# Net Reproduction Number as a Real-Time Metric of Population Reproducibility

Chiara Achangwa, Changhee Han, Jun-Sik Lim, Seonghui Cho, Sangbum Choi, Sukhyun Ryu

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Chiara Achangwa, Changhee Han, Jun-Sik Lim, Seonghui Cho, Sangbum Choi, et al.. Net Reproduction Number as a Real-Time Metric of Population Reproducibility. JMIR Public Health and Surveillance, 2025, 11, pp.e63603. 10.2196/63603. hal-05209335

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Research Letter

# Net Reproduction Number as a Real-Time Metric of Population Reproducibility

Chiara Achangwa<fnref n="1" />, PhD; Changhee Han<fnref n="2" />, MS; Jun-Sik Lim<fnref n="3" />, DVM, MPH; Seonghui Cho<fnref n="1" />, BBA; Sangbum Choi<fnref n="4" />, PhD; Sukhyun Ryu<fnref n="1" />, MD, PhD

Corresponding Author:

Sukhyun Ryu, MD, PhD

Department of Preventive Medicine, College of Medicine

The Catholic University of Korea

R6117, Omibus Park, 222 Banpo-daero

Seoul, 06591

Republic of Korea

Phone: 82 02-3147-8383

Fax: 82 02-532-3820

Email: gentryu@catholic.ac.kr

Abstract

The total fertility rate (TFR) is a biased estimate of the population reproductive potential when there is a sex-ratio imbalance at birth, and it does not account for the mortality of women of childbearing age. This study aimed to estimate the reproduction rate (R<sub>t</sub>), which adjusts for the sex-ratio imbalance and the mortality of women of childbearing age, and to assess the differences in the timing of when the population reached the replacement level of the TFR and R<sub>t</sub>. We first estimated the R<sub>t</sub> using the probability of survival in women and the number of female births. Then, using a time-series analysis, we compared the time series of the TFR and R<sub>t</sub> in the Korean population between 1975 and 2022. We found the R<sub>t</sub> showed a below replacement level of the population a year earlier than the TFR. However, the estimate of the time-series analysis of R<sub>t</sub> was not significantly different from the estimates of the TFR. Our finding suggests that the R<sub>t</sub> can provide timely information on the adjusted population reproductive potential and is easier for the public to interpret compared to TFR.

JMIR Public Health Surveill 2025;11:e63603; doi: 10.2196/63603

**Keywords:** fertility rate; reproducibility; reproduction rate; population control; Korea; sex ratio; imbalance; mortality; woman; female; childbearing age; reproductive age; giving birth; assessment; time series; Korean; impact analysis; birth control; reproduction

Introduction

Between 1962 and 1993, Korea implemented a successful family planning policy. In 1993, this policy was discontinued; in 2004, childbirth-promoting policies were implemented (Multimedia Appendix 1). In 2023, Korea had the lowest fertility rate (0.8) worldwide [1]. The total fertility rate (TFR), the average offspring number per childbearing-age females (15-49 years), is a common metric to assess population change potential. However, this cohort-based measure is biased when there is male-to-female sex-ratio imbalance at birth [2,3]. The TFR does not account for mortality rates

among childbearing-age women, possibly affecting population reproducibility [2,4]. These limitations reduce TFR's ability to accurately reflect a country's population replacement dynamics. Therefore, the net reproduction rate ($R_t$), the number of daughters a woman of childbearing age would produce under prevailing fertility and mortality conditions, is better. Like other real-time epidemiological metrics (eg, the effective reproduction number in infectious disease modeling) [5], the $R_t$ can be calculated and updated regularly with new population data; it can provide timely insights into population sustainability. The $R_t$ is easier for public understanding, as a population is below the replacement level when the $R_t < 1$ [6],

<footnote n="1">¹Department of Preventive Medicine, College of Medicine, The Catholic University of Korea, Seoul, Republic of Korea</footnote>

<footnote n="2">²Computer Information System, Georgia State University, Atlanta, GA, United States</footnote>

<footnote n="3">³IHAP, Université de Toulouse, INRAE, ENVT, Toulouse, France</footnote>

<footnote n="4">⁴Department of Statistics, Korea University, Seoul, Republic of Korea</footnote>
in contrast to the TFR, with a threshold of 2.1. Despite this,
no previous studies have evaluated the population reproduci-
bility using the R<sub>t</sub> in Korea.

This study assessed the differences in the timing of
reaching population replacement level of the TFR and R<sub>t</sub> and
the estimated difference of the time series of the TFR and R<sub>t</sub>
by two major population control policies.

segmented regression to examine the time trend and its level
change in the TFR and R<sub>t</sub>. We also conducted a cross-
correlation analysis to evaluate the temporal relationship
between the TFR and R<sub>t</sub>. Then, we compared the estimates
of R<sub>t</sub> multiplied by 2.1 (TFR threshold level) with the TFR
estimates along with 95% CIs. All analyses were conducted
using R software (version 4.4.0; R Foundation for Statistical
Computing).

Methods

We collected the annual number of live births, number of
women, mortality rate of women, and male-to-female ratio
of women of childbearing age between 1975 and 2022
through the Korean National Statistic Agency [7] to calcu-
late the TFR and R<sub>t</sub> (Multimedia Appendix 2). To iden-
tify the different estimates of policy impact (1975-1993:
family planning policy; 1993-2004: childbirth encouragement
policy), we conducted an interrupted time series (ITS) with

Results

The number of live birth number decreased from 874,030 in
1975 to 249,186 in 2022. Similarly, the male-to-female sex
ratio decreased from 112 in 1975 to 105 in 2022 (Figure
1A). The TFR remained below 2.1 since 1984 (TFR=2.04)
and decreased further to 0.78 in 2022 (Figure 1B). The R<sub>t</sub>
remained below 1 since 1983 (R<sub>t</sub>=0.98) and decreased to 0.4
in 2022 (Figure 1C).

**Figure 1.** The annual number of live births, total fertility rate (TFR), and reproduction rate (R<sub>t</sub>) in South Korea, 1975-2022. (A) The bar-colored blue and sky-blue indicate the annual number of male and female births, respectively. The blue solid line indicates the yearly sex ratio of male to female births. (B) The interrupted time series model with the TFR. The interruption (dashed vertical line) was set to 1993 (when the family planning policy was discontinued) taking into account for the transition period of the policy and 2004 (when the birth encouragement policy was implemented) to identify the changes in the TFR level and slope. The horizontal dashed line indicates a critical threshold of the TFR at 2.1. The dashed orange line indicates the annual TFR based on a counterfactual scenario without changing the birth control policy, and the orange shaded area indicates 95% confidence intervals (CIs) of the TFR. (C) The interrupted time series model with the estimated R<sub>t</sub>; the critical threshold of R<sub>t</sub>=1. An R<sub>t</sub> < 1 indicates that the population's reproductive performance falls below the replacement level. The dashed orange line indicates the annual R<sub>t</sub> based on a counterfactual scenario without changing the birth control policy, and the orange shaded area indicates 95% CIs of R<sub>t</sub>.

<figure><img src="image_2.png" /></figure>
The ITS showed an immediate increase in the mean TFR (55%) and $R_t$ (26%) and an increased slope change of 9% in the TFR and 4% in $R_t$ following the family planning policy discontinuation (Figure 1B and 1C and Table 1). After the birth encouragement policy introduction, the slope of the TFR

(3%) and $R_t$ (1%) increased, with no significant level change. When the $R_t$ was multiplied by 2.1, the estimates were within the 95% CI of the TFR estimate (Table 1). A high correlation between the TFR and $R_t$ at lag 0 indicated no temporal differences (Multimedia Appendix 3).

<table><caption>**Table 1.** Estimates from the interrupted time-series analysis using the total fertility rate and reproduction rate in South Korea, 1975-2022.</caption><thead><tr><th></th><th>Mean total fertility rate, % (95% CIs)<sup>a</sup></th><th>Mean reproduction rate, % (95% CIs)<sup>a</sup></th><th>Mean reproduction rate, (95% CIs) multiplied by 2.1<sup>b</sup></th></tr></thead><tbody><tr><td>Immediate level change following the discontinuation of family planning</td><td>54.9 (33.1 to 67.2)</td><td>25.9 (18.3 to 33.8)</td><td>54.4 (38.4 to 71.0)</td></tr><tr><td>Post-intervention slope change following the discontinuation of family planning</td><td>8.9 (7.6 to 10.4)</td><td>4.2 (3.3 to 5.5)</td><td>8.8 (6.9 to 11.6)</td></tr><tr><td>Immediate level change following the birth-encouragement policy implementation</td><td>3.2 (1.3 to 4.8)</td><td>1.2 (0.1 to 2.0)</td><td>2.5 (0.2 to 4.2)</td></tr><tr><td>Post-intervention slope change following the birth-encouragement policy implementation</td><td>5.8 (-5.5 to 16.4)</td><td>3.3 (-4.6 to 11.2)</td><td>6.9 (-9.7 to 23.5)</td></tr></tbody></table>

## Discussion

The threshold level of the population replacement was captured a year earlier through the $R_t$ compared to the TFR. This is likely due to sex-ratio imbalances in Korea.

The trend levels and slope changes of the TFR and $R_t$ increased following the birth control policy discontinuation [8]. These significant level changes were likely affected by previous birth control policies [9]. However, after the child encouragement policy implementation in 2004, the TFR and $R_t$ were far below the population replacement threshold, consistent with a previous study that reported no positive effect of child encouragement policies on the fertility rate [10], likely due to sociocultural factors influencing fertility behavior (eg, changing gender roles and economic pressures) [10]. Our study could be applied to other

countries experiencing similar socioeconomic and cultural dynamics, particularly those with comparable fertility patterns and sex-ratio imbalances [4].

This study had limitations. Sensitivity analyses were not included in the parameter estimation models. The ITS models were interrupted in 1993 to reflect the discontinuation of the family planning policy, accounting for the policy transition period. The ITS may not fully capture the nonlinear trends after 2015. We did not consider the qualitative characteristics of each policy.

The $R_t$ can be used as a useful and timely metric of population reproducibility, particularly in the presence of sex-ratio imbalance at birth. Furthermore, the $R_t$ threshold of 1 may be easier for public interpretation compared to the TFR, as the public became familiar with the $R_t$ parameter during the COVID-19 pandemic.

## Acknowledgments

Ethics approval was waived by the institutional review board at the Catholic University of Korea (2024-1205-0001). The authors attest that there was no use of generative artificial intelligence technology in the generation of text, figures, or other informational content in this manuscript. This work was supported by the Government-wide Research and Development to Advance Infectious Disease Prevention and Control, Republic of Korea (grant number RS-2023-KH140322), and the Basic Science Research Program through the National Research Foundation of Korea by the Ministry of Education (grant numbers NRF-2020R111A3066471 and 2022R1A2C1008514).

## Data Availability

The data that support the findings of this study are available on request from the corresponding author.

## Authors' Contributions

SR conceived the study and designed the statistical methods. CA, CH, LSJ, and SC collected and assimilated the data. CA, CH, LSJ, and SC performed the data analysis. CA and SR wrote the first manuscript draft. CA, SC, and SR critically reviewed and

<footnote><sup>a</sup>Estimates of the mean and 95% confidence intervals (CIs) from the interrupted time series with a segmented regression model to examine the time trend and its level change.</footnote>

<footnote><sup>b</sup>Estimates of the reproduction rate were multiplied by 2.1 (threshold level of total fertility rate) along with 95% CIs.</footnote>
edited the manuscript. All authors helped to interpret the results, critically revised the manuscript, and provided final approval of the version for publication.

**Conflicts of Interest**

None declared.

**Multimedia Appendix 1**

Key population policies in South Korea between 1970 and 2022.

[DOCX File (Microsoft Word File), 20 KB-Multimedia Appendix 1]

**Multimedia Appendix 2**

Description of total fertility rate, reproduction rate, and time-series analysis.

[DOCX File (Microsoft Word File), 23 KB-Multimedia Appendix 2]

**Multimedia Appendix 3**

Yearly lagged cross-correlation coefficients between total fertility rate and net reproduction number in South Korea (1975–2022).

[DOCX File (Microsoft Word File), 108 KB-Multimedia Appendix 3]

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**Abbreviations**

**ITS:** interrupted time series

**TFR:** total fertility rate

Edited by Amaryllis Mavragani; peer-reviewed by Atalay Aktuna, Youngsuk Ko; submitted 24.06.2024; final revised version received 22.11.2024; accepted 04.12.2024; published 12.02.2025

**Please cite as:**

Achangwa C, Han C, Lim JS, Cho S, Choi S, Ryu S

Net Reproduction Number as a Real-Time Metric of Population Reproducibility

JMIR Public Health Surveill 2025;11:e63603

URL: https://publichealth.jmir.org/2025/1/e63603

doi: 10.2196/63603
© Chiara Achangwa, Changhee Han, Jun-Sik Lim, Seonghui Cho, Sangbum Choi, Sukhyun Ryu. Originally published in JMIR Public Health and Surveillance (https://publichealth.jmir.org), 12.02.2025. This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in JMIR Public Health and Surveillance, is properly cited. The complete bibliographic information, a link to the original publication on https://publichealth.jmir.org, as well as this copyright and license information must be included.