Compartmental models in epidemiology (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Compartmental models in epidemiology" in English language version.

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Kendall DG (1956). "Deterministic and Stochastic Epidemics in Closed Populations". Contributions to Biology and Problems of Health. Vol. 4. University of California Press. pp. 149–165. doi:10.1525/9780520350717-011. MR 0084936. Zbl 0070.15101.
Kendall DG (1956). "Deterministic and Stochastic Epidemics in Closed Populations". Contributions to Biology and Problems of Health. Vol. 4. University of California Press. pp. 149–165. doi:10.1525/9780520350717-011. MR 0084936. Zbl 0070.15101.

arxiv.org

Harko T, Lobo FS, Mak MK (2014). "Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates". Applied Mathematics and Computation. 236: 184–194. arXiv:1403.2160. Bibcode:2014arXiv1403.2160H. doi:10.1016/j.amc.2014.03.030. S2CID 14509477.
Yang W, Zhang D, Peng L, Zhuge C, Hong L (2020). "Rational evaluation of various epidemic models based on the COVID-19 data of China". arXiv:2003.05666v1 [q-bio.PE].
Te Vrugt M, Bickmann J, Wittkowski R (November 2020). "Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory". Nature Communications. 11 (1): 5576. arXiv:2003.13967. Bibcode:2020NatCo..11.5576T. doi:10.1038/s41467-020-19024-0. PMC 7643184. PMID 33149128.
Croccolo F, Roman HE (October 2020). "Spreading of infections on random graphs: A percolation-type model for COVID-19". Chaos, Solitons and Fractals. 139: 110077. arXiv:2006.10490. Bibcode:2020CSF...13910077C. doi:10.1016/j.chaos.2020.110077. PMC 7332959. PMID 32834619. S2CID 219792089.
Kastalskiy, IA; Pankratova, EV; Mirkes, EM; et al. (2021). "Social stress drives the multi-wave dynamics of COVID-19 outbreaks". Scientific Reports. 11 (1): 22497. arXiv:2106.08966. Bibcode:2021NatSR..1122497K. doi:10.1038/s41598-021-01317-z. PMC 8602246. PMID 34795311.
Dolbeault, Jean; Turinici, Gabriel (2020). "Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model". Math. Model. Nat. Phenom. 15: 36. arXiv:2005.00049. doi:10.1051/mmnp/2020025.
Laguzet, Laetitia; Turinici, Gabriel (October 1, 2015). "Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009–2010 Influenza A (H1N1) Epidemic in France". Bulletin of Mathematical Biology. 77 (10): 1955–1984. arXiv:2410.03567. doi:10.1007/s11538-015-0111-7. ISSN 1522-9602. PMID 26443437.
Elie, Romuald; Hubert, Emma; Turinici, Gabriel (2020). "Contact rate epidemic control of COVID-19: an equilibrium view". Mathematical Modelling of Natural Phenomena. 15. EDP Sciences: 35. arXiv:2004.08221. doi:10.1051/mmnp/2020022.
Pastor-Satorras R, Vespignani A (April 2001). "Epidemic spreading in scale-free networks". Physical Review Letters. 86 (14): 3200–3203. arXiv:cond-mat/0010317. Bibcode:2001PhRvL..86.3200P. doi:10.1103/PhysRevLett.86.3200. hdl:2117/126209. PMID 11290142. S2CID 16298768.
Newman ME (July 2002). "Spread of epidemic disease on networks". Physical Review E. 66 (1 Pt 2): 016128. arXiv:cond-mat/0205009. Bibcode:2002PhRvE..66a6128N. doi:10.1103/PhysRevE.66.016128. PMID 12241447. S2CID 15291065.

colgate.edu

math.colgate.edu

"(p. 19) The SI Model" (PDF).

doi.org

Hamer, William (1906). "On Epidemic Disease in England -- The Evidence of Variability and of Persistency of Type, Lecture III". The Lancet. 167 (4305): 569–574. doi:10.1016/s0140-6736(01)80187-2.
Ross R (1 February 1916). "An application of the theory of probabilities to the study of a priori pathometry.—Part I". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 92 (638): 204–230. Bibcode:1916RSPSA..92..204R. doi:10.1098/rspa.1916.0007.
Ross R, Hudson H (3 May 1917). "An application of the theory of probabilities to the study of a priori pathometry.—Part II". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 93 (650): 212–225. Bibcode:1917RSPSA..93..212R. doi:10.1098/rspa.1917.0014.
Ross R, Hudson H (1917). "An application of the theory of probabilities to the study of a priori pathometry.—Part III". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 89 (621): 225–240. Bibcode:1917RSPSA..93..225R. doi:10.1098/rspa.1917.0015.
Kermack WO, McKendrick AG (1927). "A Contribution to the Mathematical Theory of Epidemics". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 115 (772): 700–721. Bibcode:1927RSPSA.115..700K. doi:10.1098/rspa.1927.0118.
Kendall DG (1956). "Deterministic and Stochastic Epidemics in Closed Populations". Contributions to Biology and Problems of Health. Vol. 4. University of California Press. pp. 149–165. doi:10.1525/9780520350717-011. MR 0084936. Zbl 0070.15101.
Engelmann, Lukas (2021-08-30). "A box, a trough and marbles: How the Reed-Frost epidemic theory shaped epidemiological reasoning in the 20th century". History and Philosophy of the Life Sciences. 43 (3): 105. doi:10.1007/s40656-021-00445-z. ISSN 1742-6316. PMC 8404547. PMID 34462807.
Harko T, Lobo FS, Mak MK (2014). "Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates". Applied Mathematics and Computation. 236: 184–194. arXiv:1403.2160. Bibcode:2014arXiv1403.2160H. doi:10.1016/j.amc.2014.03.030. S2CID 14509477.
Kröger M, Schlickeiser R (2020). "Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: Time-independent reproduction factor". Journal of Physics A. 53 (50): 505601. Bibcode:2020JPhA...53X5601K. doi:10.1088/1751-8121/abc65d. S2CID 225555567.
Schlickeiser R, Kröger M (2021). "Analytical solution of the SIR-model for the temporal evolution of epidemics. Part B: Semi-time case". Journal of Physics A. 54 (17): 175601. Bibcode:2021JPhA...54q5601S. doi:10.1088/1751-8121/abed66. hdl:20.500.11850/479548.
Simon, Cory (2020). "The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics". PeerJ Physical Chemistry. 2 (2): e14. doi:10.7717/peerj-pchem.14.
Krylova O, Earn DJ (July 2013). "Effects of the infectious period distribution on predicted transitions in childhood disease dynamics". Journal of the Royal Society, Interface. 10 (84): 20130098. doi:10.1098/rsif.2013.0098. PMC 3673147. PMID 23676892.
Hethcote H (2000). "The Mathematics of Infectious Diseases". SIAM Review. 42 (4): 599–653. Bibcode:2000SIAMR..42..599H. doi:10.1137/s0036144500371907. S2CID 10836889.
Miller JC (September 2012). "A note on the derivation of epidemic final sizes". Bulletin of Mathematical Biology. 74 (9): 2125–2141. doi:10.1007/s11538-012-9749-6. PMC 3506030. PMID 22829179. Section 4.1
Miller JC (February 2017). "Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes". Infectious Disease Modelling. 2 (1): 35–55. doi:10.1016/j.idm.2016.12.003. PMC 5963332. PMID 29928728. Section 2.1.3
Kermack WO, McKendrick AG (1927). "A Contribution to the Mathematical Theory of Epidemics". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 115 (772): 700–721. Bibcode:1927RSPSA.115..700K. doi:10.1098/rspa.1927.0118.
Hart KD, Thompson C, Burger C, Hardwick D, Michaud AH, Bulushi A, Pridemore C, Ward C, Chen J (2021). "Remote Learning of COVID-19 Kinetic Analysis in a Physical Chemistry Laboratory Class". ACS Omega. 6 (43): 29223–29232. doi:10.1021/acsomega.1c04842. PMC 8547164. PMID 34723043.
Kendall DG (1956). "Deterministic and Stochastic Epidemics in Closed Populations". Contributions to Biology and Problems of Health. Vol. 4. University of California Press. pp. 149–165. doi:10.1525/9780520350717-011. MR 0084936. Zbl 0070.15101.
Smith DK, Lauro K, Kelly D, Fish J, Lintelman E, McEwen D, Smith C, Stecz M, Ambagaspitiya TD, Chen J (2022). "Teaching Undergraduate Physical Chemistry Lab with Kinetic Analysis of COVID-19 in the United States". Journal of Chemical Education. 99 (10): 3471–3477. Bibcode:2022JChEd..99.3471S. doi:10.1021/acs.jchemed.2c00416. PMC 9799982. PMID 36589277. S2CID 251484056.
Padua RN, Tulang AB (2 December 2010). "A Density–Dependent Epidemiological Model for the Spread of Infectious Diseases". Liceo Journal of Higher Education Research. 6 (2). doi:10.7828/ljher.v6i2.62.
von Csefalvay, Chris (2023-01-01), von Csefalvay, Chris (ed.), "Host factors", Computational Modeling of Infectious Disease, Academic Press, pp. 93–119, doi:10.1016/b978-0-32-395389-4.00012-8, ISBN 978-0-323-95389-4
Hethcote HW (1989). "Three Basic Epidemiological Models". In Levin SA, Hallam TG, Gross LJ (eds.). Applied Mathematical Ecology. Biomathematics. Vol. 18. Berlin: Springer. pp. 119–144. doi:10.1007/978-3-642-61317-3_5. ISBN 3-540-19465-7.
Nakamura, G.M.; Cardoso, G.C.; Martinez, A.S. (2020). "Improved susceptible–infectious–susceptible epidemic equations based on uncertainties and autocorrelation functions". Royal Society Open Science. 7 (2): 191504. Bibcode:2020RSOS....791504N. doi:10.1098/rsos.191504. PMC 7062106. PMID 32257317.
Al-Raeei, Marwan (2021). "The basic reproduction number of the new coronavirus pandemic with mortality for India, the Syrian Arab Republic, the United States, Yemen, China, France, Nigeria and Russia with different rate of cases". Clinical Epidemiology and Global Health. 9: 147–149. doi:10.1016/j.cegh.2020.08.005. ISSN 2452-0918. PMC 7438206. PMID 32844133.
Schlickeiser R, Kröger M (2021). "Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations". Physics. 3 (2): 386. Bibcode:2021Physi...3..386S. doi:10.3390/physics3020028. hdl:20.500.11850/487253. S2CID 233589998.
Schlickeiser R, Kröger M (2024). "Mathematics of Epidemics: General solution of SIRVD, SIRV, SIRD and SIR Models". Mathematics. 12: 941. doi:10.3390/math12070941. hdl:20.500.11850/665745.
Ariyaratne P, Ramasinghe LP, Ayyash JS, Kelley TM, Plant-Collins TA, Shinkle LW, Zuercher AM, Chen J (2025). "Application and significance of SIRVB model in analyzing COVID-19 dynamics". Scientific Reports. 15: 8526. doi:10.1038/s41598-025-90260-4. PMC 11903956.
Hunziker P (2021-07-24). "Personalized-dose Covid-19 vaccination in a wave of virus Variants of Concern: Trading individual efficacy for societal benefit". Precision Nanomedicine. 4 (3): 805–820. doi:10.33218/001c.26101.
Noble JV (August 1974). "Geographic and temporal development of plagues". Nature. 250 (5469): 726–729. Bibcode:1974Natur.250..726N. doi:10.1038/250726a0. PMID 4606583. S2CID 4210869.
Te Vrugt M, Bickmann J, Wittkowski R (November 2020). "Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory". Nature Communications. 11 (1): 5576. arXiv:2003.13967. Bibcode:2020NatCo..11.5576T. doi:10.1038/s41467-020-19024-0. PMC 7643184. PMID 33149128.
Croccolo F, Roman HE (October 2020). "Spreading of infections on random graphs: A percolation-type model for COVID-19". Chaos, Solitons and Fractals. 139: 110077. arXiv:2006.10490. Bibcode:2020CSF...13910077C. doi:10.1016/j.chaos.2020.110077. PMC 7332959. PMID 32834619. S2CID 219792089.
Kastalskiy, IA; Pankratova, EV; Mirkes, EM; et al. (2021). "Social stress drives the multi-wave dynamics of COVID-19 outbreaks". Scientific Reports. 11 (1): 22497. arXiv:2106.08966. Bibcode:2021NatSR..1122497K. doi:10.1038/s41598-021-01317-z. PMC 8602246. PMID 34795311.
Paxson, Wei; Shen, Bo-Wen (2022-10-01). "A KdV–SIR Equation and Its Analytical Solutions for Solitary Epidemic Waves". International Journal of Bifurcation and Chaos. 32 (13): 2250199–2250780. Bibcode:2022IJBC...3250199P. doi:10.1142/S0218127422501991. ISSN 0218-1274. S2CID 253314121.
Dolbeault, Jean; Turinici, Gabriel (2020). "Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model". Math. Model. Nat. Phenom. 15: 36. arXiv:2005.00049. doi:10.1051/mmnp/2020025.
Berihuete, Ángel; Sánchez-Sánchez, Marta; Suárez-Llorens, Alfonso (2021). "A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve". Mathematics. 9 (3): 228. doi:10.3390/math9030228. hdl:10498/24604. ISSN 2227-7390.
Berestycki, Henri; Desjardins, Benoît; Weitz, Joshua S.; Oury, Jean-Marc (2023). "Epidemic modeling with heterogeneity and social diffusion". Journal of Mathematical Biology. 86 (4): 60. doi:10.1007/s00285-022-01861-w. PMC 10039364. PMID 36964799.
Gao S, Teng Z, Nieto JJ, Torres A (2007). "Analysis of an SIR epidemic model with pulse vaccination and distributed time delay". Journal of Biomedicine & Biotechnology. 2007: 64870. doi:10.1155/2007/64870. PMC 2217597. PMID 18322563.
Fine, Paul E. M.; Clarkson, Jacqueline A. (1986). "Individual versus public priorities in the determination of optimal vaccination policies". American Journal of Epidemiology. 124 (6). Oxford University Press: 1012–1020. doi:10.1093/oxfordjournals.aje.a114471. PMID 3096132.
Bauch, Chris T.; Earn, David J. D. (2004). "Vaccination and the theory of games". Proceedings of the National Academy of Sciences. 101 (36). National Acad Sciences: 13391–13394. Bibcode:2004PNAS..10113391B. doi:10.1073/pnas.0403823101. hdl:10214/14336. PMID 15329411.
Shim, Eunha; Chapman, Gretchen B; Townsend, Jeffrey P; Galvani, Alison P (2012). "The influence of altruism on influenza vaccination decisions". Journal of the Royal Society Interface. 9 (74). The Royal Society: 2234–2243. doi:10.1098/rsif.2012.0115. PMC 3405754. PMID 22496100.
Laguzet, Laetitia; Turinici, Gabriel (October 1, 2015). "Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009–2010 Influenza A (H1N1) Epidemic in France". Bulletin of Mathematical Biology. 77 (10): 1955–1984. arXiv:2410.03567. doi:10.1007/s11538-015-0111-7. ISSN 1522-9602. PMID 26443437.
Elie, Romuald; Hubert, Emma; Turinici, Gabriel (2020). "Contact rate epidemic control of COVID-19: an equilibrium view". Mathematical Modelling of Natural Phenomena. 15. EDP Sciences: 35. arXiv:2004.08221. doi:10.1051/mmnp/2020022.
Diekmann, O.; Heesterbeek, J. A. P.; Metz, J. A. J. (1990-06-01). "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 (4): 365–382. doi:10.1007/BF00178324. hdl:1874/8051. ISSN 1432-1416. PMID 2117040. S2CID 22275430.
Heffernan, J.M; Smith, R.J; Wahl, L.M (2005-09-22). "Perspectives on the basic reproductive ratio". Journal of the Royal Society Interface. 2 (4): 281–293. doi:10.1098/rsif.2005.0042. ISSN 1742-5689. PMC 1578275. PMID 16849186.
van den Driessche, P.; Watmough, James (2002-11-01). "Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission". Mathematical Biosciences. 180 (1): 29–48. doi:10.1016/S0025-5564(02)00108-6. ISSN 0025-5564. PMID 12387915. S2CID 17313221.
van den Driessche, P.; Watmough, James (2008), Brauer, Fred; van den Driessche, Pauline; Wu, Jianhong (eds.), "Further Notes on the Basic Reproduction Number", Mathematical Epidemiology, Lecture Notes in Mathematics, vol. 1945, Berlin, Heidelberg: Springer, pp. 159–178, doi:10.1007/978-3-540-78911-6_6, ISBN 978-3-540-78911-6, retrieved 2022-11-08
Diekmann O, Heesterbeek JA, Metz JA (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 (4): 365–82. doi:10.1007/BF00178324. hdl:1874/8051. PMID 2117040. S2CID 22275430.
Wohl S, Schaffner SF, Sabeti PC (September 2016). "Genomic Analysis of Viral Outbreaks". Annual Review of Virology. 3 (1): 173–195. doi:10.1146/annurev-virology-110615-035747. PMC 5210220. PMID 27501264.
Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L, et al. (June 2003). "Transmission dynamics and control of severe acute respiratory syndrome". Science. 300 (5627): 1966–70. Bibcode:2003Sci...300.1966L. doi:10.1126/science.1086616. PMC 2760158. PMID 12766207.
Rihan, Fathalla A.; Anwar, M. Naim (2012). "Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate". International Journal of Differential Equations. 2012: 1–13. doi:10.1155/2012/408637.
Blower SM, McLean AR, Porco TC, Small PM, Hopewell PC, Sanchez MA, Moss AR (August 1995). "The intrinsic transmission dynamics of tuberculosis epidemics". Nature Medicine. 1 (8): 815–21. doi:10.1038/nm0895-815. PMID 7585186. S2CID 19795498.
Ma Y, Horsburgh CR, White LF, Jenkins HE (September 2018). "Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis". Epidemiology and Infection. 146 (12): 1478–1494. doi:10.1017/S0950268818001760. PMC 6092233. PMID 29970199.
Bartlett MS (1957). "Measles periodicity and community size". Journal of the Royal Statistical Society, Series A. 120 (1): 48–70. doi:10.2307/2342553. JSTOR 2342553. S2CID 91114210.
May RM, Lloyd AL (December 2001). "Infection dynamics on scale-free networks". Physical Review E. 64 (6 Pt 2): 066112. Bibcode:2001PhRvE..64f6112M. doi:10.1103/PhysRevE.64.066112. PMID 11736241.
Pastor-Satorras R, Vespignani A (April 2001). "Epidemic spreading in scale-free networks". Physical Review Letters. 86 (14): 3200–3203. arXiv:cond-mat/0010317. Bibcode:2001PhRvL..86.3200P. doi:10.1103/PhysRevLett.86.3200. hdl:2117/126209. PMID 11290142. S2CID 16298768.
Newman ME (July 2002). "Spread of epidemic disease on networks". Physical Review E. 66 (1 Pt 2): 016128. arXiv:cond-mat/0205009. Bibcode:2002PhRvE..66a6128N. doi:10.1103/PhysRevE.66.016128. PMID 12241447. S2CID 15291065.
Wong F, Collins JJ (November 2020). "Evidence that coronavirus superspreading is fat-tailed". Proceedings of the National Academy of Sciences of the United States of America. 117 (47): 29416–29418. Bibcode:2020PNAS..11729416W. doi:10.1073/pnas.2018490117. PMC 7703634. PMID 33139561. S2CID 226242440.

dx.doi.org

Hamer, William (1906). "On Epidemic Disease in England -- The Evidence of Variability and of Persistency of Type, Lecture III". The Lancet. 167 (4305): 569–574. doi:10.1016/s0140-6736(01)80187-2.

github.com

The COVID-19 Data Repository. The Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU); the preprocessed data are here: World in Data project.

handle.net

hdl.handle.net

Schlickeiser R, Kröger M (2021). "Analytical solution of the SIR-model for the temporal evolution of epidemics. Part B: Semi-time case". Journal of Physics A. 54 (17): 175601. Bibcode:2021JPhA...54q5601S. doi:10.1088/1751-8121/abed66. hdl:20.500.11850/479548.
Schlickeiser R, Kröger M (2021). "Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations". Physics. 3 (2): 386. Bibcode:2021Physi...3..386S. doi:10.3390/physics3020028. hdl:20.500.11850/487253. S2CID 233589998.
Schlickeiser R, Kröger M (2024). "Mathematics of Epidemics: General solution of SIRVD, SIRV, SIRD and SIR Models". Mathematics. 12: 941. doi:10.3390/math12070941. hdl:20.500.11850/665745.
Berihuete, Ángel; Sánchez-Sánchez, Marta; Suárez-Llorens, Alfonso (2021). "A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve". Mathematics. 9 (3): 228. doi:10.3390/math9030228. hdl:10498/24604. ISSN 2227-7390.
Bauch, Chris T.; Earn, David J. D. (2004). "Vaccination and the theory of games". Proceedings of the National Academy of Sciences. 101 (36). National Acad Sciences: 13391–13394. Bibcode:2004PNAS..10113391B. doi:10.1073/pnas.0403823101. hdl:10214/14336. PMID 15329411.
Diekmann, O.; Heesterbeek, J. A. P.; Metz, J. A. J. (1990-06-01). "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 (4): 365–382. doi:10.1007/BF00178324. hdl:1874/8051. ISSN 1432-1416. PMID 2117040. S2CID 22275430.
Diekmann O, Heesterbeek JA, Metz JA (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 (4): 365–82. doi:10.1007/BF00178324. hdl:1874/8051. PMID 2117040. S2CID 22275430.
Pastor-Satorras R, Vespignani A (April 2001). "Epidemic spreading in scale-free networks". Physical Review Letters. 86 (14): 3200–3203. arXiv:cond-mat/0010317. Bibcode:2001PhRvL..86.3200P. doi:10.1103/PhysRevLett.86.3200. hdl:2117/126209. PMID 11290142. S2CID 16298768.

harvard.edu

ui.adsabs.harvard.edu

Ross R (1 February 1916). "An application of the theory of probabilities to the study of a priori pathometry.—Part I". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 92 (638): 204–230. Bibcode:1916RSPSA..92..204R. doi:10.1098/rspa.1916.0007.
Ross R, Hudson H (3 May 1917). "An application of the theory of probabilities to the study of a priori pathometry.—Part II". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 93 (650): 212–225. Bibcode:1917RSPSA..93..212R. doi:10.1098/rspa.1917.0014.
Ross R, Hudson H (1917). "An application of the theory of probabilities to the study of a priori pathometry.—Part III". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 89 (621): 225–240. Bibcode:1917RSPSA..93..225R. doi:10.1098/rspa.1917.0015.
Kermack WO, McKendrick AG (1927). "A Contribution to the Mathematical Theory of Epidemics". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 115 (772): 700–721. Bibcode:1927RSPSA.115..700K. doi:10.1098/rspa.1927.0118.
Harko T, Lobo FS, Mak MK (2014). "Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates". Applied Mathematics and Computation. 236: 184–194. arXiv:1403.2160. Bibcode:2014arXiv1403.2160H. doi:10.1016/j.amc.2014.03.030. S2CID 14509477.
Kröger M, Schlickeiser R (2020). "Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: Time-independent reproduction factor". Journal of Physics A. 53 (50): 505601. Bibcode:2020JPhA...53X5601K. doi:10.1088/1751-8121/abc65d. S2CID 225555567.
Schlickeiser R, Kröger M (2021). "Analytical solution of the SIR-model for the temporal evolution of epidemics. Part B: Semi-time case". Journal of Physics A. 54 (17): 175601. Bibcode:2021JPhA...54q5601S. doi:10.1088/1751-8121/abed66. hdl:20.500.11850/479548.
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ncbi.nlm.nih.gov

Engelmann, Lukas (2021-08-30). "A box, a trough and marbles: How the Reed-Frost epidemic theory shaped epidemiological reasoning in the 20th century". History and Philosophy of the Life Sciences. 43 (3): 105. doi:10.1007/s40656-021-00445-z. ISSN 1742-6316. PMC 8404547. PMID 34462807.
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Smith DK, Lauro K, Kelly D, Fish J, Lintelman E, McEwen D, Smith C, Stecz M, Ambagaspitiya TD, Chen J (2022). "Teaching Undergraduate Physical Chemistry Lab with Kinetic Analysis of COVID-19 in the United States". Journal of Chemical Education. 99 (10): 3471–3477. Bibcode:2022JChEd..99.3471S. doi:10.1021/acs.jchemed.2c00416. PMC 9799982. PMID 36589277. S2CID 251484056.
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