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@article{abbey1952,
title={An examination of the {R}eed-{F}rost theory of epidemics},
author={Abbey, H.},
journal={Human Biology},
volume={24},
number={3},
pages={201},
year={1952},
publisher={Johns Hopkins Press}
}
@article{althaus2014,
title={Estimating the reproduction number of {E}bola virus {(EBOV)} during the 2014 outbreak in {W}est Africa},
author={Althaus, C.L.},
journal={PLoS Currents},
volume={6},
year={2014},
publisher={Public Library of Science}
}
@book{Anderson1991,
author = "Anderson, W.",
title = "Continuous-Time {M}arkov Chains: An Applications-Oriented Approach",
year = "1991",
publisher = "Springer-Verlag"
}
@book{Anderson1992,
title={Infectious Diseases of Humans: Dynamics and Control},
author={Anderson, R.M. and May, R.M.},
year={1992},
publisher={Oxford University Press}
}
@article{andersson1998,
title={A threshold limit theorem for the stochastic logistic epidemic},
author={Andersson, H. and Djehiche, B.},
journal={Journal of Applied Probability},
pages={662--670},
volume={35},
number={3},
year={1998},
publisher={Applied Probability Trust}
}
@book{Andersson2000,
author = "Andersson, H. and Britton, T.",
title = "Stochastic Epidemic Models and Their Statistical Analysis",
year = "2000",
publisher = "Springer"
}
@article{artalejo2012,
title={On the time to extinction from quasi-stationarity: A unified approach},
author={Artalejo, J.R.},
journal={Physica A: Statistical Mechanics and its Applications},
volume={391},
number={19},
pages={4483--4486},
year={2012},
publisher={Elsevier}
}
@book{Asmussen1983,
author = "Asmussen, S. and Hering, H.",
title = "Branching Processes",
year = "1983",
publisher = "Birkhauser",
series = "Progress in Probability and Statistics"
}
@book{Athreya1972,
author = "Athreya, K. and Ney, P.",
title = "Branching Processes",
year = "1972",
publisher = "Springer",
}
@article{Ball1997,
author = {Ball, F.},
journal = {Annals of Applied Probability},
pages = {46--89},
title = {Epidemics in populations with two levels of mixing},
volume = {7},
year = {1997},
publisher={Institute of Mathematical Statistics}
}
@article{Ball1999,
author = {Ball, F.},
journal = {Mathematical Biosciences},
pages = {41--67},
title = {Stochastic and deterministic models for {SIS} epidemics among a population partitioned into households},
volume = {156},
year = {1999},
publisher = {Elsevier}
}
@book{bailey1975,
author = {Bailey, N.T.J.},
year = {1975},
title = {The Mathematical Theory of Epidemics},
publisher = {Hafner}
}
@article{barbour1975,
title={The duration of the closed stochastic epidemic},
author={Barbour, A.D.},
journal={Biometrika},
volume={62},
number={2},
pages={477--482},
year={1975},
publisher={Biometrika Trust}
}
@article{Barbour2008,
title={Laws of large numbers for epidemic models with countably many types},
author={Barbour, A.D. and Luczak, M.J.},
journal={The Annals of Applied Probability},
volume={18},
number={6},
pages={2208--2238},
year={2008},
publisher={Institute of Mathematical Statistics}
}
@article{Barbour2010,
author = {Barbour, A.D. and Pollett, P.K.},
journal = {Journal of Applied Probability},
number = {20},
pages = {934--946},
title = {Total variation approximation for quasi-stationary distributions},
volume = {946},
year = {2010},
publisher={Applied Probability Trust}
}
@article{bedford2012,
title={Canalization of the evolutionary trajectory of the human influenza virus},
author={Bedford, Trevor and Rambaut, Andrew and Pascual, Mercedes},
journal={BMC Biology},
volume={10},
number={1},
pages={38},
year={2012},
publisher={BioMed Central}
}
@article{bedford2014,
title={Integrating influenza antigenic dynamics with molecular evolution},
author={Bedford, Trevor and Suchard, Marc A and Lemey, Philippe and Dudas, Gytis and Gregory, Victoria and Hay, Alan J and McCauley, John W and Russell, Colin A and Smith, Derek J and Rambaut, Andrew},
journal={Elife},
volume={3},
pages={e01914},
year={2014},
publisher={eLife Sciences Publications Limited}
}
@article{bedford2015,
title={Global circulation patterns of seasonal influenza viruses vary with antigenic drift},
author={Bedford, T. and Riley, S. and Barr, I.G. and Broor, S. and Chadha, M. and Cox, N.J. and Daniels, R.S. and Gunasekaran, C.P. and Hurt, A.C. and Kelso, A. and Klimov, A. and Lewis, N.S. and Li, X. and McCauley, J.W. and Odagiri, T. and Potdar, V. and Rambaut, A. and Shu, Y. and Skepner, E. and Smith, D.J. and Suchard, M.A. and Tashiro, M. and Wang, D. and Xu, X. and Lemey P. and Russell, C.A.},
journal={Nature},
volume={523},
number={7559},
pages={217-220},
year={2015},
publisher={Nature Publishing Group}
}
@book{Bender1999,
title={Advanced Mathematical Methods for Scientists and Engineers {I}},
author={Bender, C.M. and Orszag, S.A.},
year={1999},
publisher={Springer Science \& Business Media}
}
@article{bichara2014,
title={Global analysis of multi-strains {SIS}, {SIR} and {MSIR} epidemic models},
author={Bichara, Derdei and Iggidr, Abderrahman and Sallet, Gauthier},
journal={Journal of Applied Mathematics and Computing},
volume={44},
number={1-2},
pages={273--292},
year={2014},
publisher={Springer}
}
@incollection{blanchet2013,
title={Empirical Analysis of a Stochastic Approximation Approach for Computing Quasi-stationary Distributions},
author={Blanchet, J. and Glynn, P. and Zheng, S.},
booktitle={EVOLVE-A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II},
pages={19--37},
year={2013},
publisher={Springer}
}
@article{brown2009,
title={Prospects for an influenza vaccine that induces cross-protective cytotoxic {T} lymphocytes},
author={Brown, Lorena E and Kelso, Anne},
journal={Immunology and Cell Biology},
volume={87},
number={4},
pages={300--308},
year={2009},
publisher={Wiley Online Library}
}
@article{cattiaux2009,
title={Quasi-stationary distributions and diffusion models in population dynamics},
author={Cattiaux, P. and Collet, P. and Lambert, A. and Mart{\'\i}nez, S. and M{\'e}l{\'e}ard, S. and San Mart{\'\i}n, J.},
journal={The Annals of Probability},
volume={37},
number={5},
pages={1926--1969},
year={2009},
publisher={Institute of Mathematical Statistics}
}
@article{cavender1978,
title="Quasi-Stationary Distributions of Birth-and-Death Processes",
author = "Cavender, J.A.",
journal = "Advances in Applied Probability",
publisher = "Applied Probability Trust",
volume = "10",
number = "3",
year = "1978",
pages = "570--586"
}
@article{chambers2015,
title={Identification of hemagglutinin residues responsible for {H3N2} antigenic drift during the 2014-2015 influenza season},
author={Chambers, B.S and Parkhouse, K. and Ross, T.M. and Alby, K. and Hensley, S.E.},
journal={Cell Reports},
volume={12},
number={1},
pages={1-6},
year={2015},
publisher={Elsevier}
}
@article{cintron2009,
title={The estimation of the effective reproductive number from disease outbreak data.},
author={Cintr{\'o}n-Arias, A. and Castillo-Ch{\'a}vez, C. and Bettencourt, L.M. and Lloyd, A.L. and Banks, H.T.},
journal={Mathematical Biosciences and Engineering},
volume={6},
number={2},
pages={261--282},
year={2009},
publisher = {AIMS}
}
@article{chao1982,
title= {A General Purpose Unequal Probability Sampling Plan},
author = {Chao, M.T.},
journal = {Biometrika},
volume = {69},
number = {3},
pages = {653--656},
year = {1982},
publisher = {Oxford University Press}
}
@article{champagnat2012,
title={Birth and death processes with neutral mutations},
author={Champagnat, Nicolas and Lambert, Amaury and Richard, Mathieu},
journal={International Journal of Stochastic Analysis},
volume={2012},
year={2012},
publisher={Hindawi Publishing Corporation}
}
@article{chen2005,
title={Stopping-time resampling for sequential {M}onte {C}arlo methods},
author={Chen, Y. and Xie, J. and Liu, Jun S.},
journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
volume={67},
number={2},
pages={199--217},
year={2005},
publisher={Wiley}
}
@article{chopin2002,
title={A sequential particle filter method for static models},
author={Chopin, N.},
journal={Biometrika},
volume={89},
number={3},
pages={539--552},
year={2002},
publisher={Biometrika Trust}
}
@article{clancy2003,
title ="A note on quasi-stationary distributions of birth-death processes and the {SIS} logistic epidemic",
author ="Clancy, D. and Pollett, P.K.",
journal ="Journal of Applied Probability",
volume = "40",
pages = "821--825",
year = "2003",
publisher = "Applied Probability Trust"
}
@article{clancy2010,
title={The effect of waning immunity on long-term behaviour of stochastic models for the spread of infection},
author={Clancy, D. and Mendy, S.T.},
journal={Journal of Mathematical Biology},
volume={61},
number={4},
pages={527--544},
year={2010},
publisher={Springer}
}
@book{collet2013,
title={Quasi-Stationary Distributions: {M}arkov Chains, Diffusions and Dynamical Systems},
author={Collet, P. and Martinez, S. and San Martin, J.},
year={2001},
publisher={Springer}
}
@article{cowling2010,
title={The effective reproduction number of pandemic influenza: prospective estimation},
author={Cowling, B.J. and Lau, M.S.Y. and Ho, L. and Chuang, S. and Tsang, T. and Liu, S. and Leung, P. and Lo, S. and Lau, E.H.Y.},
journal={Epidemiology (Cambridge, Mass.)},
volume={21},
number={6},
pages={842--846},
year={2010},
publisher={Wolterss Kluwer}
}
@techreport{crisan2000,
title = {Convergence of {S}equential {M}onte {C}arlo Methods},
author = {Crisan, D. and Doucet, A.},
year = {2000},
institution = {Department of Engineering, University of Cambridge},
number = {381}
}
@article{darroch1967,
title={On Quasi-Stationary Distributions in Absorbing Continuous-Time Finite {M}arkov Chains},
author={Darroch, J.N. and Seneta, E.},
journal={Journal of Applied Probability},
volume={4},
number={1},
pages={192--196},
year={1967},
publisher={Applied Probability Trust}
}
@Book{delmoral2004,
author = {Del Moral, P.},
title = {Feynman-{K}ac Formulae: Genealogical and Interacting Particle Systems with Applications},
year = {2004},
publisher={Springer-Verlag, New York}
}
@inproceedings{douc2005,
title={Comparison of resampling schemes for particle filtering},
author={Douc, R. and Capp{\'e}, O.},
booktitle={Proceedings of 4th International Symposium on Image and Signal Processing and Analysis (ISPA)},
pages={64--69},
year={2005},
organization={IEEE}
}
@book{doucet2001,
title={Sequential {M}onte {C}arlo methods in practice},
author={Doucet, A. and De Freitas, N. and Gordon, N.},
year={2001},
publisher={Springer}
}
@incollection{doucet2009,
title={A tutorial on particle filtering and smoothing: {F}ifteen years later},
author={Doucet, A. and Johansen, A.M.},
booktitle = {Handbook of Nonlinear Filtering},
year = {2009},
pages = {656-704},
publisher = {Oxford University Press}
}
@article{delmoral2006,
title={Sequential {M}onte {C}arlo samplers},
author={Del Moral, P. and Doucet, A. and Jasra, A.},
journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
volume={68},
number={3},
pages={411--436},
year={2006},
publisher={Wiley}
}
@book{dlmf,
title={NIST Handbook of Mathematical Functions},
author={Clark, C.W. and Olver, F.W.J. and Boisvert, R.F. and Lozier, D.W.},
year={2010},
publisher={Cambridge University Press}
}
@article{dudley1968,
author = "Dudley, R. M.",
journal = "Ann. Math. Statist.",
month = "10",
number = "5",
pages = "1563--1572",
publisher = "The Institute of Mathematical Statistics",
title = "Distances of Probability Measures and Random Variables",
volume = "39",
year = "1968"
}
@book{durrett2013,
title={Probability: Theory and Examples},
author={Durrett, R.},
year={2010},
publisher={Cambridge University Press}
}
@article{ewens1963,
title={The diffusion equation and a pseudo-distribution in genetics},
author={Ewens, W.J.},
journal={Journal of the Royal Statistical Society. Series B (Methodological)},
pages={405--412},
year={1963},
publisher={Wiley}
}
@article{Ferrari1995,
author = "Ferrari, P.A. and Kesten, H. and Martinez, S. and Picco, P.",
title = "Existence of quasi-stationary Distributions. A Renewal Dynamical Approach",
year = "1995",
journal = "The Annals of Probability",
volume = "23",
number = "2",
pages = "501--521",
publisher = "Institute of Mathematical Statistics"
}
@article{fitch1997,
title={Long term trends in the evolution of {H(3) HA1} human {I}nfluenza type {A}},
author={Fitch, W.M. and Bush, R.M. and Bender, C.A. and Cox, N.J.},
journal={Proceedings of the National Academy of Sciences},
volume={94},
number={15},
pages={7712--7718},
year={1997},
publisher={National Academy of Sciences}
}
@article{geweke1989,
author = {Geweke, J.},
journal = {Econometrica},
number = {6},
pages = {1317-1339},
publisher = {Wiley},
title = {Bayesian Inference in Econometric Models Using Monte Carlo Integration},
volume = {57},
year = {1989}
}
@article{girvan2002,
title={Simple model of epidemics with pathogen mutation},
author={Girvan, M. and Callaway, D.S. and Newman, M.E.J. and Strogatz, S.H.},
journal={Physical Review E},
volume={65},
number={3},
pages={031915},
year={2002},
publisher={APS}
}
@article{gog2002,
title={Dynamics and selection of many-strain pathogens},
author={Gog, J.R. and Grenfell, B.T.},
journal={Proceedings of the National Academy of Sciences},
volume={99},
number={26},
pages={17209--17214},
year={2002},
publisher={National Academy of Sciences}
}
@inproceedings{gordon1993,
title={Novel approach to nonlinear/non-{G}aussian {B}ayesian state estimation},
author={Gordon, N.J. and Salmond, D.J. and Smith, A.F.M.},
booktitle={IEE Proceedings F (Radar and Signal Processing)},
volume={140 (2)},
pages={107--113},
year={1993},
organization={IET}
}
@article{griffin2016,
title = {Simulation of Quasistationary Distributions on Reducible State Spaces},
author = {Griffin, A. and Jenkins, P.A. and Roberts, G.O and Spencer, S.E.F.},
journal = {Advances in Applied Probability},
year = {2017},
volume = {49},
issue = {3}
}
@book{grimmett2001,
title={Probability and Random Processes},
author={Grimmett, G. and Stirzaker, D.},
year={2001},
publisher={Oxford University Press}
}
@article{groisman2012,
title = "Simulation of quasi-stationary distributions on countable spaces",
author = "Groisman, P. and Jonckheere, M.",
year = "2013",
journal = "{M}arkov Processes and Related Fields",
volume = "19",
number = "3",
pages = "521-542"
}
@article{hairer2014,
title={Spectral gaps for a {M}etropolis-{H}astings algorithm in infinite dimensions},
author={Hairer, M. and Stuart, A.M. and Vollmer, S.J.},
journal={Annals of Applied Probability},
volume={24},
number={6},
pages={2455--2490},
year={2014},
publisher={Institute of Mathematical Statistics}
}
@article{jacka1995,
title= "Weak convergence of conditioned processes on a countable state space",
author= "Jacka, S.D. and Roberts, G.O.",
journal= "Journal of Applied Probability",
pages= "902--916",
volume= "32",
number = "4",
year= "1995",
publisher = "Applied Probability Trust"
}
@article{jenkins2012,
title={Stopping-time Resampling and Population Genetic Inference Under Coalescent Models},
author={Jenkins, P.A.},
journal={Statistical Applications in Genetics and Molecular Biology},
volume={11},
number={1},
pages={Article 9},
year={2012},
publisher = {De Gruyter}
}
@article{kamo2002,
title={The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model},
author={Kamo, M. and Sasaki, A.},
journal={Physica D: Nonlinear Phenomena},
volume={165},
number={3},
pages={228--241},
year={2002},
publisher={Elsevier}
}
@article{karlin1957,
title={The differential equations of birth-and-death processes, and the {S}tieltjes moment problem},
author={Karlin, S. and McGregor, J.L.},
journal={Transactions of the American Mathematical Society},
pages={489-546},
year={1957},
publisher={American Mathematical Society}
}
@techreport{KCE2013,
author = "Beutels, P. and Vandendijck, Y. and Willem, L. and Goeyvaerts, N. and Blommaert, A. and Van Kerckhove, K. and Bilcke, J. and Hanqu, G. and Neels, P. and Thiry, N. and Liesenborgs, J. and Hens, N.",
title = "\emph{Seasonal influenza vaccination: prioritizing children or other target groups? Part {II}: cost-effectiveness analysis.}",
note = "{KCE} Reports 204. D/2013/10.273/43.",
type = "Health Technology Assessment",
institution = "Brussels: Belgian Health Care Knowledge Centre (KCE)",
year = "2013"
}
@inproceedings{kermack1927,
title={A contribution to the mathematical theory of epidemics},
author={Kermack, W.O. and McKendrick, A.G.},
booktitle={Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering sciences},
volume={115},
number={772},
pages={700--721},
year={1927},
organization={The Royal Society}
}
@article{kilbourne2006,
title={Influenza pandemics of the 20th century},
author={Kilbourne, E.D.},
journal={Emerging Infectious Diseases},
volume={12},
number={1},
pages={9},
year={2006},
publisher={Centers for Disease Control}
}
@book{kelly2011,
title={Reversibility and Stochastic Networks},
author={Kelly, F.P.},
year={2011},
publisher={Cambridge University Press}
}
@article{kendall1948,
title={On the Generalized "Birth-and-Death" Process},
author={Kendall, D.},
journal={Annals of Mathematical Statistics},
volume={19},
number={1},
pages={1--15},
year={1948},
publisher={Institute of Mathematical Statistics}
}
@article{kingman1963,
author = "Kingman, J. F. C.",
title = "The Exponential Decay of {M}arkov Transition Probabilities",
volume = "s3-13",
number = "1",
pages = "337-358",
year = "1963",
journal = "Proceedings of the London Mathematical Society",
publisher="Oxford University Press"
}
@article{kong1994,
title={Sequential imputations and {B}ayesian missing data problems},
author={Kong, A. and Liu, J.S. and Wong, W.H.},
journal={Journal of the American Statistical Association},
volume={89},
number={425},
pages={278--288},
year={1994},
publisher={Taylor \& Francis}
}
@article{kryscio1989,
title={On the extinction of the {SIS} stochastic logistic epidemic},
author={Kryscio, R.J and Lef{\'e}vre, C.},
journal={Journal of Applied Probability},
pages={685--694},
year={1989},
publisher={Applied Probability Trust}
}
@article{kucharski2016,
title={Capturing the dynamics of pathogens with many strains},
author={Kucharski, Adam J and Andreasen, Viggo and Gog, Julia R},
journal={Journal of Mathematical Biology},
volume={72},
number={1-2},
pages={1--24},
year={2016},
publisher={Springer}
}
@incollection{kurtz1997,
title={A conceptual proof of the {K}esten-{S}tigum theorem for multi-type branching processes},
author={Kurtz, T. and Lyons, R. and Pemantle, R. and Peres, Y.},
booktitle={Classical and Modern Branching Processes},
pages={181--185},
year={1997},
publisher={Springer}
}
@article{lambert2008,
author = {Lambert, A.},
title = {Population dynamics and random genealogies},
journal = {Stochastic Models},
year = 2008,
volume = 24,
pages = {45--163},
publisher = {Taylor \& Francis}
}
@article{Lefevre1990a,
author = "Lef{\'e}vre, C. and Picard, P.",
title = "A Non-Standard Family of Polynomials and the Final Size Distribution of {R}eed-{F}rost Epidemic Processes",
year = "1990",
journal = "Advances in Applied Probability",
volume = "22",
pages = "25--48",
publisher = "Applied Probability Trust"
}
@article{Lefevre1990b,
author = "Lef{\'e}vre, C. and Picard, P.",
title = "A Unified Analysis if the Final Size and Severity Distribution in Collective {R}eed-{F}rost Epidemic Processes",
year = "1990",
journal = "Advances in Applied Probability",
volume = "22",
number = "2",
pages = "269--294",
publisher = "Applied Probability Trust"
}
@article{liu1995,
title={Blind deconvolution via sequential imputations},
author={Liu, J.S. and Chen, R.},
journal={Journal of the American Statistical Association},
volume={90},
number={430},
pages={567--576},
year={1995},
publisher={Taylor \& Francis}
}
@article{liu1998,
title={Sequential {M}onte {C}arlo methods for dynamic systems},
author={Liu, J.S. and Chen, R.},
journal={Journal of the American Statistical Association},
volume={93},
number={443},
pages={1032--1044},
year={1998},
publisher={Taylor \& Francis}
}
@article{liu2011,
author = "Liu, W. and Zhang, H.",
title = "Quasi-stationary Distributions in Linear Birth and Death Processes",
year = "2011",
journal = "Journal of Mathematics Research",
volume = "3",
number = "1",
pages = "27-32",
publisher = "Canadian Center of Science and Education"
}
@article{mandl1959,
author = {Mandl, P.},
title = {On the asymptotic behaviour of probabilities within groups of states of a homogeneous {M}arkov chain},
year = {1960},
journal = {{\u{C}}asopis Pro P{\v{e}}stov{\'{a}}n{\'{\i}} Matematiky},
number = {84},
pages = {140--149}
}
@article{mandl1961,
title={Spectral theory of semi-groups connected with diffusion processes and its application},
author={Mandl, P.},
journal={Czechoslovak Mathematical Journal},
volume={11},
number={4},
pages={558--569},
year={1961},
publisher={Institute of Mathematics, Academy of Sciences of the Czech Republic}
}
@article{martinez2012,
title={Existence and uniqueness of a quasi-stationary distribution for {M}arkov processes with fast return from infinity},
author={Martinez, S. and Martin, J.S. and Villemonais, D.},
journal={Journal of Applied Probability},
volume = {51},
month = {9},
number = {3},
pages = {756--768},
year={2014},
publisher = {Applied Probability Trust}
}
@article{martins2012,
title={Stationarity in moment closure and quasi-stationarity of the {SIS} model},
author={Martins, J. and Pinto, A. and Stollenwerk, N.},
journal={Mathematical Biosciences},
volume={236},
number={2},
pages={126--131},
year={2012},
publisher={Elsevier}
}
@article{meehan2018,
title={Coupled, multi-strain epidemic models of mutating pathogens},
author={Meehan, Michael T and Cocks, Daniel G and Trauer, James M and McBryde, Emma S},
journal={Mathematical Biosciences},
volume={296},
pages={82--92},
year={2018},
publisher={Elsevier}
}
@article{meleard2012,
author = "M\'{e}l\'{e}ard, S. and Villemonais, D.",
journal = "Probability Surveys",
pages = "340--410",
title = "Quasi-stationary distributions and population processes",
volume = "9",
year = "2012",
publisher = "The Institute of Mathematical Statistics and the Bernoulli Society"
}
@article{moy1967,
title={Extensions of a limit theorem of {E}verett, {U}lam and {H}arris on multitype branching processes to a branching process with countably many types},
author={Moy, S.C.},
journal={The Annals of Mathematical Statistics},
volume={38},
number={4},
pages={992--999},
year={1967},
publisher={Institute of Mathematical Statistics}
}
@article{nair1993,
title= "On the relationship between {$\mu$}-invariant measures and quasi-stationary distributions for continuous-time {M}arkov chains",
author= "Nair, M.G. and Pollett, P.K.",
journal= "Advances in Applied Probability",
volume = "25",
number = "1",
pages= "82--102",
year= "1993",
publisher = "Applied Probability Trust"
}
@article{Nasell1999,
author = "N{\aa}sell, I.",
title = "On the quasi-stationary distribution of the stochastic logistic epidemic",
year = "1999",
journal = "Mathematical Biosciences",
volume = "156",
pages = "21--40",
publisher = "Elsevier"
}
@article{nasell2002,
title={Stochastic models of some endemic infections},
author={N{\aa}sell, I.},
journal={Mathematical Biosciences},
volume={179},
number={1},
pages={1--19},
year={2002},
publisher={Elsevier}
}
@article{neal2006,
title={Multitype randomized {R}eed-{F}rost epidemics and epidemics upon random graphs},
author={Neal, P.},
journal={The Annals of Applied Probability},
volume={16},
number={3},
pages={1166--1189},
year={2006},
publisher={Institute of Mathematical Statistics}
}
@article{neal2014,
title={Endemic behaviour of {SIS} epidemics with general infectious period distributions},
author={Neal, P.},
journal={Advances in Applied Probability},
volume={46},
number={1},
pages={241--255},
year={2014},
publisher={Applied Probability Trust}
}
@incollection{nishiura2009,
title={The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends},
author={Nishiura, H. and Chowell, G.},
booktitle={Mathematical and Statistical Estimation Approaches in Epidemiology},
pages={103--121},
year={2009},
publisher={Springer}
}
@book{norris1997,
author = "Norris, J.R.",
title = {{M}arkov Chains},
publisher = {Cambridge University Press},
year = {1997}
}
@article{oneill2007,
title={Constructing population processes with specified quasi-stationary distributions},
author={O'Neill, P.D.},
journal={Stochastic Models},
volume={23},
number={3},
pages={439--449},
year={2007},
publisher={Taylor \& Francis}
}
@article{olivera2005,
title = {How to simulate the quasistationary state},
author = {de Oliveira, M.M. and Dickman, R.},
journal = {Physical Review E},
volume = {71},
issue = {1},
pages = {016129},
year = {2005},
publisher = {American Physical Society}
}
@book{olver2010,
title={{NIST} Handbook of Mathematical Functions},
author={Olver, F.W.J.},
year={2010},
publisher={Cambridge University Press}
}
@article{parisi2013,
title={Heterogeneity in antibody range and the antigenic drift of {I}nfluenza {A} viruses},
author={Parisi, A. and Lopes, J.S. and Nunes, An. and Gomes, M.G.M.},
journal={Ecological Complexity},
volume={14},
pages={157--165},
year={2013},
publisher={Elsevier}
}
@article{pellis2012,
title={Reproduction numbers for epidemic models with households and other social structures. {I:} {D}efinition and calculation of {$R_0$}},
author={Pellis, L. and Ball, F. and Trapman, P.},
journal={Mathematical Biosciences},
volume={235},
number={1},
pages={85--97},
year={2012},
publisher={Elsevier}
}
@article{pollett1998,
author = {P. K. Pollett},
journal = {Advances in Applied Probability},
number = {3},
pages = {600-621},
publisher = {Applied Probability Trust},
title = {Reversibility, Invariance and {$\mu$}-Invariance},
volume = {20},
year = {1988}
}
@article{pollett1999,
author = "Pollett, P.K.",
title = "Quasi-stationary Distributions for continuous time {M}arkov Chains when absorption is not certain",
year = "1999",
journal = "Journal of Applied Probability",
volume = "36",
pages = "268--272",
publisher = "Applied Probability Trust"
}
@article{pollett1999b,
author = "van Doorn, E.A. and Pollett, P.K.",
title = "Quasi-Stationary Distributions for Reducible Absorbing {M}arkov Chains in Discrete Time",
year = "1999",
journal = "{M}arkov Processes and Related Fields",
volume = "15",
pages = "191--204",
publisher = "Polymat"
}
@article{puri1968,
author = "Puri, P.S.",
title = "Interconnected Birth and Death Processes",
volume = "5",
number = "2",
pages = "334--349",
year = "1968",
journal = "Journal of Applied Probability",
publisher = "Applied Probability Trust"
}
@article{renshaw1973,
author = "Renshaw, E.",
title = "Interconnected Population Processes",
volume = "10",
pages = "1--14",
year = "1973",
journal = "Journal of Applied Probability",
publisher = "Applied Probability Trust"
}
@article{roberts2019,
title={A simple influenza model with complicated dynamics},
author={Roberts, MG and Hickson, RI and McCaw, JM and Talarmain, L},
journal={Journal of Mathematical Biology},
volume={78},
number={3},
pages={607--624},
year={2019},
publisher={Springer}
}