Time-varying and state-dependent recovery rates in epidemiological models

Infectious Disease Modelling - Tập 2 Số 4 - Trang 419-430 - 2017
Scott Greenhalgh1,2, Troy Day1
1Department of Mathematics and Statistics, Queen’s University, Jeffery Hall, Kingston, ON, K7L 3N6, Canada
2Department of Mathematics, Siena College, Loudonville, NY 12211, USA

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Alexander, 2005, Bifurcation analysis of an SIRS epidemic model with generalized incidence, SIAM Journal on Applied Mathematics, 65, 1794, 10.1137/040604947

Arino, 2006, Time delays in epidemic models, 539

Bailey, 1975

Ball, 1983, The threshold behaviour of epidemic models, Journal of Applied Probability, 20, 227, 10.2307/3213797

Ball, 1986, A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models, Advances in Applied Probability, 18, 289, 10.2307/1427301

Ball, 1991, Dynamic population epidemic models, Mathematical Biosciences, 107, 299, 10.1016/0025-5564(91)90011-7

Britton, 2010, Stochastic epidemic models: A survey, Mathematical Biosciences, 225, 24, 10.1016/j.mbs.2010.01.006

Clancy, 1999, Outcomes of epidemic models with general infection and removal rate functions at certain stopping times, Journal of Applied Probability, 36, 799, 10.1239/jap/1032374635

Clancy, 2014, SIR epidemic models with general infectious period distribution, Statistics & Probability Letters, 85, 1, 10.1016/j.spl.2013.10.017

Cliff, 1981

Diekmann, 1990, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28, 10.1007/BF00178324

van den Driessche, 2000, A simple SIS epidemic model with a backward bifurcation, Journal of Mathematical Biology, 40, 525, 10.1007/s002850000032

van den Driessche, 2002, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 10.1016/S0025-5564(02)00108-6

Feng, 2007, Epidemiological models with non-exponentially distributed disease stages and applications to disease control, Bulletin of Mathematical Biology, 69, 1511, 10.1007/s11538-006-9174-9

Fenner, 1988

Finkelstein, 2002, On the reversed hazard rate, Reliability Engineering & System Safety, 78, 71, 10.1016/S0951-8320(02)00113-8

Fowler, 2015, Simple approximations for epidemics with exponential and fixed infectious periods, Bulletin of Mathematical Biology, 77, 1539, 10.1007/s11538-015-0095-3

Gough, 1977, The estimation of latent and infectious periods, Biometrika, 64, 559, 10.1093/biomet/64.3.559

Greenhalgh, 2015, Disease elimination and re-emergence in differential-equation models, Journal of Theoretical Biology, 387, 174, 10.1016/j.jtbi.2015.09.037

Greenhalgh, 2015, The epidemiological impact of HIV antiretroviral therapy on malaria in children, AIDS, 29, 473, 10.1097/QAD.0000000000000550

Heffernan, 2005, Perspectives on the basic reproductive ratio, Journal of the Royal Society, Interface/the Royal Society, 2, 281, 10.1098/rsif.2005.0042

Hethcote, 1980, Integral equation models for endemic infectious diseases, Journal of Mathematical Biology, 9, 37, 10.1007/BF00276034

Hopkins, 2013, Disease eradication, New England Journal of Medicine, 368, 54, 10.1056/NEJMra1200391

Jones, 2009, Kumaraswamy's distribution: A beta-type distribution with some tractability advantages, Statistical Methodology, 6, 70, 10.1016/j.stamet.2008.04.001

Keeling, 1999, Stochastic dynamics and a power law for measles variability, Philosophical Transactions of the Royal Society B: Biological Sciences, 354, 769, 10.1098/rstb.1999.0429

Keeling, 2007

Korobeinikov, 2005, Non-linear incidence and stability of infectious disease models, Mathematical Medicine and Biology: A Journal of the IMA, 22, 113, 10.1093/imammb/dqi001

Krylova, 2013, Effects of the infectious period distribution on predicted transitions in childhood disease dynamics, Journal of The Royal Society Interface, 10, 10.1098/rsif.2013.0098

Lawless, 2002

Liu, 1987, Dynamical behavior of epidemiological models with nonlinear incidence rates, Journal of Mathematical Biology, 25, 359, 10.1007/BF00277162

Liu, 1986, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, Journal of Mathematical Biology, 23, 187, 10.1007/BF00276956

Lloyd, 2001, Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods, Proceedings of the Royal Society B: Biological Sciences, 268, 985, 10.1098/rspb.2001.1599

Lloyd, 2001, Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics, Theoretical Population Biology, 60, 59, 10.1006/tpbi.2001.1525

Martcheva, 2015

Nájera, 2011, Some lessons for the future from the global malaria eradication programme (1955–1969), PLoS Medicine, 8, e1000412, 10.1371/journal.pmed.1000412

Normile, 2008, Rinderpest. Driven to extinction, Science (New York, N.Y.), 319, 1606, 10.1126/science.319.5870.1606

Pearson, 1893, Contributions to the mathematical theory of evolution, Proceedings of the Royal Society of London, 54, 329, 10.1098/rspl.1893.0079

Pearson, 1895, Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 186, 343, 10.1098/rsta.1895.0010

Ponciano, 2011, First principles modeling of nonlinear incidence rates in seasonal epidemics, PLoS Computational Biology, 7, e1001079, 10.1371/journal.pcbi.1001079

Rhind, 1909, Tables to facilitate the computation of the probable errors of the chief constants of skew frequency distributions, Biometrika, 7, 127, 10.1093/biomet/7.1-2.127

Roberts, 2015, Nine challenges for deterministic epidemic models, Epidemics, 10, 49, 10.1016/j.epidem.2014.09.006

Rodriguez, 2007

Ruan, 2003, Dynamical behavior of an epidemic model with a nonlinear incidence rate, Journal of Differential Equations, 188, 135, 10.1016/S0022-0396(02)00089-X

Schuster, 2016

Simpson, 1952, Infectiousness of communicable diseases in the household (measles, chickenpox, and mumps), Lancet (London, England), 2, 549, 10.1016/S0140-6736(52)91357-3

Sobol, 2001, Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation, 55, 271, 10.1016/S0378-4754(00)00270-6

Tarning, 2012, Population pharmacokinetics and pharmacodynamics of piperaquine in children with uncomplicated falciparum malaria, Clinical Pharmacology and Therapeutics, 91, 497, 10.1038/clpt.2011.254