This paper aims to study how the increase in vaccination rate in Israel affect to the behavior of COVID-19 reproduction rate, from 19 December 2020, to 25 April 2021. Multiple advanced econometrics methodologies are used to analyze the degree of persistence, to understand the relationship between these two times series and the long-term behavior. The results of our study indicate that the vaccinations cause long-run effects to COVID-19 reproduction rate and the vaccination provides useful information to predict the COVID-19 reproduction rate. Also, we determine whatever exogenous shocks related with the virus reproduction will have a very short impact over time. The first change in trend occurs on 13 January 2021, with 24.37% of the population vaccinated and when it can be seen that the increased rate of vaccinations causes the infection rate to decrease.

1. Asselah T, Durantel D, Pasmant E, et al. COVID-19: Discovery, diagnostics and drug development. Journal of Hepatology. 2021; 74(1): 168-184. doi: 10.1016/j.jhep.2020.09.031

2. Li Q, Guan X, Wu P, et al. Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia. New England Journal of Medicine. 2020; 382(13): 1199-1207. doi: 10.1056/nejmoa2001316

3. Zaim S, Chong JH, Sankaranarayanan V, et al. COVID-19 and Multiorgan Response. Current Problems in Cardiology. 2020; 45(8): 100618. doi: 10.1016/j.cpcardiol.2020.100618

4. Li YD, Chi WY, Su JH, et al. Coronavirus vaccine development: from SARS and MERS to COVID-19. Journal of Biomedical Science. 2020; 27(1). doi: 10.1186/s12929-020-00695-2

5. Holshue ML, DeBolt C, Lindquist S, et al. First Case of 2019 Novel Coronavirus in the United States. New England Journal of Medicine. 2020; 382(10): 929-936. doi: 10.1056/nejmoa2001191

6. Cruz BS, and de Oliveira-Dias M. COVID-19: From outbreak to pandemic. Global Scientific Journals. 2020; 8(3).

7. Flaxman S, Mishra S, Gandy A, et al. Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Nature. 2020; 584(7820): 257-261. doi: 10.1038/s41586-020-2405-7

8. Sanche S, Lin YT, Xu C, et al. High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerging Infectious Diseases. 2020; 26(7): 1470-1477. doi: 10.3201/eid2607.200282

9. Rawat K, Kumari P, Saha L. COVID-19 vaccine: A recent update in pipeline vaccines, their design and development strategies. European Journal of Pharmacology. 2021; 892: 173751. doi: 10.1016/j.ejphar.2020.173751

10. Calina D, Docea A, Petrakis D, et al. Towards effective COVID-19 vaccines: Updates, perspectives and challenges (Review). International Journal of Molecular Medicine. 2020; 46(1): 3-16. doi: 10.3892/ijmm.2020.4596

11. Lurie N, Saville M, Hatchett R, et al. Developing COVID-19 Vaccines at Pandemic Speed. New England Journal of Medicine. 2020; 382(21): 1969-1973. doi: 10.1056/nejmp2005630

12. Mishra SK, Tripathi T. One year update on the COVID-19 pandemic: Where are we now? Acta Tropica. 2021; 214: 105778. doi: 10.1016/j.actatropica.2020.105778

13. Britton A, Jacobs Slifka KM, Edens C, et al. Effectiveness of the Pfizer-BioNTech COVID-19 Vaccine Among Residents of Two Skilled Nursing Facilities Experiencing COVID-19 Outbreaks—Connecticut, December 2020–February 2021. MMWR Morbidity and Mortality Weekly Report. 2021; 70(11): 396-401. doi: 10.15585/mmwr.mm7011e3

14. Kustin T, Harel N, Finkel U, et al. Evidence for increased breakthrough rates of SARS-CoV-2 variants of concern in BNT162b2 mRNA vaccinated individuals. Nat Med. 2021; 27: 1379–1384. doi: 10.1101/2021.04.06.21254882

15. Haas EJ, Angulo FJ, McLaughlin JM, et al. (2021). Impact and effectiveness of mRNA BNT162b2 vaccine against SARS-CoV-2 infections and COVID-19 cases, hospitalisations, and deaths following a nationwide vaccination campaign in Israel: an observational study using national surveillance data. The Lancet. 2021; 397(10287): 1819-1829. doi: 10.1016/S0140-6736(21)00947-8

16. Saban M, Myers V, Wilf-Miron R. Changes in infectivity, severity and vaccine effectiveness against delta COVID-19 variant ten months into the vaccination program: The Israeli case. Preventive Medicine. 2022; 154: 106890. doi: 10.1016/j.ypmed.2021.106890

17. Kulhánek V. The impact of vaccinations on the development of COVID-19 pandemic. Univerzita Karlova, Fakulta sociálních věd; 2023.

18. Li AY, Hannah TC, Durbin J, et al. Multivariate Analysis of Factors Affecting COVID-19 Case and Death Rate in U.S. Counties: The Significant Effects of Black Race and Temperature. The American Journal of the Medical Sciences. 2020. doi: 10.1101/2020.04.17.20069708

19. Şahin M. Impact of weather on COVID-19 pandemic in Turkey. Science of The Total Environment. 2020; 728: 138810. doi: 10.1016/j.scitotenv.2020.138810

20. Velasco JM, Tseng WC, Chang CL. Factors Affecting the Cases and Deaths of COVID-19 Victims. International Journal of Environmental Research and Public Health. 2021; 18(2): 674. doi: 10.3390/ijerph18020674

21. Toharudin T, Pontoh RS, Caraka RE, et al. National Vaccination and Local Intervention Impacts on COVID-19 Cases. Sustainability. 2021; 13(15): 8282. doi: 10.3390/su13158282

22. Rustagi V, Bajaj M, Tanvi, et al. Analyzing the Effect of Vaccination Over COVID Cases and Deaths in Asian Countries Using Machine Learning Models. Frontiers in Cellular and Infection Microbiology. 2022; 11. doi: 10.3389/fcimb.2021.806265

23. Chen X, Huang H, Ju J, et al. Impact of vaccination on the COVID-19 pandemic in U.S. states. Scientific Reports. 2022; 12(1). doi: 10.1038/s41598-022-05498-z

24. Kayano T, Sasanami M, Kobayashi T, et al. Number of averted COVID-19 cases and deaths attributable to reduced risk in vaccinated individuals in Japan. The Lancet Regional Health—Western Pacific. 2022; 28: 100571. doi: 10.1016/j.lanwpc.2022.100571

25. Watson OJ, Barnsley G, Toor J, et al. Global impact of the first year of COVID-19 vaccination: a mathematical modelling study. The Lancet infectious diseases. 2022; 22(9): 1293-1302. doi: 10.1016/S1473-3099(22)00320-6

26. Jain V, Serisier A, Lorgelly P. The Real-World Impact of Vaccination on COVID-19 Cases During Europe’s Fourth Wave. International Journal of Public Health. 2022; 67. doi: 10.3389/ijph.2022.1604793

27. Liu Y, Liu J, Xia H, et al. Neutralizing Activity of BNT162b2-Elicited Serum. New England Journal of Medicine. 2021; 384(15): 1466-1468. doi: 10.1056/nejmc2102017

28. Goldberg Y, Mandel M, Bar-On YM, et al. Waning Immunity after the BNT162b2 Vaccine in Israel. New England Journal of Medicine. 2021; 385(24). doi: 10.1056/nejmoa2114228

29. Rosen B, Waitzberg R, Israeli A. Israel’s rapid rollout of vaccinations for COVID-19. Israel Journal of Health Policy Research. 2021; 10(1). doi: 10.1186/s13584-021-00440-6

30. Dagan N, Barda N, Kepten E, et al. BNT162b2 mRNA COVID-19 Vaccine in a Nationwide Mass Vaccination Setting. New England Journal of Medicine. 2021; 384(15): 1412-1423. doi: 10.1056/nejmoa2101765

31. Hassan-Smith Z, Hanif W, & Khunti K. Who should be prioritised for COVID-19 vaccines? The Lancet. 2020; 396(10264): 1732-1733. doi: 10.1016/S0140-6736(20)32224-8

32. Levine-Tiefenbrun M, Yelin I, Katz R, et al. Initial report of decreased SARS-CoV-2 viral load after inoculation with the BNT162b2 vaccine. Nature Medicine. 2021; 27(5): 790-792. doi: 10.1038/s41591-021-01316-7

33. Amit S, Beni SA, Biber A, et al. Postvaccination COVID-19 among Healthcare Workers, Israel. Emerging Infectious Diseases. 2021; 27(4): 1220-1222. doi: 10.3201/eid2704.210016

34. Broutin H, Mantilla-Beniers NB, Simondon F, et al. Epidemiological impact of vaccination on the dynamics of two childhood diseases in rural Senegal. Microbes and Infection. 2005; 7(4): 593-599. doi: 10.1016/j.micinf.2004.12.018

35. Xiao D, Wu K, Tan X, et al. The impact of the vaccination program for hemorrhagic fever with renal syndrome in Hu County, China. Vaccine. 2014; 32(6): 740-745. doi: 10.1016/j.vaccine.2013.11.024

36. Althouse BM, Scarpino SV. Asymptomatic transmission and the resurgence of Bordetella pertussis. BMC Medicine. 2015; 13(1). doi: 10.1186/s12916-015-0382-8

37. Shioda K, de Oliveira LH, Sanwogou J, et al. Identifying signatures of the impact of rotavirus vaccines on hospitalizations using sentinel surveillance data from Latin American countries. Vaccine. 2020; 38(2): 323-329. doi: 10.1016/j.vaccine.2019.10.010

38. Biswas PK, Islam MdZ, Debnath NC, et al. Modeling and Roles of Meteorological Factors in Outbreaks of Highly Pathogenic Avian Influenza H5N1. Viboud C, ed. PLoS ONE. 2014; 9(6): e98471. doi: 10.1371/journal.pone.0098471

39. Wang H, Tian CW, Wang WM, et al. Time-series analysis of tuberculosis from 2005 to 2017 in China. Epidemiology and Infection. 2018; 146(8): 935-939. doi: 10.1017/s0950268818001115

40. Bohdanov S, Polyvianna Y, Chumachenko T, et al. Forecasting of salmonellosis epidemic proces in Ukraine using autoregressive integrated moving average model. Przeglad Epidemiologiczny. 2020; 74(2): 346-354. doi: 10.32394/pe.74.27

41. Bai J, Perron P. Computation and analysis of multiple structural change models. Journal of Applied Econometrics. 2002; 18(1): 1-22. doi: 10.1002/jae.659

42. Ritchie H, Ortiz-Ospina E, Beltekian D, et al. Coronavirus Pandemic (COVID-19). Available online: https://ourworldindata.org/coronavirus (accessed on 2 April 2024).

43. Dickey DA, Fuller WA. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. 1979; 74(366): 427. doi: 10.2307/2286348

44. Phillips PCB, Perron P. Testing for a unit root in time series regression. Biometrika. 1988; 75(2): 335-346. doi: 10.1093/biomet/75.2.335

45. Kwiatkowski D, Phillips PC, Schmidt P, and Shin Y. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics. 1992; 54(1-3): 159-178. doi: 10.1016/0304-4076(92)90104-Y

46. Elliott G, Rothenberg TJ, Stock JH. Efficient Tests for an Autoregressive Unit Root. Econometrica. 1996; 64(4): 813. doi: 10.2307/2171846

47. Diebold FX, Rudebusch GD. Long memory and persistence in aggregate output. Journal of Monetary Economics. 1991; 28(1): 139-162.

48. Hassler U, Wolters J. On the power of unit root tests against fractional alternatives. Journal of Econometrics. 1994; 63(1): 285-303. doi: 10.1016/0165-1765(94)90049-3

49. Lee J, Schmidt P. On the power of the KPSS test of stationarity against fractionally integrated alternatives. Journal of Econometrics. 1996; 73(2): 285-302. doi: 10.1016/0304-4076(95)01741-0

50. Akaike H. Maximum likelihood identification of Gaussian autoregressive moving average models. Biometrika. 1973; 60(2): 255-265. doi: 10.1093/biomet/60.2.255

51. Akaike H. A Bayesian extension of the minimum AIC procedure of autoregressive model fitting. Biometrika. 1979; 66(2): 237-242. doi: 10.1093/biomet/66.2.237

52. Breitung J, Candelon B. Testing for short- and long-run causality: A frequency-domain approach. Journal of Econometrics. 2006; 132(2): 363-378. doi: 10.1016/j.jeconom.2005.02.004

53. Tastan H. Testing for Spectral Granger Causality. The Stata Journal: Promoting communications on statistics and Stata. 2015; 15(4): 1157-1166. doi: 10.1177/1536867x1501500411

54. Ciner C. Eurocurrency interest rate linkages: A frequency domain analysis. International Review of Economics & Finance. 2011; 20(4): 498-505. doi: 10.1016/j.iref.2010.09.006

55. Kırca M, Canbay Ş, Pirali K. Is the relationship between oil-gas prices index and economic growth in Turkey permanent? Resources Policy. 2020; 69: 101838. doi: 10.1016/j.resourpol.2020.101838

56. Geweke J. Measurement of Linear Dependence and Feedback between Multiple Time Series. Journal of the American Statistical Association. 1982; 77(378): 304-313. doi: 10.1080/01621459.1982.10477803

57. Johansen S, Nielsen M. Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model. Econometrica. 2012; 80(6): 2667-2732. doi: 10.3982/ecta9299

58. Crowley PM, & Mayes DG. How fused is the euro area core? An evaluation of growth cycle co-movement and synchronization using wavelet analysis. Journal of Business and Economic Statistics. 2009; 27(2): 271-287.

59. Aguiar‐Conraria L, Soares MJ. The Continuous Wavelet Transform: Moving Beyond Uni—and Bivariate Analysis. Journal of Economic Surveys. 2013; 28(2): 344-375. doi: 10.1111/joes.12012

60. Aguiar-Conraria L, Azevedo N, Soares MJ. Using wavelets to decompose the time–frequency effects of monetary policy. Physica A: Statistical Mechanics and its Applications. 2008; 387(12): 2863-2878. doi: 10.1016/j.physa.2008.01.063

61. Sowell F. Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics. 1992; 53(1-3): 165-188. doi: 10.1016/0304-4076(92)90084-5

62. Perron P, Vogelsang TJ. Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions. Journal of Business & Economic Statistics. 1992; 10(4): 467-470. doi: 10.1080/07350015.1992.10509923