The Testing of Epidemiological Concepts during the COVID-19 Pandemic
Main Article Content
Mauricio Canals L.
http://orcid.org/0000-0001-5256-4439
http://orcid.org/0000-0001-5256-4439
Abstract
The COVID-19 pandemic had a profound global impact, marked by high morbidity and mortality rates. It also placed substantial strain on epidemiological understanding, complicating efforts to measure the pandemic's scale and speed of transmission, as well as the implementation of mitigation and control strategies. Throughout the pandemic, key epidemiological concepts—such as the basic reproductive number, serial interval, incidence rate, fatality rate, and effective reproductive number—came under intense scrutiny. New concepts, like incidence moments, were even developed to better assess the scale of the outbreak and support temporal forecasting.
In this analysis, we trace the chronological relationship between the progression of the pandemic and the application of these key epidemiological concepts. We briefly examine their historical development, definitions, significance, interconnections, and how they informed both non-pharmaceutical interventions and, later, pharmaceutical measures with the introduction of vaccines. We show that the reproductive number proved to be a particularly valuable tool, guiding the design of epidemiological interventions and helping to define conditions for herd immunity and the vaccination threshold. In contrast, crude case fatality rates were often misleading, requiring adjustments to account for the time lag between infection and death. While incidence rates and reproductive numbers were essential for understanding disease burden and transmission dynamics, they were unsufficent in forecast future case counts. The concept of herd immunity was also critical, but its implications were frequently misunderstood. It was necessary to clarify that reaching the herd immunity threshold does not abruptly end an epidemic, and to highlight its dependence on vaccination thresholds and vaccine effectiveness.
Article Details
How to Cite
L., Mauricio Canals.
The Testing of Epidemiological Concepts during the COVID-19 Pandemic.
Medical Research Archives, [S.l.], v. 13, n. 4, apr. 2025.
ISSN 2375-1924.
Available at: <https://esmed.org/MRA/mra/article/view/6476>. Date accessed: 18 may 2025.
doi: https://doi.org/10.18103/mra.v13i4.6476.
Section
Research Articles
The Medical Research Archives grants authors the right to publish and reproduce the unrevised contribution in whole or in part at any time and in any form for any scholarly non-commercial purpose with the condition that all publications of the contribution include a full citation to the journal as published by the Medical Research Archives.
References
1. World Health Organization. COVID-19 deaths dashboard. World Health Organization. https://data.who.int/dashboards/covid19/deaths?n=o. Published 2025. Accessed March 17, 2025.
2. Mizumoto K, Kagaya K, Chowell G. Transmissibility of 2019 novel coronavirus: zoonotic vs. human-to-human transmission, China, 2019-2020. medRxiv preprint. Published March 16, 2020. doi:10.1101/2020.03.16.20037036.
3. Wang J, Wang Z. Strengths, Weaknesses, Opportunities and Threats (SWOT) Analysis of China’s Prevention and Con trol Strategy for the COVID-19 Epidemic. Int J Environ Res Public Health. 2020; 17(7):2235. doi:10.3390/ijerph17072235.
4. Salazar Mather T, Gallo Marin B, Medina Perez G, Christophers B, Paiva ML, Oliva R et al. Love in the time of COVID-19: negligence in the Nicaraguan response. Lancet Glob Health. 2020; 8(6): E773. doi: 10.1016/S2214109X(20)301315.
5. Sebastiani G, Massa M, Riboli E.. Covid–19 epidemic in Italy: evolution, projections and impact of government measures. Eur J Epidemiol. 2020; 35:341-345. doi: 10.1007/s10654-020-00631-6.
6. Peña S, Cuadrado C, Rivera-Aguirre A, Hasdell R, Nazif-Munoz J, Yusuf M et al. PoliMap: A taxonomy proposal for mapping and understanding the global policy response to COVID-19. Polimap COVID-19. 2020; [accessed 2020]. https://polimap.org/.
7. Nussbaumer‐Streit B, Mayr V, Dobrescu AI, Chapman A, Per sad E, Klerings I, et al. Quarantine alone or in combination with other public health measures to control COVID-19: a rapid review. Cochrane Database Syst Rev. 2020; 15(9):9. doi:10.1002/14651858.CD013574/full.
8. WHO-Europe. Strengthening the health system response to COVID-19. Recommendations for the WHO European Region. Policy brief 2020; [accessed 2020]. http://www.euro.who.int/__data/assets/pdf_file/0003/436350/strengthening-health-system-responseCOVID-19.pdf?ua=1.
9. WHO. Overview of Public Health and Social Measures in the context of COVID-19. 2020; [accessed 2020]. https://www.who.int/publications/i/item/overview-of-public-health-and-social-measures-in-the-context- of-covid-19 .
10. WHO. Critical preparedness, readiness and response actions for COVID-19: Interim guidance; 2020; [accessed 2020]. https://www.who.int/publications/i/item/critical-preparedness-readiness-and-response-actions-for-covid-19
11. Chilean Government COVID-19 Official Reports 2020; [accessed 2020]. https://www.gob.cl/coronavirus/cifrasoficiales/
12. Cori A, Ferguson NM, Fraser C, Cauchemez S. A new framework and software to estimate time-varying reproduction numbers during epidemics. Am J Epidemiol. 2013;178(9):1505–12. doi:10.1093/aje/kwt133.
13. Nishiura H, Linton NM, Akhmetzhanov AR. Serial interval of novel coronavirus (COVID-19) infections. Int J Infect Dis. 2020; 93: 284-6. doi: 10.1016/j.ijid.2020.02.060.
14. Sanche S, Lin YT, Xu C, Romero-Severson E, Hengartner N, Ke R. High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerg Infect Dis. 2020; 26(7):1470-1477. doi:103201/eid2607.200282.
15. Lee VL, Chiew CJ, Khong WX. Interrupting transmission of COVID-19: lessons from containment efforts in Singapore. J Travel Med. 2020; 13:taaa039. doi:10.1093/jtm/taaa039.
16. Russell T, Hellewell J, Abbott S, Golding N, Gibbs H, Jarvis CI, et al. Using a delay-adjusted case fatality ratio to estimate under-reporting. CMMID; London School of Hygiene & Tropical Medicine; 2020. [accessed 03/2025]. CMMID Repository. https://cmmid.github.io/topics/covid19/global_cfr_estimates.html.
17. Russell TW, Hellewell J, Jarvis CI, van Zandvoort K, Abbott S, Rat nayake R, et al. Estimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted data from the outbreak on the Diamond Princess cruise ship. Euro Surveill. 2020; 25(12): 2000256. doi: 10.2807/1560-7917.ES.2020.25.12.2000256.
18. Gonzalez RI, Muñoz F, Moya PS, Kiwi M. Is a COVID19 quarantine justified in Chile or USA right now? MedRxiv 2020. [accessed 2020]. doi: 10.1101/2020.03.23.20042002.
19. Canals M. Evolución de la virulencia de SARS CoV-2 en Chile. Rev Chil Infectol. 2023; 40(6):644-650. doi: 10.4067/s0716-10182023000600650.
20. Morens DM, Breman JG, Calisher GH, Doherty PC, Hahn BH, Keush GT, et al. The origin of COVID-19 and why it matters. Am J Trop Med Hyg. 2020; 103(3): 955-959. doi: 10.4269/ajtmh.20-0849.
21. Liu Y, Gayle AA, Wilder-Smith A, Rocklöv J. The reproductive number of COVID-19 is higher compared to SARS coronavirus. J Travel Med. 2020; 27(2): taaa021. doi: 10.1093/jtm/taaa021.
22. Billah A, Miah M, Khan N. Reproductive number of coronavirus: A systemaatic review and meta-analysis based on global level evidence. PLoS One. 2020; 15(1): e0242128. doi:10.1371/journal.pone.0242128.
23. Böckh R. Statistiches Jahrbuch der Stat Berlin. P. Stankiewitz, 1886; Berlin.
24. Heffernan JM, Smith RJ, Wahl LM. 2015. Perspectives on the basic reproductive ratio. J. R. Soc. Interface. 2015; 2(4):281-293. doi: 10.1098/rsif.2005.0042.
25. Lotka A. Elements of physical biology. Williams & Wilkins, 1925; Baltimore
26. Fine PEM. Ross’s a priori pathometry - a perspective. Proc Roy Soc Med. 1975; 68: 547-551.
27. Massad E, Bezerra FA. Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations. Mem Inst Oswaldo Cruz. 107(4): 564-567. doi: 10.1590/s0074-02762012000400022
28. Lotka A. A contribution to quantitative epidemiology. J Wash Acad Sci. 1919; 9(3): 73-77.
29. Kermack WO, McKendrick AG. A Contribution to the Mathematical Theory of Epidemics. Proc Roy Soc Lond. A. 1927; 115: 700-721.
30. Macdonald G. The analysis of the sporozoite rate. Trop Dis Bull. 1952; 49: 569-586.
31. Bailey N. The mathematical theory of infectious diseases and its applications. Griffin 1975; London.
32. Dietz K. Transmission and control of arbovirus diseases. In Ludwig D, Cooke KL (eds) Epidemiology (.) SIAM. 1975; 104-121. Philadelphia, 1975. p. 104-21.
33. Dietz K. The incidence of infectious diseases under influence of seasonal fluctuations. Lect Notes Biomath. 1976; 11: 1-15.
34. Anderson R, May R. Population biology of infectious diseases: Part I. Nature 1979; 280: 361-367.
35. May R, Anderson RM. 1979. Population biology of infectious diseases: Part II. Nature. 1979; 280, 455-461.
36. Anderson R. Epidemiology. In: Cox FEG (ed) Modern Parasitology 1993; 75-116. Blackwell Scientific Publications, Oxford.
37. 37.- Canals M. Learning from the COVID-19 pandemic: Concepts for good decision-making. Rev Med Chile 2020;148: 415-20. https://www.scielo.cl/pdf/rmc/v148n3/0717-6163 rmc-148-03-0418.pdf.
38. Canals M. Concepts for good decision-making during the COVID-19 pandemic in Chile. Point of View. Rev Chil Infectol. 2020; 37(2): 170-2. doi: 10.4067/s071610182920000200170.
39. Davies NG, Abbott S, Barnard RC, Jarvis CL, Kucharski AJ, Munday JD. Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England. Science 2021; 372. doi: 10.1126/science. abg3055.
40. Banho CA, Sacchetto L, Campos GR, Bittar C, Possebon FS, Ullman LS, et al. Impact of SARS-CoV-2 Gamma lineage introduction and COVID-19 vaccination on the epidemiological landscape of a Brazilian city. Comm. Med. 2022; 2: 41. doi: 10.1038/s43856-022-00108-5.
41. Liu Y, Rocklöv J. The effective reproductive number of the Omicron variant of SARS-CoV-2 is several times relative to Delta. J Trav Med. 2022;1-4. doi.org/10.1093/jtm/taac037
42. Nishiura H, Klinkenberg D, Roberts M, Heesterbeek JAP. Early epidemiological assesment of the virulence of infectious diseases: a case study o fan influenza pandemic. PLoSONE. 2009; 4(8):e6852. doi:10.1371/journal.pone.0006852.
43. Smith CEG. Prospects for the control of infectious disease. Proc Roy Soc Med. 1970; 63: 1181-90. PMID: 5530322
44. Gostic KM, McGough L, Baskerville E, Abbott S, Joshi K, Tedijanto C, et al. Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput Biol .2020; 16(12): e1008409. doi: 10.1371/journal.pcbi.1008409.
45. Gostic KM, McGough L, Baskerville EB, Abbott S, Joshi K, Tedijanto C, et al. Correction: Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput Biol. 2021; 17(12): e1009679. doi:10.1371/journal.pcbi.1009679.
46. Wallinga J, Teunis P. Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures. Amer J Epidemiol. 2004;160(6):509–516. doi:10.1093/aje/kwh255.
47. Wallinga J, Lipsitch M. How generation intervals shape the relationship between growth rates and reproductive numbers. Proc Biol Sci. 2007;274(1609):599–604. doi:10.1098/rspb.2006.3754
48. Bettencourt LMA, Ribeiro RM. Real Time Bayesian Estimation of the Epidemic Potential of Emerging Infectious Diseases. PLoS ONE. 2008;3(5):e2185. doi:10.1371/journal.pone.0002185.
49. an der Heiden M, Hamouda O. Schätzung der aktuellen Entwicklung der SARS-CoV-2- Epidemie in Deutschland—Nowcasting. Epidemiologisches Bulletin. 2020;2020(17):10–15. https://edoc.rki.de/handle/176904/6650.4
50. RKI. COVID-19 Datenhub; 2020. https://npgeo-corona-npgeo-de.hub.arcgis.com/datasets/dd4580c810204019a7b8eb3e0b329dd6_0/explore
51. Canals M, Cuadrado C, Canals A, Johannessen K, Lefio LA, Bertoglia MP, Eguiguren P, Siches I, Iglesias V, Arteaga O. Epidemic trends, public health response and health system capacity: The Chilean experience in COVID-19 epidemic. Rev Panam Salud Publica 2020; 44, e99.doi: 10.26633/RORP.2020.99.
52. Canals M, Canals A, Cuadrado C. Incidence moments: A simple method for study the memory and short-term forecast of the COVID-19 incidence time-series. Epidemiol Meth. 2022;11(s1):20210029.doi: 10.15151/em-2021-0029.
53. Canals M, Canals A. Incidence moments: Short term forecast of the COVID-19 incidence rate in Chile. Rev Med Chile 2023; 151:823-829. doi: 10.4067/s0034-98872023000700823.
54. Fine PEM, Eames K, Heymann DL. ‘‘Herd Immunity’’: a rough guide. Clin Infect Dis. 2011; 52 (7): 911-6. doi: 10.1093/cid/cir007.
55. Fine PEM. John Brownlee and the measurement of infectiousness: an historical study in epidemic theory. J R Statist Soc A. 1979; 142 (3): 347-62. doi: 10.2307/2982487
56. Fine P E M. Herd immunity: history, theory, practice. Epidemiol Rev. 1993; 15: 265-302. doi: 10.1093/oxfordjournals.epirev.a036121.
57. Anderson R M, May R M. Infectious diseases of humans: dynamics and control. Oxford University Press, 1991; Oxford, UK.
58. Bjϕrnstad BJ, Shea K, Krzywinski M, Altman N. The SEIRS models for infectious diseases dynamics. Nat Methods 2020, 17: 555-8. doi: 10.1038/s41592-020-0856-2
59. Scherer A, McLean A. Mathematical models of vaccination. Br Med Bull 2002; 62: 187-99. doi: 10.1093/bmb/62.1.187
60. Suryawanshi YN, Biswas DA. Herd immunity to fight against COVID-19: a narrative review. Cureus. 2023; 15(1): e33575. doi:10.7759/cureus.33575.
61. Mossong J, Hens N, Jit M, Beutels P, Auranen K, et al. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med. 2008; Mar 25; 5 (3): e74. doi:10.1371/journal.pmed.0050074.
62. Colizza V, Barrat A, Barthe ´lemy M, Vespigniani A. The role of the airline transportation network in the prediction and predictability of global epidemics. Proc Natl Acad Sci USA 2006; 2006 103 (7) 2015-2020. doi: 10.1073/pnas.0510525103.
63. Britton T, Ball F, Trapman P. A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS CoV-2. Science 2020; 14; 369 (6505): 846-9. doi: 10.1126/science.abc6810.
64. Lourenço J, Pinotti F, Thompson C, Gupta S. The impact of host resistance on cumulative mortality and the threshold of herd immunity for SARS-CoV-2. 2020; doi: 10.1101 /2020.07.15.20154294 doi: medRxiv pr
65. Fredericksen LS, Zhang Y, Foged C, Thakur A. The long road towards COVID-19 herd immunity: vaccine platform thecnologies and mass immunization strategies. Front Immunol.2020; 11: 1817. doi: 10.3389/fimmu.2020.01817.
66. J. P. Townsend, H. B. Hassler, Z. Wang, S. Miura, J. Singh, S. Kumar, N. H. Ruddle, A. P. Galvani, A. Dornburg, The durability of immunity against reinfection by sars-cov-2: a com parative evolutionary study, The Lancet Microbe 2 (12) (2021) e666 e675.
67. Townsend JP, Hassler HB, Sah P, Dornburg A. The durability of natural infection and vaccine-induced immunity against future infections of SARS-CoV-2. PNAS. 2022; 119 (31) e2204336119. doi:10.1073/pnas.2204336119.
68. S. M. Hirabara, T. D. A. Serdan, R. Gorjao, L. N. Masi, T. C. Pithon-Curi, D. T. Covas, R. Curi, E. L. Durigon, SARS-COV-2 variants: Di erences and potential of immune evasion, Front. Cell. Infect. Microbiol. 11 (2021) 781429.
69. J. Angulo, C. Martinez-Valdebenito, C. Pardo-Roa, L. I. Almonacid, E. Fuentes-Luppichini, A. M. Contreras, C. Maldonado, N. Le Corre, F. Melo, R. A. Medina, M. Ferrés, Assessment of mutations associated with genomic variants of SARS-CoV-2: RT-qPCR as a rapid and abordable tool to monitoring known circulating variants in chile, 2021, Front. Med. (Laussanne). 2022;9: 841073. doi:10.3389/fmed.2022.841073.
70. P. Nordström, M. Ballin, A. Nordström, Risk of SARS-CoV-2 reinfection and COVID-19 hospitalisation in individuals with natural and hybrid immunity: a retrospective, total population cohort study in sweden, Lancet Infect. Dis.2022; 22 (6): 781790. doi: 10.1016/S1473-3099(22)00143-8
71. Fine. PEM. The interval between succesive cases of an infectious disease. Amer J Epidemiol. 2003; 158(11): 1039-47. doi:10.1093/aje/kwg251.
72. Canals M, Canals A. Resumen analítico de la experiencia chilena de la pandemia COVID-19, 2020-2022. Cuad Méd Soc. 2022; 62(23): 7-18. doi: 10.56116/cms. v62.n3.2022.374.
2. Mizumoto K, Kagaya K, Chowell G. Transmissibility of 2019 novel coronavirus: zoonotic vs. human-to-human transmission, China, 2019-2020. medRxiv preprint. Published March 16, 2020. doi:10.1101/2020.03.16.20037036.
3. Wang J, Wang Z. Strengths, Weaknesses, Opportunities and Threats (SWOT) Analysis of China’s Prevention and Con trol Strategy for the COVID-19 Epidemic. Int J Environ Res Public Health. 2020; 17(7):2235. doi:10.3390/ijerph17072235.
4. Salazar Mather T, Gallo Marin B, Medina Perez G, Christophers B, Paiva ML, Oliva R et al. Love in the time of COVID-19: negligence in the Nicaraguan response. Lancet Glob Health. 2020; 8(6): E773. doi: 10.1016/S2214109X(20)301315.
5. Sebastiani G, Massa M, Riboli E.. Covid–19 epidemic in Italy: evolution, projections and impact of government measures. Eur J Epidemiol. 2020; 35:341-345. doi: 10.1007/s10654-020-00631-6.
6. Peña S, Cuadrado C, Rivera-Aguirre A, Hasdell R, Nazif-Munoz J, Yusuf M et al. PoliMap: A taxonomy proposal for mapping and understanding the global policy response to COVID-19. Polimap COVID-19. 2020; [accessed 2020]. https://polimap.org/.
7. Nussbaumer‐Streit B, Mayr V, Dobrescu AI, Chapman A, Per sad E, Klerings I, et al. Quarantine alone or in combination with other public health measures to control COVID-19: a rapid review. Cochrane Database Syst Rev. 2020; 15(9):9. doi:10.1002/14651858.CD013574/full.
8. WHO-Europe. Strengthening the health system response to COVID-19. Recommendations for the WHO European Region. Policy brief 2020; [accessed 2020]. http://www.euro.who.int/__data/assets/pdf_file/0003/436350/strengthening-health-system-responseCOVID-19.pdf?ua=1.
9. WHO. Overview of Public Health and Social Measures in the context of COVID-19. 2020; [accessed 2020]. https://www.who.int/publications/i/item/overview-of-public-health-and-social-measures-in-the-context- of-covid-19 .
10. WHO. Critical preparedness, readiness and response actions for COVID-19: Interim guidance; 2020; [accessed 2020]. https://www.who.int/publications/i/item/critical-preparedness-readiness-and-response-actions-for-covid-19
11. Chilean Government COVID-19 Official Reports 2020; [accessed 2020]. https://www.gob.cl/coronavirus/cifrasoficiales/
12. Cori A, Ferguson NM, Fraser C, Cauchemez S. A new framework and software to estimate time-varying reproduction numbers during epidemics. Am J Epidemiol. 2013;178(9):1505–12. doi:10.1093/aje/kwt133.
13. Nishiura H, Linton NM, Akhmetzhanov AR. Serial interval of novel coronavirus (COVID-19) infections. Int J Infect Dis. 2020; 93: 284-6. doi: 10.1016/j.ijid.2020.02.060.
14. Sanche S, Lin YT, Xu C, Romero-Severson E, Hengartner N, Ke R. High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerg Infect Dis. 2020; 26(7):1470-1477. doi:103201/eid2607.200282.
15. Lee VL, Chiew CJ, Khong WX. Interrupting transmission of COVID-19: lessons from containment efforts in Singapore. J Travel Med. 2020; 13:taaa039. doi:10.1093/jtm/taaa039.
16. Russell T, Hellewell J, Abbott S, Golding N, Gibbs H, Jarvis CI, et al. Using a delay-adjusted case fatality ratio to estimate under-reporting. CMMID; London School of Hygiene & Tropical Medicine; 2020. [accessed 03/2025]. CMMID Repository. https://cmmid.github.io/topics/covid19/global_cfr_estimates.html.
17. Russell TW, Hellewell J, Jarvis CI, van Zandvoort K, Abbott S, Rat nayake R, et al. Estimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted data from the outbreak on the Diamond Princess cruise ship. Euro Surveill. 2020; 25(12): 2000256. doi: 10.2807/1560-7917.ES.2020.25.12.2000256.
18. Gonzalez RI, Muñoz F, Moya PS, Kiwi M. Is a COVID19 quarantine justified in Chile or USA right now? MedRxiv 2020. [accessed 2020]. doi: 10.1101/2020.03.23.20042002.
19. Canals M. Evolución de la virulencia de SARS CoV-2 en Chile. Rev Chil Infectol. 2023; 40(6):644-650. doi: 10.4067/s0716-10182023000600650.
20. Morens DM, Breman JG, Calisher GH, Doherty PC, Hahn BH, Keush GT, et al. The origin of COVID-19 and why it matters. Am J Trop Med Hyg. 2020; 103(3): 955-959. doi: 10.4269/ajtmh.20-0849.
21. Liu Y, Gayle AA, Wilder-Smith A, Rocklöv J. The reproductive number of COVID-19 is higher compared to SARS coronavirus. J Travel Med. 2020; 27(2): taaa021. doi: 10.1093/jtm/taaa021.
22. Billah A, Miah M, Khan N. Reproductive number of coronavirus: A systemaatic review and meta-analysis based on global level evidence. PLoS One. 2020; 15(1): e0242128. doi:10.1371/journal.pone.0242128.
23. Böckh R. Statistiches Jahrbuch der Stat Berlin. P. Stankiewitz, 1886; Berlin.
24. Heffernan JM, Smith RJ, Wahl LM. 2015. Perspectives on the basic reproductive ratio. J. R. Soc. Interface. 2015; 2(4):281-293. doi: 10.1098/rsif.2005.0042.
25. Lotka A. Elements of physical biology. Williams & Wilkins, 1925; Baltimore
26. Fine PEM. Ross’s a priori pathometry - a perspective. Proc Roy Soc Med. 1975; 68: 547-551.
27. Massad E, Bezerra FA. Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations. Mem Inst Oswaldo Cruz. 107(4): 564-567. doi: 10.1590/s0074-02762012000400022
28. Lotka A. A contribution to quantitative epidemiology. J Wash Acad Sci. 1919; 9(3): 73-77.
29. Kermack WO, McKendrick AG. A Contribution to the Mathematical Theory of Epidemics. Proc Roy Soc Lond. A. 1927; 115: 700-721.
30. Macdonald G. The analysis of the sporozoite rate. Trop Dis Bull. 1952; 49: 569-586.
31. Bailey N. The mathematical theory of infectious diseases and its applications. Griffin 1975; London.
32. Dietz K. Transmission and control of arbovirus diseases. In Ludwig D, Cooke KL (eds) Epidemiology (.) SIAM. 1975; 104-121. Philadelphia, 1975. p. 104-21.
33. Dietz K. The incidence of infectious diseases under influence of seasonal fluctuations. Lect Notes Biomath. 1976; 11: 1-15.
34. Anderson R, May R. Population biology of infectious diseases: Part I. Nature 1979; 280: 361-367.
35. May R, Anderson RM. 1979. Population biology of infectious diseases: Part II. Nature. 1979; 280, 455-461.
36. Anderson R. Epidemiology. In: Cox FEG (ed) Modern Parasitology 1993; 75-116. Blackwell Scientific Publications, Oxford.
37. 37.- Canals M. Learning from the COVID-19 pandemic: Concepts for good decision-making. Rev Med Chile 2020;148: 415-20. https://www.scielo.cl/pdf/rmc/v148n3/0717-6163 rmc-148-03-0418.pdf.
38. Canals M. Concepts for good decision-making during the COVID-19 pandemic in Chile. Point of View. Rev Chil Infectol. 2020; 37(2): 170-2. doi: 10.4067/s071610182920000200170.
39. Davies NG, Abbott S, Barnard RC, Jarvis CL, Kucharski AJ, Munday JD. Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England. Science 2021; 372. doi: 10.1126/science. abg3055.
40. Banho CA, Sacchetto L, Campos GR, Bittar C, Possebon FS, Ullman LS, et al. Impact of SARS-CoV-2 Gamma lineage introduction and COVID-19 vaccination on the epidemiological landscape of a Brazilian city. Comm. Med. 2022; 2: 41. doi: 10.1038/s43856-022-00108-5.
41. Liu Y, Rocklöv J. The effective reproductive number of the Omicron variant of SARS-CoV-2 is several times relative to Delta. J Trav Med. 2022;1-4. doi.org/10.1093/jtm/taac037
42. Nishiura H, Klinkenberg D, Roberts M, Heesterbeek JAP. Early epidemiological assesment of the virulence of infectious diseases: a case study o fan influenza pandemic. PLoSONE. 2009; 4(8):e6852. doi:10.1371/journal.pone.0006852.
43. Smith CEG. Prospects for the control of infectious disease. Proc Roy Soc Med. 1970; 63: 1181-90. PMID: 5530322
44. Gostic KM, McGough L, Baskerville E, Abbott S, Joshi K, Tedijanto C, et al. Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput Biol .2020; 16(12): e1008409. doi: 10.1371/journal.pcbi.1008409.
45. Gostic KM, McGough L, Baskerville EB, Abbott S, Joshi K, Tedijanto C, et al. Correction: Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput Biol. 2021; 17(12): e1009679. doi:10.1371/journal.pcbi.1009679.
46. Wallinga J, Teunis P. Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures. Amer J Epidemiol. 2004;160(6):509–516. doi:10.1093/aje/kwh255.
47. Wallinga J, Lipsitch M. How generation intervals shape the relationship between growth rates and reproductive numbers. Proc Biol Sci. 2007;274(1609):599–604. doi:10.1098/rspb.2006.3754
48. Bettencourt LMA, Ribeiro RM. Real Time Bayesian Estimation of the Epidemic Potential of Emerging Infectious Diseases. PLoS ONE. 2008;3(5):e2185. doi:10.1371/journal.pone.0002185.
49. an der Heiden M, Hamouda O. Schätzung der aktuellen Entwicklung der SARS-CoV-2- Epidemie in Deutschland—Nowcasting. Epidemiologisches Bulletin. 2020;2020(17):10–15. https://edoc.rki.de/handle/176904/6650.4
50. RKI. COVID-19 Datenhub; 2020. https://npgeo-corona-npgeo-de.hub.arcgis.com/datasets/dd4580c810204019a7b8eb3e0b329dd6_0/explore
51. Canals M, Cuadrado C, Canals A, Johannessen K, Lefio LA, Bertoglia MP, Eguiguren P, Siches I, Iglesias V, Arteaga O. Epidemic trends, public health response and health system capacity: The Chilean experience in COVID-19 epidemic. Rev Panam Salud Publica 2020; 44, e99.doi: 10.26633/RORP.2020.99.
52. Canals M, Canals A, Cuadrado C. Incidence moments: A simple method for study the memory and short-term forecast of the COVID-19 incidence time-series. Epidemiol Meth. 2022;11(s1):20210029.doi: 10.15151/em-2021-0029.
53. Canals M, Canals A. Incidence moments: Short term forecast of the COVID-19 incidence rate in Chile. Rev Med Chile 2023; 151:823-829. doi: 10.4067/s0034-98872023000700823.
54. Fine PEM, Eames K, Heymann DL. ‘‘Herd Immunity’’: a rough guide. Clin Infect Dis. 2011; 52 (7): 911-6. doi: 10.1093/cid/cir007.
55. Fine PEM. John Brownlee and the measurement of infectiousness: an historical study in epidemic theory. J R Statist Soc A. 1979; 142 (3): 347-62. doi: 10.2307/2982487
56. Fine P E M. Herd immunity: history, theory, practice. Epidemiol Rev. 1993; 15: 265-302. doi: 10.1093/oxfordjournals.epirev.a036121.
57. Anderson R M, May R M. Infectious diseases of humans: dynamics and control. Oxford University Press, 1991; Oxford, UK.
58. Bjϕrnstad BJ, Shea K, Krzywinski M, Altman N. The SEIRS models for infectious diseases dynamics. Nat Methods 2020, 17: 555-8. doi: 10.1038/s41592-020-0856-2
59. Scherer A, McLean A. Mathematical models of vaccination. Br Med Bull 2002; 62: 187-99. doi: 10.1093/bmb/62.1.187
60. Suryawanshi YN, Biswas DA. Herd immunity to fight against COVID-19: a narrative review. Cureus. 2023; 15(1): e33575. doi:10.7759/cureus.33575.
61. Mossong J, Hens N, Jit M, Beutels P, Auranen K, et al. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med. 2008; Mar 25; 5 (3): e74. doi:10.1371/journal.pmed.0050074.
62. Colizza V, Barrat A, Barthe ´lemy M, Vespigniani A. The role of the airline transportation network in the prediction and predictability of global epidemics. Proc Natl Acad Sci USA 2006; 2006 103 (7) 2015-2020. doi: 10.1073/pnas.0510525103.
63. Britton T, Ball F, Trapman P. A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS CoV-2. Science 2020; 14; 369 (6505): 846-9. doi: 10.1126/science.abc6810.
64. Lourenço J, Pinotti F, Thompson C, Gupta S. The impact of host resistance on cumulative mortality and the threshold of herd immunity for SARS-CoV-2. 2020; doi: 10.1101 /2020.07.15.20154294 doi: medRxiv pr
65. Fredericksen LS, Zhang Y, Foged C, Thakur A. The long road towards COVID-19 herd immunity: vaccine platform thecnologies and mass immunization strategies. Front Immunol.2020; 11: 1817. doi: 10.3389/fimmu.2020.01817.
66. J. P. Townsend, H. B. Hassler, Z. Wang, S. Miura, J. Singh, S. Kumar, N. H. Ruddle, A. P. Galvani, A. Dornburg, The durability of immunity against reinfection by sars-cov-2: a com parative evolutionary study, The Lancet Microbe 2 (12) (2021) e666 e675.
67. Townsend JP, Hassler HB, Sah P, Dornburg A. The durability of natural infection and vaccine-induced immunity against future infections of SARS-CoV-2. PNAS. 2022; 119 (31) e2204336119. doi:10.1073/pnas.2204336119.
68. S. M. Hirabara, T. D. A. Serdan, R. Gorjao, L. N. Masi, T. C. Pithon-Curi, D. T. Covas, R. Curi, E. L. Durigon, SARS-COV-2 variants: Di erences and potential of immune evasion, Front. Cell. Infect. Microbiol. 11 (2021) 781429.
69. J. Angulo, C. Martinez-Valdebenito, C. Pardo-Roa, L. I. Almonacid, E. Fuentes-Luppichini, A. M. Contreras, C. Maldonado, N. Le Corre, F. Melo, R. A. Medina, M. Ferrés, Assessment of mutations associated with genomic variants of SARS-CoV-2: RT-qPCR as a rapid and abordable tool to monitoring known circulating variants in chile, 2021, Front. Med. (Laussanne). 2022;9: 841073. doi:10.3389/fmed.2022.841073.
70. P. Nordström, M. Ballin, A. Nordström, Risk of SARS-CoV-2 reinfection and COVID-19 hospitalisation in individuals with natural and hybrid immunity: a retrospective, total population cohort study in sweden, Lancet Infect. Dis.2022; 22 (6): 781790. doi: 10.1016/S1473-3099(22)00143-8
71. Fine. PEM. The interval between succesive cases of an infectious disease. Amer J Epidemiol. 2003; 158(11): 1039-47. doi:10.1093/aje/kwg251.
72. Canals M, Canals A. Resumen analítico de la experiencia chilena de la pandemia COVID-19, 2020-2022. Cuad Méd Soc. 2022; 62(23): 7-18. doi: 10.56116/cms. v62.n3.2022.374.