Sensitivity Analysis of SEIRS Model with Quarantine on the Spread of Covid-19

Wiwik Tri Hardianti; Hadi Sumarno; Paian Sianturi

doi:10.31764/jtam.v6i4.9627

Sensitivity Analysis of SEIRS Model with Quarantine on the Spread of Covid-19

Wiwik Tri Hardianti, Hadi Sumarno, Paian Sianturi

Abstract

Since the Covid-19 pandemic, various mathematical models have been developed to describe its spread using the compartment model. The purpose of this research was to construct a new model of Covid-19. This formulated model is an application of SEIRS epidemic model by Zhang & Teng (2007) and a modification of the Covid-19 model by Chatterjee et al. (2020) by adding variations of quarantine. The model is analyzed by determining the disease-free fixed point and basic reproduction number 〖(R〗_0) through the next generation matrix method. The next step is to analyze the sensitivity to find out the parameters that have the most influence on the spread of Covid-19. The disease will not spread in the population if the value of R_0<1, while the disease will spread if the value of R_0>1. The result of the sensitivity analysis stated the parameters that can be controlled and have the most significant effect, respectively, are the transmission rate from symptomatic infected individuals (β_2 ),transmission rates from asymptomatic infected individuals (β_1 ), quarantine rates for symptomatic infected individuals (θ_3), and quarantine rates for asymptomatic infected individuals (θ_2). Parameters β_2 and β_1 have a negative index, while θ_3 and θ_2 have a negative index. It means decreasing the transmission rate from infected individuals and increasing the quarantine rate for infected individuals can decrease the spread of Covid-19. Therefore there will not be an outbreak in the long term.

Keywords

SEIRS; Quarantine; Covid-19 pandemic; Basic Reproduction Number; Sensitivity Analysis.

Full Text:

DOWNLOAD [PDF]

References

Allen, L. J. S., & Lahodny, G. E. (2012). Extinction thresholds in deterministic and stochastic epidemic models. Journal of Biological Dynamics, 6(2), 590–611. https://doi.org/10.1080/17513758.2012.665502

Amaku, M., Covas, D. T., Bezerra Coutinho, F. A., Azevedo, R. S., & Massad, E. (2021). Modelling the impact of contact tracing of symptomatic individuals on the COVID-19 epidemic. Clinics, 76, e2639. https://doi.org/10.6061/CLINICS/2021/E2639

Batista, M. (2020). Estimation of the final size of the COVID-19 epidemic. MedRxiv, Nesteruk, 2020.02.16.20023606. https://doi.org/10.1101/2020.02.16.20023606

Bhadauria, A. S., Pathak, R., & Chaudhary, M. (2021). A SIQ mathematical model on COVID-19 investigating the lockdown effect. Infectious Disease Modelling, 6, 244–257. https://doi.org/10.1016/j.idm.2020.12.010

Blackwood, J. C., & Childs, L. M. (2018). An introduction to compartmental modeling for the budding infectious disease modeler. Letters in Biomathematics, 5(1), 195–221. https://doi.org/10.1080/23737867.2018.1509026

Carcione, J. M., Santos, J. E., Bagaini, C., & Ba, J. (2020). A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model. Frontiers in Public Health, 8(May), 230, 1-13. https://doi.org/10.3389/fpubh.2020.00230

Cascella, M., Rajnik, M., Cuomo, A., Dulebohn, S. C., & Di Napoli, R. (2022). Features, Evaluation and Treatment Coronavirus (COVID-19). StatPearls, 1-17. http://www.ncbi.nlm.nih.gov/pubmed/32150360

Chan, K. H., & Yuen, K. Y. (2020). COVID-19 epidemic: Disentangling the re-emerging controversy about medical facemasks from an epidemiological perspective. sInternational Journal of Epidemiology, 49(4), 1063–1066. https://doi.org/10.1093/ije/dyaa044

Chatterjee, K., Chatterjee, K., Kumar, A., & Shankar, S. (2020). Healthcare impact of COVID-19 epidemic in India: A stochastic mathematical model. Medical Journal Armed Forces India, 76(2), 147–155. https://doi.org/10.1016/j.mjafi.2020.03.022

Chitnis, N., Hyman, J. M., & Cushing, J. M. (2008). Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of Mathematical Biology, 70(5), 1272–1296. https://doi.org/10.1007/s11538-008-9299-0

Chowdhury, S. M. E. K., Forkan, M., Ahmed, S. F., Agarwal, P., Shawkat Ali, A. B. M., & Muyeen, S. M. (2022). Modeling the SARS-CoV-2 parallel transmission dynamics: Asymptomatic and symptomatic pathways. Computers in Biology and Medicine, 143(January), 105264. https://doi.org/10.1016/j.compbiomed.2022.105264

Fentie Bezabih, A., Kenassa Edessa, G., & Rao Koya, P. (2020). Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic. American Journal of Applied Mathematics, 8(5), 247. https://doi.org/10.11648/j.ajam.20200805.12

Huang, C., Wang, Y., Li, X., Ren, L., Zhao, J., Hu, Y., Zhang, L., Fan, G., Xu, J., Gu, X., Cheng, Z., Yu, T., Xia, J., Wei, Y., Wu, W., Xie, X., Yin, W., Li, H., Liu, M., … Cao, B. (2020). Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. The Lancet, 395(10223), 497–506. https://doi.org/10.1016/S0140-6736(20)30183-5

Khan, M. A., & Atangana, A. (2020). Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alexandria Engineering Journal, 59(4), 2379–2389. https://doi.org/10.1016/j.aej.2020.02.033

Kraemer, M., Yang, C.-H., Gutierrez, B., Wu, C.-H., & Klein, B. (2020). The effect of human mobility and control measures on the COVID-19 epidemic in China. Science, 368 (6490), 493-497. https://doi.org/10.1126/science.abb4218

Li, R., Pei, S., Chen, B., Song, Y., Zhang, T., Yang, W., & Shaman, J. (2020). Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2). Science, 368(6490), 489–493. https://doi.org/10.1126/science.abb3221

Li, Y., Shi, J., Xia, J., Duan, J., Chen, L., Yu, X., Lan, W., Ma, Q., Wu, X., Yuan, Y., Gong, L., Yang, X., Gao, H., & Wu, C. (2020). Asymptomatic and Symptomatic Patients With Non-severe Coronavirus Disease (COVID-19) Have Similar Clinical Features and Virological Courses: A Retrospective Single Center Study. Frontiers in Microbiology, 11(June), 1–8. https://doi.org/10.3389/fmicb.2020.01570

Matrajt, L., & Leung, T. (2020). Effectiveness of Social Distancing for COVID-19. Emerging Infectious Diseases, 26(8), 1740–1748. https://www.medrxiv.org/content/10.1101/2020.03.03.20028423v3.

Mayorga, L., Samartino, C. G., Flores, G., Masuelli, S., Sánchez, M. V, Mayorga, L. S., & Sánchez, C. G. (2020). Mayorga-2020-A modelling study highlights the.pdf. 1–11.

Okuonghae, D., & Omame, A. (2020). Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria. Chaos, Solitons and Fractals,139(110032), 1-18. https://doi.org/10.1016/j.chaos.2020.110032

Riyapan, P., Shuaib, S. E., & Intarasit, A. (2021). A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand. Computational and Mathematical Methods in Medicine, 2021(664483), 1-11. https://doi.org/10.1155/2021/6664483

Sameni, R. (2020). Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus. Grenoble (FR): Cornell University, 1–19. http://arxiv.org/abs/2003.11371

Sanyaolu, A., Okorie, C., Marinkovic, A., & Patidar, R. (2020). Comorbilidad y su impacto en pacientes con COVID-19. SN Comprehensive Clinical Medicine, 2, 1069–1076.

Van Den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1–2), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6

Wang, D., Hu, B., Hu, C., Zhu, F., Liu, X., Zhang, J., Wang, B., Xiang, H., Cheng, Z., Xiong, Y., Zhao, Y., Li, Y., Wang, X., & Peng, Z. (2020). Clinical Characteristics of 138 Hospitalized Patients with 2019 Novel Coronavirus-Infected Pneumonia in Wuhan, China. JAMA - Journal of the American Medical Association, 323(11), 1061–1069. https://doi.org/10.1001/jama.2020.1585

Wang, J., Kaperak, C., Sato, T., & Sakuraba, A. (2021). COVID-19 reinfection: A rapid systematic review of case reports and case series. Journal of Investigative Medicine, 69(6), 1253–1255. https://doi.org/10.1136/jim-2021-001853

WHO. (2020). WHO Coronavirus Disease. In WHO.int (p. 1). https://covid19.who.int

Worldometer. (2021). Coronavirus Cases: Statistics and Charts - Worldometer. https://www.worldometers.info/coronavirus/coronavirus-cases

Zhang, T., & Teng, Z. (2007). On a nonautonomous SEIRS model in epidemiology. Bulletin of Mathematical Biology, 69(8), 2537–2559. https://doi.org/10.1007/s11538-007-9231-z

DOI: https://doi.org/10.31764/jtam.v6i4.9627