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Commentary Open Access
Volume 7 | Issue 1

Control of epidemics: Testing, vaccinations, and monitoring

  • 1Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
+ Affiliations - Affiliations

*Corresponding Author

Igor Nesteruk, inesteruk@yahoo.com

Received Date: December 02, 2025

Accepted Date: December 31, 2025

Abstract

Increasing the test-per-case ratio was recommended to reduce the number of cases and deaths per capita. In particular, due to a synchronous increase in the number of tests alongside the rise in new cases and very high levels of the tests-per-case ratio, the COVID-19 pandemic in New Zealand was largely controlled before October 2021. After February 2022, an abrupt decline in the tests-to-case ratio led to a record number of cases and deaths at a relatively high vaccination level. Recent COVID-19 mortality rates in New Zealand are comparable with the global endemic level and the global flu mortality. Thus, the existing vaccines cannot reduce the number of COVID-19-related deaths per capita. Nevertheless, the lower values of case fatality risk CFR in more vaccinated countries in 2020–2022 still have to encourage people to be vaccinated, especially the elderly and persons with weak immunity. A recent huge increase in the case fatality risk is connected with the decrease in COVID-19 testing. Since many cases are hidden (asymptomatic), the estimation of real epidemic dynamics and correct CFR values needs complicated models, taking into account asymptomatic patients, re-infections, newborns, etc. To monitor the real epidemic dynamics (e.g., to calculate the rate of increase in the real number of infectious persons over time), a new reproduction number (recently proposed by the author) can be recommended.

Keywords

Efficiency of vaccinations, Testing efficacy, Mathematical modeling of infectious diseases, Statistical methods, COVID-19 pandemic, COVID-19 in New Zealand

Commentary

Effective epidemic control on the population level means that the numbers of cases and deaths have to be as low as possible, e.g., we can use the averaged (smoothed) number of new daily cases DCC and deaths DDC per million [1,2] for different moments in order to estimate the corresponding control efficacy. The application of the relative (per capita) characteristics allows comparing the effectiveness of epidemic combating in different countries and regions, but only after taking into account other factors. In particular, very low DCC and DDC values registered in Africa during the COVID-19 pandemic [2,3] do not mean that European strategies were less effective. Much lower median population age in African countries and many asymptomatic cases in children and young people led to much lower DCC and DDC figures [4]. Higher testing level (average daily numbers of tests per thousand DTC) in Europe also allowed revealing more infections [4]. On the other hand, the high values of the tests-per-case ratio TC=DTC*1000/DCC (or low values of the test positivity rate DCC/(DTC*1000)) allowed some countries to decrease DCC and DDC figures, and to control the COVID-19 pandemic completely even at low vaccination levels [2].

The effective epidemic control on the population level also means low values of the case fatality risk CFR=DDC/DCC, which allow decreasing the number of deaths even at high numbers of cases. CFR is the probability of dying for a person who tested positive, which can be decreased by improving immunity (e.g., due to vaccinations) and effective treatment. Case fatality risks demonstrated decreasing trends with the increase of COVID-19 vaccination levels in 2020–2022 [2,4–6], when the testing levels were high enough to register reliable figures both in the numerator and the denominator of the CFR formula. This fact has to encourage people to be vaccinated, especially the elderly and persons with weak immunity [6]. Unfortunately, in 2022 and 2023, the numbers of COVID-19 cases per capita have not demonstrated any decreasing trends with the increase of the vaccination levels, and the decrease in CFR was not enough to reduce DDC values significantly [2,4–6]. We will show that the recent average daily number of deaths per million is still high in New Zealand.

Investigations of the COVID-19 pandemic dynamics presented in [2] allowed us to conclude that “increasing the test per case ratio and application of quarantine restrictions for the entire population, including vaccinated people, can be recommended to reduce the negative consequences of epidemics”. It is quite difficult to test the feasibility of these recommendations using the example of the COVID-19 pandemic, since quarantine restrictions were lifted before publication of the paper [2] and most countries stopped reporting new cases to WHO [3].

According to [2], New Zealand gives us examples of a synchronous increase in the number of tests with an increase in the number of new cases and very high levels of the tests-per-case ratio TC before October 2021. The epidemic was completely controlled since the average number of new daily cases DCC and deaths DDC per million were less than 15 and 0.025, respectively. After February 2022, an abrupt decline in the TC values led to a record number of cases and deaths at a relatively high vaccination level.

Let us analyze the recent COVID-19 situation in New Zealand with the use of datasets available in [7]. In 7 days (17–23 November 2025), 162 new cases and 5 new deaths were registered. Taking into account the population of New Zealand 5.3 million [8], we can calculate the values of DCC=162/(7*5.3)=4.4 and DDC=5/(7*5.3)=0.135. Close figures can be obtained using the recent records during 30 days (25.10.2025–23.11.2025), [7]: DCC=695/(30*5.3)=4.4 and DDC=16/(30*5.3)=0.1. Both DCC values are much lower than the global lower endemic level 37.2, calculated in [5] with the use of 2022 datasets [1,9]. Nevertheless, DDC figures are comparable with the lower endemic level 0.124, [5] and much higher than the number of deaths before October 2021 despite very high vaccination level (as of November 2025, 82.9% of 12+ have completed primary course; 57.2% of eligible 50+ have received second booster; 71.0% of eligible 18+ have received first booster, [10]). Recent DDC figures in New Zealand are close to the global flu mortality 0.1–0.18, [5,11].

The low number of new cases registered in New Zealand in November 2025 is a result of reduced testing levels. The decreasing trend in DCC values started in many countries already in 2023 and caused the significant increase of the case fatality risk CFR=DDC/DCC, [2,4]. E.g., in New Zealand, DCC was equal to 1,079 in 2022 and 245 in 2023; CFR=0.0011 and 0.003, respectively, [4]. Unfortunately, we have found no recent information about the daily number of tests per thousand (DTC), but very high levels of the case fatality risk for periods 17–23 November 2025 (CFR=5/162=0.031) and 25.10.2025–23.11.2025 (CFR=16/695=0.023) indicate a further decrease in the testing level in comparison with June 2022, when DTC was around 0.6, [12]. Since many cases were not revealed, the estimation of real epidemic dynamics and correct CFR values needs complicated models, taking into account asymptomatic patients, re-infections, newborns, etc (e.g., [13–15]).

It is possible to estimate the minimal testing level, which could make the COVID-19 epidemic controllable in New Zealand. Taking into account the critical value of the tests per case ratio TC* =200, which was enough to control the epidemic before October 2021 (see Figure 7 in [2]), and the recent DCC value 4.4, we can conclude that the daily number of tests per thousand has to be higher than DTC* =200*4.4/1000=0.88. Due to the large number of unregistered cases, this is only a lower estimation. But the control of COVID-19 looks realistic in New Zealand, where the maximum DTC values were approximately 10 times higher in August 2021 and allowed stopping an abrupt increase in the daily number of new cases (see Figure 7 in [2]).

To control new waves of COVID-19 and other epidemics, we need to monitor their dynamics. In particular, the real-time estimations of the effective reproduction numbers Rt [16] can be used. Since the definition of Rt and methods of its estimation [17–23] use only visible (registered) numbers of cases, they cannot reflect the dynamics of epidemics with many hidden (asymptomatic) patients. To monitor the real epidemic dynamics (e.g., to calculate the rate of increasing the real numbers of infectious persons over time τ), a new reproduction number Rτ(t) was introduced [24]. The method of its estimation uses the numbers of visible cases only and was successfully applied for the pertussis epidemic in England [24], the COVID-19 pandemic in Austria and Tanzania [25], and for monitoring a new COVID-19 wave in Ukraine in the summer of 2025, [26].

Ethical Approval Statement

No human or animal experiments were used in the study. The statistical information used is public and available on the Internet.

Author statements

The author declares no conflict of interest.

Acknowledgements

The author is grateful to Hiroshi Nishiura, Robin Thompson, Matt Keeling, Paul Brown, and Oleksii Rodionov for their support and for providing very useful information.

References

1. COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU). Available from: https://github.com/owid/covid-19-data/tree/master/public/data.

2. Nesteruk I. Impact of vaccination and testing levels on the COVID-19 waves. Journal of Allergy and Infectious Diseases. 2024 Jul 26;5(1):44–55.

3. World Health Organization. COVID-19 Cases, World. Geneva: World Health Organization. Available from: https://data.who.int/dashboards/covid19/cases.

4. Nesteruk I. Trends of the COVID-19 dynamics in 2022 and 2023 vs. the population age, testing and vaccination levels. Frontiers in Big Data. 2024 Jan 10;6:1355080.

5. Nesteruk I. Should we ignore SARS-CoV-2 disease?. Epidemiology & Infection. 2024 Jan;152:e57.

6. Nesteruk I. Impact of SARS-CoV-2 vaccinations on pandemic dynamics: Trends in cases, deaths, and fatality risks. Journal of Allergy and Infectious Diseases. 2025 Apr 14;6(1):17–24.

7. Health New Zealand. COVID-19 reporting. Available from: https://www.tewhatuora.govt.nz/for-health-professionals/data-and-statistics/covid-19/reporting.

8. Worldometer. New Zealand Population. Available from: https://www.worldometers.info/world-population/new-zealand-population/.

9. Nesteruk I. Endemic characteristics of SARS-CoV-2 infection. Sci Rep. 2023 Sep 8;13(1):14841.

10. Health New Zealand. COVID-19 vaccine data. Available from: https://www.tewhatuora.govt.nz/for-health-professionals/data-and-statistics/covid-19/vaccine.

11. Paget J, Spreeuwenberg P, Charu V, Taylor RJ, Iuliano AD, Bresee J, et al. Global mortality associated with seasonal influenza epidemics: New burden estimates and predictors from the GLaMOR Project. J Glob Health. 2019 Dec;9(2):020421.

12. Our World in Data. Daily COVID-19 tests per 1,000 people. Available from: https://ourworldindata.org/grapher/daily-tests-per-thousand-people-smoothed-7-day?mapSelect=~NZL&globe=1&globeRotation=-41.55%2C172.95.

13. Keeling MJ, Rohani P. Modeling infectious diseases in humans and animals. Princeton University Press; 2008.

14. Nesteruk I. General SIR model for visible and hidden epidemic dynamics. Front Artif Intell. 2025 Feb 24;8:1559880.

15. Nesteruk I. How Re-Infections and Newborns Can Impact Visible and Hidden Epidemic Dynamics?. Computation. 2025 May 9;13(5):113.

16. R-bloggers. Effective reproduction number estimation. Available from: https://www.r-bloggers.com/2020/04/effective-reproduction-number-estimation/.

17. Hamouda O. Schätzung der aktuellen entwicklung der SARS-CoV-2-epidemie in deutschland–nowcasting. Epid Bull. 2020;17:10–5.

18. 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 Nov 1;178(9):1505–12.

19. Arroyo-Marioli F, Bullano F, Kucinskas S, Rondón-Moreno C. Tracking R of COVID-19: A new real-time estimation using the Kalman filter. PLoS One. 2021 Jan 13;16(1):e0244474.

20. Thompson RN, Stockwin JE, van Gaalen RD, Polonsky JA, Kamvar ZN, Demarsh PA, et al. Improved inference of time-varying reproduction numbers during infectious disease outbreaks. Epidemics. 2019 Dec;29:100356.

21. Ogi-Gittins I, Hart WS, Song J, Nash RK, Polonsky J, Cori A, et al. A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. Epidemics. 2024 Jun;47:100773.

22. Demongeot J, Oshinubi K, Rachdi M, Seligmann H, Thuderoz F, Waku J. Estimation of daily reproduction numbers during the COVID-19 outbreak. Computation. 2021 Oct 18;9(10):109.

23. Nesteruk I, Brown P. Impact of Ukrainian Refugees on the COVID-19 Pandemic Dynamics after 24 February 2022. Computation. 2024 Apr 3;12(4):70.

24. Nesteruk I. New reproduction numbers for the visible and real epidemic dynamics. Advances in Public Health. 2025;2025(1):5469282.

25. Nesteruk I. Reproduction numbers for epidemics with hidden cases, re-infections and newborns. medRxiv. 2025:2025–05. doi: 10.1101/2025.05.28.25328507.

26. Nesteruk I. Real Infection Spreading Rates for the COVID-19 pandemic in Ukraine estimated with the Use of the Novel Reproduction Number. Research Square Posted September 26th, 2025. DOI: https://doi.org/10.21203/rs.3.rs-7710352/v1.

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