TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Combating new COVID-19 variants in Indonesia : Is accelerating four-dose vaccinations sufficient?

* , ,

* Corresponding author · click or hover a name for details

pp. 2491–2517Vol. 28Issue 7October 2025DOI: 10.47974/JIM-1999XML
Received:
04 Dec 2023
Published Online:
08 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-1999
Pages:
2491–2517

Abstract

As new COVID-19 variants continue to emerge globally, we develop an SISI-type mathematical model to determine whether the transmission risks arising when such a new variant enters Indonesia can be mitigated by solely accelerating the country’s ongoing four-dose vaccination programme. We begin by determining the model’s basic reproduction number, as well as the model’s equilibria and their stability. Subsequently, employing parameter values representing the country’s situation as of March 20, 2023, we conduct a numerical sensitivity analysis in two simulated cases corresponding to two different levels of the new variant’s transmission. The results show that, a satisfactory mitigation relying solely on vaccinations necessitates a drastic acceleration in the low-transmission case, and proves unachievable in the high-transmission case. Accordingly, we recommend that the acceleration of the ongoing four-dose vaccinations be carried out in conjunction with other intervention measures, such as improvements of the vaccine’s efficacy and the disease’s recovery rate.

Keywords

Subject Classifications

92D3034D05

References

[1] Z. Agur, L. Cojocaru, G. Mazor, R. M. Anderson, and Y. L. Danon, “Pulse mass measles vaccination across age cohorts,” Proc. Natl. Acad. Sci. U.S.A., vol. 90, pp. 11698 (1993).
[2] H. M. Al-Saedi and H. H. Hameed, “Mathematical modeling for COVID-19 pandemic in Iraq,” J. Interdiscip. Math., vol. 24, pp. 1407–1427 (2021).
[3] H. Altawalah, “Antibody responses to natural SARS-CoV-2 infection or after COVID-19 vaccination,” Vaccines, vol. 9, p. 910 (2021).
[4] F. Andi, A. Kurmala, and R. Nasution, “68.57 million Indonesians receive third COVID-19 vaccine dose,” ANTARA, Jan. 2 (2023). [Online]. Available: https://en.antaranews.com/news/268248/6857-million-indonesians-receive-third-covid-19-vaccine-dose.
[5] R. Arora, A. Agrawal, R. Arora, R. C. Poonia, and V. Madaan, “Prediction and forecasting of COVID-19 outbreak using regression and ARIMA models,” J. Interdiscip. Math., vol. 24, pp. 227–243 (2021).
[6] M. A. Babu, M. M. Ahmmed, A. Ferdousi, M. M. Rahman, M. Saiduzzaman, V. Bhatnagar, L. Raja, and R. C. Poonia, “The mathematical and machine learning models to forecast the COVID-19 outbreaks in Bangladesh,” J. Interdiscip. Math., vol. 25, pp. 753–772 (2022).
[7] V. Bhatnagar, R. C. Poonia, P. Nagar, S. Kumar, V. Singh, L. Raja, and P. Dass, “Descriptive analysis of COVID-19 patients in the context of India,” J. Interdiscip. Math., vol. 24, pp. 489–504 (2021).
[8] N. Chitnis, J. M. Hyman, and J. M. Cushing, “Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model,” Bull. Math. Biol., vol. 70, pp. 1272–1296 (2008).
[9] A. Devi, M. Jakhar, and Y. Singh, “Qualitative analysis of 2019-nCoV mathematical model via an efficient computational technique,” J. Interdiscip. Math., vol. 24, pp. 425–441 (2021).
[10] O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, “On the definition and the computation of the basic reproduction ratio R0 in the models for infectious disease in heterogeneous populations,” J. Math. Biol., vol. 28, pp. 365–382 (1990).
[11] P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Math. Biosci., vol. 180, pp. 29–48 (2002).
[12] A. d’Onofrio, “Stability properties of pulse vaccination strategy in SEIR epidemic model,” Math. Biosci., vol. 179, pp. 57–72 (2002).
[13] R. S. Dubey, M. N. Mishra, and P. Goswami, “Effect of Covid-19 in India: A prediction through mathematical modeling using Atangana Baleanu fractional derivative,” J. Interdiscip. Math., vol. 25, pp. 2431–2444 (2022).
[14] D. J. D. Earn, P. Rohani, and B. T. Grenfell, “Persistence, chaos and synchrony in ecology and epidemiology,” Proc. R. Soc. B: Biol. Sci., vol. 265, pp. 7–10 (1998).
[15] W. Fernandez, “The Ministry Of Health has not seen the BF.7 subvariant sign will develop in Indonesia,” VOI, Dec. 29 (2022). [Online]. Available: https://voi.id/en/news/240250.
[16] A. Firdaus, Fardah, and S. Haryati, “Over 62 million Indonesians have received COVID-19 booster,” ANTARA, Sept. 19 (2022). [Online]. Available: https://en.antaranews.com/news/250537/over-62-million-indonesians-have-received-covid-19-booster.
[17] P. Harjule, V. Tiwari, and A. Kumar, “Mathematical models to predict COVID-19 outbreak: An interim review,” J. Interdiscip. Math., vol. 24, pp. 259–284 (2021).
[18] R. Hidayat, “Indonesia ends all Covid-19 restrictions,” Jakarta Daily, Dec. 31 (2022). [Online]. Available: https://www.jakartadaily.id/health/pr-1626370985/indonesia-ends-all-covid-19-restrictions.
[19] S. Khandelwal and A. Chaudhary, “COVID-19 pandemic & cyber security issues: Sentiment analysis and topic modeling approach,” J. Discrete Math. Sci. Cryptogr., vol. 25, pp. 987–997 (2022).
[20] G. Li, Y. Fan, Y. Lai, T. Han, Z. Li, P. Zhou, P. Pan, W. Wang, D. Hu, X. Liu, Q. Zhang, and J. Wu, “Coronavirus infections and immune responses,” J. Med. Virol., vol. 92, pp. 399–459 (2020).
[21] E. Margarini and M. Anindita, “Waspada 3 varian baru Covid-19 di Indonesia,” Direktorat Promosi Kesehatan dan Pemberdayaan Masyarakat Kementerian Kesehatan RI, May 11 (2021). [Online]. Available: https://promkes.kemkes.go.id/waspada-3-varian-baru-covid-19-di-indonesia.
[22] K. A. Matsumaya, “A new study suggests that the Omicron variant is over four times more transmissible in its early stage than Delta,” Fortune, Dec. 9 (2021). [Online]. Available: https://fortune.com/2021/12/08/omicron-covid-variant-data-more-transmissible-than-delta-new-study/.
[23] K. Modi, L. Umate, K. Makade, R. S. Dubey, and P. Agarwal, “Simulation based study for estimation of COVID-19 spread in India using SEIR model,” J. Interdiscip. Math., vol. 24, pp. 245–258 (2021).
[24] M. Mohammed, “COVID-19: What we know about new Omicron variant BF.7,” The Wire Science, Dec. 21 (2022). [Online]. Available: https://science.thewire.in/health/covid-19-new-Omicron-variant-bf-7-explained/.
[25] B. Mufarida, “PPKM dicabut, epidemiolog sebut garis batas pandemi Covid-19 belum terlampaui,” SINDO News, Jan. 1 (2023). [Online]. Available: https://nasional.sindonews.com/read/984545/15/ppkm-dicabut-epidemiolog-sebut-garis-batas-pandemi-covid-19-belum-terlampaui-1672552873.
[26] D. E. Muthiariny and M. Arkyasa, “Indonesia starts offering second COVID-19 vaccine booster for public starting Jan. 24,” Tempo.co, Jan. 23 (2023). [Online]. Available: https://en.tempo.co/amp/1682968/indonesia-starts-offering-second-covid-19-vaccine-booster-for-public-starting-jan-24.
[27] S. R. Nayak, V. Arora, U. Sinha, and R. C. Poonia, “A statistical analysis of COVID-19 using Gaussian and probabilistic model,” J. Interdiscip. Math., vol. 4, pp. 19–32 (2021).
[28] S. S. Negi, N. Sharma, and P. S. Rana, “A SEIAR mathematical model to analyse the effect of COVID-19 pandemic over the crowded and dense populated regions,” J. Interdiscip. Math., vol. 25, pp. 2063–2071 (2022).
[29] S. Olivia, J. Gibson, and R. Nasrudin, “Indonesia in the time of Covid-19,” Emerg. Microbes Infect., vol. 1, pp. 1–6 (2012).
[30] L. Owen, J. Hoseana, and B. Yong, “A numerical study of codimension-two bifurcations of an SIR-type model for COVID-19 and their epidemiological implications,” Commun. Biomathematical Sci., vol. 6, pp. 156–168 (2023).
[31] V. Pinandhita, “Update COVID-19 RI 20 Maret 2023: Tambah 234 kasus baru, kasus aktif jadi 3.660,” Detik Health, Mar. 20 (2023). [Online]. Available: https://health.detik.com/berita-detikhealth/d-6629452/update-covid-19-ri-20-maret-2023-tambah-234-kasus-baru-kasus-aktif-jadi-3660.
[32] H. Qi, B. Liu, X. Wang, and L. Zhang, “The humoral response and antibodies against SARS-CoV-2 infection,” Nat. Immunol., vol. 23, pp. 1008–1020 (2022).
[33] B. Roy, J. K. Dhillon, N. Habib, and B. Pugazhandhi, “Global variants of COVID-19: Current understanding,” J. Biomed. Sci., vol. 8, pp. 8–11 (2021).
[34] Satuan Tugas Penanganan COVID-19, “Situasi COVID-19 Nasional,” [Online]. Available: https://covid19.go.id/situasi
[35] S. Satyagraha and K. Kenzu, “Expecting a better Indonesian economy in 2023,” ANTARA, Jan. 6 (2023). [Online]. Available: https://en.antaranews.com/news/268683/expecting-a-better-indonesian-economy-in-2023.
[36] S. Singh, “New COVID-19 variant ‘Eris’ spreading quickly in UK: Report,” Business Today, Aug. 5 (2023). [Online]. Available: https://www.businesstoday.in/latest/world/story/new-covid-19-variant-eris-spreading-quickly-in-uk-report-392954-2023-08-05.
[37] J. K. Singh, S. Anand, and S. K. Srivastava, “Is BF.7 more infectious than other Omicron subtypes: Insights from structural and simulation studies of BF.7 spike RBD variant,” Int. J. Biol. Macromol., vol. 238, p. 124154 (2023).
[38] V. Singh, R. C. Poonia, S. Kumar, P. Dass, P. Agarwal, V. Bhatnagar, and L. Raja, “Prediction of COVID-19 corona virus pandemic based on time series data using support vector machine,” J. Discrete Math. Sci. Cryptogr., vol. 23, pp. 1583–1597 (2020).
[39] L. W. Somathilake, “A mathematical model for control strategies of COVID-19,” J. Interdiscip. Math., vol. 25, pp. 2365–2386 (2022).
[40] G. Suroyo and S. Sulaiman, “Indonesia’s GDP speeds up on easing COVID-19 curbs, brisk exports,” Reuters, Feb. 7 (2022). [Online]. Available: https://www.reuters.com/markets/asia/indonesias-q4-gdp-accelerateseasing-covid-19-curbs-high-exports-2022-02-07/
[41] A. Suryahadi, R. A. Izzati, and D. Suryadarma, “Estimating the impact of Covid-19 on poverty in Indonesia,” Bull. Indones. Econ. Stud., vol. 56, pp. 175–192 (2020).
[42] S. Susilawati, R. Falefi, and A. Purwoko, “Impact of COVID-19’s pandemic on the economy of Indonesia,” Budapest Int. Res. Crit. Inst.-J., vol. 3, pp. 1147–1156 (2020).
[43] A. Swaroop, “Here’s what you need to know about the new coronavirus variant called Arcturus,” Lifestyle Asia, Apr. 14 (2023). [Online]. Available: https://www.lifestyleasia.com/ind/whats-on/news-whats-on/coronavirus-new-variant-arcturus-origin-symptoms-precautions/.
[44] M. D. Swartz, S. M. DeSantis, A. Yaseen, F. A. Brito, M. A. Valerio-Shewmaker, S. E. Messiah, L. G. Leon-Novelo, H. W. Kohl, C. L. Pinzon-Gomez, T. Hao, S. Zhang, Y. Talebi, J. Yoo, J. R. Ross, M. O. Gonzalez, L. Wu, S. H. Kelder, M. Silberman, S. Tuzo, S. J. Pont, J. A. Shuford, D. Lakey, and E. Boerwinkle, “Antibody duration after infection from SARS-CoV-2 in the Texas coronavirus antibody response survey,” J. Infect. Dis., vol. 227, pp. 193–201 (2023).
[45] D. A. Swasono and N. H. Suhanda, “A strong middle class is the backbone of Indonesia’s economy,” East Asia Forum, Mar. 17 (2023). [Online]. Available: https://www.eastasiaforum.org/2023/03/17/a-strong-middle-class-is-the-backbone-of-indonesias-economy/
[46] G. T. Tilahun and H. T. Alemneh, “Mathematical modeling and optimal control analysis of COVID-19 in Ethiopia,” J. Interdiscip. Math., vol. 24, pp. 2101–2120 (2021).
[47] R. Triwadani, “Indonesian officials and media fight vaccine hesitancy, misinformation,” Asian Polit. Policy, vol. 13, pp. 635–639 (2021).
[48] F. N. Ulya and A. N. K. Movanita, “PPKM dicabut, epidemiolog: Kita dalam posisi sangat rawan dan berisiko,” Kompas.com, Dec. 31 (2022). [Online]. Available: https://nasional.kompas.com/read/2022/12/31/16072131/ppkm-dicabut-epidemiolog-kita-dalam-posisi-sangat-rawan-dan-berisiko.
[49] A. A. I. P. Wahyuni, “Antisipasi ancaman serangan Covid-19 varian Omicron,” Direktorat Jenderal Pelayanan Kesehatan Kementerian Kesehatan RI, Aug. 3 (2022). [Online]. Available: https://yankes.kemkes.go.id/view_artikel/941/antisipasi-ancaman-serangan-covid-19-varian-omicron.
[50] M. Walrath-Holdridge, “What to know about COVID Pirola: How new lineage BA.2.86 differs from other variants,” USA Today, Aug. 22 (2023). [Online]. Available: https://www.usatoday.com/story/news/health/2023/08/21/pirola-covid-lineage-not-omicron-variant/70644689007/.
[51] S. D. Warbhe, N. K. Lamba, and K. C. Deshmukh, “Impact of COVID-19: A mathematical model,” J. Interdiscip. Math., vol. 24, pp. 77–87 (2021).
[52] World Health Organization (WHO), “Statement on the fifteenth meeting of the International Health Regulations (2005) Emergency Committee regarding the coronavirus disease (COVID-19) pandemic,” WHO, May 5 (2023). [Online]. Available: https://www.who.int/news/item/05-05-2023-statement-on-the-fifteenth-meeting-of-the-international-health-regulations-(2005)-emergency-committee-regarding-the-coronavirus-disease-(covid-19)-pandemic.
[53] B. Yong, L. Owen, and J. Hoseana, “Mathematical analysis of an epidemic model for COVID-19: how important is the people’s cautiousness level for eradication?,” Lett. Biomathematics, vol. 9, pp. 3–22 (2022).
[54] B. Yong, J. Hoseana, and L. Owen, “A design of governmental policies for the eradication of COVID-19 in Jakarta using an SIR-type mathematical model,” Commun. Math. Biol. Neurosci., vol. 2022, Article ID 26 (2022).
[55] B. Yong, J. Hoseana, and L. Owen, “From pandemic to a new normal: strategies to optimise governmental interventions in Indonesia based on an SVEIQHR-type mathematical model,” Infect. Dis. Modell., vol. 7, pp. 346–363 (2022).

Views: 218Downloads: 73Citations: 1