gilligan. The new sensitivity tools are based on a variational analysis involving the adjoint equation. The new approach provides a relatively inexpensive way to obtain derivative information about model output with respect to parameters. We use this approach to determine the sensitivity of a quantity of interest (the force of infection from rats and their fleas to humans) to various model parameters, determine a region over which linearization at a specific parameter reference point is valid, develop a global picture of the output surface, and search for maxima and minima in a given region in the parameter space.},
URL = {http://rsif.royalsocietypublishing.org/content/5/26/1099.abstract},
eprint = {http://rsif.royalsocietypublishing.org/content/5/26/1099.full.pdf+html},
journal = {Journal of The Royal Society Interface}
}
