An Analysis of Covid-19 Transmission in Indonesia and Saudi Arabia
DOI:
https://doi.org/10.5614/cbms.2020.3.1.3Keywords:
Covid-19, Deterministic, Stochastic, Reproductive ratio, Probability of extinctionAbstract
An outbreak of novel coronavirus has been happening in more than 200 countries and has shocked society. Several measures have been implemented to slowing down the epidemics while waiting for vaccine and pharmaceutical intervention. Using a deterministic and stochastic model, we assess the effectiveness of current strategies: reducing the transmission rate and speeding up the time to detect infected individuals. The reproductive ratio and the probability of extinction are determined. We found that the combination of both strategies is effective to slow down the epidemics. We also find that speeding up the time to detect infected individuals without reducing the transmission rate is not sufficient to slow down the epidemics.References
World Health Organization, Coronavirus disease (COVID-19) Pandemic, https://www.who.int/emergencies/diseases/novel-coronavirus-2019, Accessed on April 16, 2020.
WorldMeter, COVID-19 CORONAVIRUS PANDEMIC, https://www.worldometers.info/coronavirus/#countries.
Kucharski, A. J., Russell, T. W., Diamond, C., Liu, Y., Edmunds, J., Funk, S., Eggo, R. M., Sun, F., Jit, M., Munday, J. D., Davies, N., Gimma, A., Van Zandvoort, K., Gibbs, H., Hellewell, J., Jarvis, C. I., Clifford, S., Quilty, B. J., Bosse, N. I., Abbott, S., Klepac, P., and Flasche, S., Early dynamics of transmission and control of COVID-19: a mathematical modelling study, The Lancet Infectious Diseases, 2020.
Yang, S. Cao, P., Du, P., Wu, Z., Zhuang, Z., Yang, L., Yu, X., Zhou, Q., Feng, X., Wang, X., Li, W., Liu, E., Chen, J., Chen, Y. and He, D., Early estimation of the case fatality rate of COVID-19 in mainland China: a data-drivenanalysis, Annals of translational medicine, 8(4), pp. 128-128, Feb. 2020.
Prem, K., Liu, Y., Russell, T. W., Kucharski, A. J, Eggo, R. M., Davies, N., Flasche, S., Clifford, S., Pearson, C. A. B., Munday, J. D., Abbott, S., Gibbs, H., Rosello, A., Quilty, B.J., Jombart, T., Sun, F., Diamond, C., Gimma, A., Zandvoort, K. v., Funk, S., Jarvis, C. I., Edmunds, W.J., Bosse, N.I., Hellewell, J., Jit M. and Klepac. P., The effect ofcontrol strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modellingstudy, The Lancet Public Health, 2020.
Mizumoto, K., Kagaya, K., Zarebski, A. and Chowell, G., Estimating the asymptomatic proportion of coronavirus disease 2019 (covid-19) cases on board the diamond princess cruise ship, yokohama, japan, 2020., Eurosurveillance, 25(10), 2020.
Lai, S., Ruktanonchai, N.W., Zhou, L., Prosper, O., Luo, W., Floyd, J.R., Wesolowski, A., Zhang, C., Du, X., Yu, H. and Tatem, A.J., Effect of non-pharmaceutical interventions for containing the COVID-19 outbreak: an observational and modelling study, medRxiv, 2020.
Yang, Z., Zeng, Z., Wang, K., Wong, S.S., Liang, W., Zanin, M., Liu, P., Cao, X., Gao, Z., Mai, Z. and Liang, J., Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions, Journal of Thoracic Disease, 12(3), pp. 165-174, 2020.
Rong, X., Yang, L., Chu, H. and Fan, M., Effect of delay in diagnosis on transmission of COVID-19, Mathematical Biosciences and Engineering, 17(3), pp.2725-2740, 2020.
Wang, L., Wang, J., Zhao, H., Shi, Y., Wang, K., Wu, P. and Shi, L., Modelling and assessing the effects of medical resources on transmission of novel coronavirus (COVID-19) in Wuhan, China., Mathematical Biosciences and Engineering, 17(mbe-17-04-165):2936, 2020.
Yang, C. and Wang, J., A mathematical model for the novel coronavirus epidemic in Wuhan, China., Mathematical Biosciences and Engineering, 17(3), pp.2708-2724, 2020.
Zhou, W., Wang, A., Xia, F., Xiao, Y. and Tang, S., Effects of media reporting on mitigating spread of COVID-19 in the early phase of the outbreak, Mathematical Biosciences and Engineering, 17(mbe-17-03-147):2693, 2020
Tang, B., Bragazzi, N.L., Li, Q., Tang, S., Xiao, Y. and Wu, J., An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov), Infectious disease modelling, 5, pp.248-255, 2020.
Soewono, E., On the analysis of Covid-19 transmission in Wuhan, Diamond Princess and Jakarta-cluster, Communication in Biomathematical Sciences, 3(1), pp. 9-18, 2020.
Nuraini, N., Khairudin, K. and Apri, M., Modeling Simulation of COVID-19 in Indonesia based on Early Endemic Data, Communication in Biomathematical Sciences, (1), pp.1-8, 2020.
He, S., Tang, S. and Rong, L., A discrete stochastic model of the COVID-19 outbreak: Forecast and control, Math. Biosci. Eng, 17, pp. 2792-2804, 2020.
Zhang, Y., You, C., Cai, Z., Sun, J., Hu, W. and Zhou, X.H., Prediction of the COVID-19 outbreak based on a realistic stochastic model, medRxiv, 2020.
Alshammari, S.M. and Mikler, A.R., Modeling Spread of Infectious Diseases at the Arrival Stage of Hajj, In International Conference on Bioinformatics and Biomedical Engineering (pp. 430-442), Springer, Cham, April, 2018.
Alasmawi, H., Aldarmaki, N. and Tridane, A., Modeling of a Super-Spreading Event of the Mers-Corona Virus during the Hajj Season using Simulation of the Existing Data, International Journal of Statistics in Medical and Biological Research, 1:24-30, 2017.
Chowell, G., Nishiura, H. and Bettencourt, L.M., Comparative estimation of the reproduction number for pandemic influenza from daily case notification data, Journal of the Royal Society Interface, 4(12), pp.155-166, 2007.
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.
Favier, C., D'egallier, N., Rosa-Freitas, M.G., Boulanger, J.P., Costa Lima, J.R., Luitgards-Moura, J.F., Menk`es, C.E., Mondet, B., Oliveira, C., Weimann, E.T.S. and Tsouris, P., Early determination of the reproductive number for vector-borne diseases: the case of dengue in Brazil, Tropical Medicine International Health, 11(3), pp.332-340, 2006.
Chowell, G., Ammon, C.E., Hengartner, N.W. and Hyman, J.M., Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions, Journal of theoretical biology, 241(2), pp.193-204, 2006.
Allen, L.J., An introduction to stochastic epidemic models, In Mathematical epidemiology (pp. 81-130), Springer, Berlin, Heidelberg, 2008.
Ndii, M.Z. and Supriatna, A.K., Stochastic mathematical models in epidemiology, Information, 20(9A), pp.6185-6196, 2017.
Ndii, M.Z., Pemodelan Matematika Dinamika Populasi Dan Penyebaran Penyakit Teori, Aplikasi, Dan Numerik, Deepublish, 2018.
Allen L. J. S. and Jr. L., Extinction thresholds in deterministic and stochastic epidemic models, Journal of Biological Dynamics, 6, pp. 590-611, 2012.
