Data-Driven Generating Operator in SEIRV Model for COVID-19 Transmission
DOI:
https://doi.org/10.5614/cbms.2023.6.1.6Keywords:
COVID-19 vaccine rollout, immunity waning, boosters timing, dynamic operatorAbstract
The COVID-19 (SARS-CoV-2) vaccine has been extensively implemented through large-scale programs in numerous countries as a preventive measure against the resurgence of COVID-19 cases. In line with this vaccination effort, the Indonesian government has successfully inoculated over 74% of its population. Nevertheless, a significant decline in the duration of vaccine-induced immunity has raised concerns regarding the necessity of additional inoculations, such as booster shots. Prior to proceeding with further inoculation measures, it is imperative for the government to assess the existing level of herd immunity, specifically determining whether it has reached the desired threshold of 70%. To shed light on this matter, our objective is to ascertain the herd immunity level following the initial and subsequent vaccination programs, while also proposing an optimal timeframe for conducting additional inoculations. This study utilizes COVID-19 data from Jakarta and employs the SEIRV model, which integrates time-dependent parameters and incorporates an additional compartment to represent the vaccinated population. By formulating a dynamic generator based on the cumulative cases function, we are able to comprehensively evaluate the analytical and numerical aspects of all state dynamics. Simulation results reveal that the number of individuals protected by the vaccine increases following the vaccination program; however, this number subsequently declines due to the waning effect of the vaccine. Our estimates indicate that the vaccination program in Jakarta has achieved herd immunity levels exceeding 70% from October 2021 to February 2022, thus underscoring the necessity of rolling out further inoculations no later than February 2022.
References
Anderson, D.E., Sivalingam, V., Kang, A.E.Z., Ananthanarayanan, A., Arumugam, H., Jenkins, T.M., Hadjiat, Y. and Eggers, M., Povidone-iodine demonstrates rapid in vitro virucidal activity against SARS-CoV-2, The virus causing COVID-19 disease, Infectious Diseases and Therapy, 9(3), pp. 669-675, 2020.
Pedersen, S.F. and Ho, Y.C., SARS-CoV-2: a storm is raging, The Journal of Clinical Investigation, 130(5), pp. 2202-2205, 2020.
Wu, Z. and McGoogan, J.M., Characteristics of and important lessons from the coronavirus disease 2019 (COVID-19) outbreak in China: summary of a report of 72 314 cases from the Chinese Center for Disease Control and Prevention, Jama, 323(13), pp. 1239-1242, 2020.
Nguyen, L.H., Drew, D.A., Graham, M.S., Joshi, A.D., Guo, C.G., Ma, W., Mehta, R.S., Warner, E.T., Sikavi, D.R., Lo, C.H. and Kwon, S., Risk of COVID-19 among front-line health-care workers and the general community: a prospective cohort study, The Lancet Public Health, 5(9), pp. e475-e483, 2020.
Stadnytskyi, V., Anfinrud, P. and Bax, A., Breathing, speaking, coughing or sneezing: What drives transmission of SARS-CoV-2?, Journal of Internal Medicine, 290(5), pp. 1010-1027, 2021.
Zhou, P., Yang, X.L., Wang, X.G., Hu, B., Zhang, L., Zhang, W., Si, H.R., Zhu, Y., Li, B., Huang, C.L. and Chen, H.D., A pneumonia outbreak associated with a new coronavirus of probable bat origin, Nature, 579(7798), pp. 270-273, 2020.
Zhu, N., Zhang, D., Wang, W., Li, X., Yang, B., Song, J., Zhao, X., Huang, B., Shi, W., Lu, R. and Niu, P., A novel coronavirus from patients with pneumonia in China, 2019, New England Journal of Medicine, 2020.
Putri, S.A.E., Varian-varian Covid-19, Apa Perbedaannya?, Satuan Tugas Penanganan COVID-19, Dinas Kesehatan DKI Jakarta, https://corona.jakarta.go.id/id/artikel/varian-varian-covid-19-apa-perbedaannya, (January 19, 2022).
Viana, R., Moyo, S., Amoako, D.G., Tegally, H., Scheepers, C., Althaus, C.L., Anyaneji, U.J., Bester, P.A., Boni, M.F., Chand, M. and Choga, W.T., Rapid epidemic expansion of the SARS-CoV-2 Omicron variant in southern Africa, Nature, 603(7902), pp. 679-686, 2022.
Servellita, V., Syed, A.M., Morris, M.K., Brazer, N., Saldhi, P., Garcia-Knight, M., Sreekumar, B., Khalid, M.M., Ciling, A., Chen, P.Y. and Kumar, G.R., Neutralizing immunity in vaccine breakthrough infections from the SARS-CoV-2 Omicron and Delta variants, Cell, 185(9), pp. 1539-1548, 2022.
Satuan Tugas Penanganan COVID-19, Perkembangan Kasus Per-Hari (Grafik Gabungan), Peta Sebaran, 2021, Pemerintah Provinsi DKI Jakarta, https://corona.jakarta.go.id/id/peta-persebaran, (March 5, 2021).
Feikin, D.R., Higdon, M.M., Abu-Raddad, L.J., Andrews, N., Araos, R., Goldberg, Y., Groome, M.J., Huppert, A., O?Brien, K.L., Smith, P.G. and Wilder-Smith, A., Duration of effectiveness of vaccines against SARS-CoV-2 infection and COVID-19 disease: results of a systematic review and meta-regression, The Lancet, 2022.
Mentri Kesehatan, Keputusan Menteri Kesehatan Republik Indonesia (Decree of the Minister of Health of the Republic of Indonesia) NOMOR HK.01.07/MENKES/4638/2021 Tentang Petunjuk Teknis Pelaksanaan Vaksinasi Dalam Rangka Penanggulangan Pandemi Corona Virus Disease 2019 (COVID-19), Kementrian Kesehatan RI, https://farmalkes.kemkes.go.id/peraturan/kepmenkes/, (May 7, 2021).
Mentri Kesehatan, Keputusan Menteri Kesehetan Republik Indonesia (Decree of the Minister of Health of the Republic of Indonesia) NOMOR HK.01.07/MENKES/4641/2021 Tentang Petunjuk Teknis Pelaksanaan Vaksinasi
Dalam Rangka Penanggulangan Pandemi Corona Virus Disease 2019 (COVID-19), Kementrian Kesehatan RI, https://farmalkes.kemkes.go.id/peraturan/kepmenkes/, (August 31, 2021).
Richards, F.J., A flexible growth function for empirical use, Journal of Experimental Botany, 10(2), pp. 290-301, 1959.
De Silva, U.C., Warachit, J., Waicharoen, S. and Chittaganpitch, M., A preliminary analysis of the epidemiology of influenza A (H1N1) v virus infection in Thailand from early outbreak data, June-July 2009, Eurosurveillance, 14(31), 2009.
World Health Organization, Coronavirus disease (COVID-19) Pandemic, World Health Organization, https://www.who.int/healthtopics/coronavirus, (December 31, 2020).
World Health Organization, Coronavirus disease (COVID-19): Herd immunity, lockdowns and COVID-19, World Health Organization, https://www.who.int/news-room/questions-and-answers/item/herd-immunity-lockdowns-and-covid-19, (December 31, 2020).
World Health Organization, How do vaccines work?, World Health Organization, https://www.who.int/news-room/featurestories/detail/how-do-vaccines-work, (December 8, 2020).
World Health Organization, Coronavirus disease (COVID-19): Herd immunity, lockdowns and COVID-19, World Health Organization, https://www.who.int/emergencies/diseases/novel-coronavirus-2019/question-and-answers-hub/q-a-detail/herd-immunitylockdowns-and-covid-19, (December 31, 2020).
Harvard Health Publising, If you've been exposed to the coronavirus, Harvard Health Publising, https://www.health.harvard.edu/diseases-and-conditions/if-youve-been-exposed-to-the-coronavirus, (April 18, 2023).
Kementrian Kesehatan, Virus Corona Varian Baru B.117, B.1351, B.1617 Sudah Ada di Indonesia, Redaksi Sehat Negeriku, https://sehatnegeriku.kemkes.go.id/baca/rilis-media/20210504/1737688/virus-corona-varian-baru-b-117-b-1351-b-1617-sudah-ada-di-indonesia/, (May 4, 2021).
Kementrian Kesehatan, Varian Omicron Terdeteksi di Indonesia, Redaksi Sehat Negeriku, https://sehatnegeriku.kemkes.go.id/baca/umum/20211216/2738991/varian-omicron-terdeteksi-di-indonesia/, (December 16, 2021).
Lei, Y.C, and Zhang, S.Y., Features and Partial Derivatives of Bertalanffy-Richards Growth Model in Forestry, Nonlinear Analysis: Modelling and Control, 9(1), pp. 65-73, 2004.
Diekmann, O., Heesterbeek, J.A.P. and Roberts, M.G, The construction of next-generation matrices for compartmental epidemic models, Journal of The Royal Society Interface, 7(47), pp. 873-885, 2010.
Susanto, H., Tjahjono, V., Hasan, A. Kasim, M., Nuraini, N., Putri, E., Kusdiantara, R. and Kurniawan. How many can you infect? Simple (and naive) methods of estimating the reproduction number, Communication in Biomathematical Sciences, 3, pp. 28-36, 2020.
Ndii, N.Z., Hadisoemarto, P., Agustian, D. and Supriatna, A.K., An analysis of Covid-19 transmission in Indonesia and Saudi Arabia, Communication in Biomathematical Sciences, 3(1), pp. 19-27, 2020.
Mugnaine, M., Gabrick, E.C., Protachevicz, P.R., Iarosz, K.C., de Souza, S.L., Almeida, A.C., Batista, A.M., Caldas, I.L., Szezech Jr, J.D. and Viana, R.L., Control attenuation and temporary immunity in a cellular automata SEIR epidemic model, Chaos, Solitons & Fractals, 155, p.111784, 2022.
Meng, L. and Zhu, W., Analysis of SEIR epidemic patch model with nonlinear incidence rate, vaccination and quarantine strategies, Mathematics and Computers in Simulation, 200, pp. 489-503, 2022.
Wintachai, P. and Prathom, K., Stability analysis of SEIR model related to efficiency of vaccines for COVID-19 situation, Heliyon, 7(4), p. e06812, 2021.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Communication in Biomathematical Sciences

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.