Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model
DOI:
https://doi.org/10.5614/cbms.2021.4.1.5Keywords:
COVID-19, social awereness, rapid test, basic reproduction number, transcritical bifurcation, optimal control, cost effectiveness analysisAbstract
In this article, we propose and analyze a mathematical model of COVID-19 transmission among a closed population, with social awareness and rapid test intervention as the control variables. For this, we have constructed the model using a compartmental system of the ordinary differential equations. Dynamical analysis regarding the existence and local stability of equilibrium points is conducted rigorously. Our analysis shows that COVID-19 will disappear from the population if the basic reproduction number is less than one, and persist if the basic reproduction number is greater than one. In addition, we have shown a trans-critical bifurcation phenomenon based on our proposed model when the basic reproduction number equals one. From the elasticity analysis, we have observed that rapid testing is more promising in reducing the basic reproduction number as compared to a media campaign to improve social awareness on COVID-19. Using the Pontryagin Maximum Principle (PMP), the characterization of our optimal control problem is derived analytically and solved numerically using the forward-backward iterative algorithm. Our cost-effectiveness analysis shows that using rapid test and media campaigns partially are the best intervention strategy to reduce the number of infected humans with the minimum cost of intervention. If the intervention is to be implemented as a single intervention, then using solely the rapid test is a more promising and low-cost option in reducing the number of infected individuals vis-a-vis a media campaign to increase social awareness as a single intervention.
References
Aldila, D., Khoshnaw, S.H., Safitri, E., Anwar, Y.R., Bakry, A.R., Samiadji, B.M., Anugerah, D.A., H, M.F.A.G., Ayulani, I.D., Salim, S.N.,A., Mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia, Chaos, Solitons & Fractals 139, pp. 110042, 2020.
Aldila, D., Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia, Chaos, Solitons and Fractals 141, p. 110364, 2020.
Aldila, D., Optimal control problem on COVID-19 disease transmission model considering medical mask, disinfectants and media campaign, E3S Web of Conferences 202, p. 12009, 2020.
Aldila, D. , Ndii, M.Z. , Samiadji, B.M., Optimal control on COVID-19 eradication program in indonesia under the effect of community awareness, Mathematical Biosciences and Engineering 17(6), pp. 6355-6389, 2020.
Ahmed, I., Modu, G. U., Yusuf, A., Kumam, P., Yusuf, I., A mathematical model of coronovirus disease (COVID-19) containing asymptomatic and symptomtaic classes, ScienceDirect: Results in Physics 21, p. 103776, 2021.
Ndii, M. Z., Hadisoemarto, P., Agustian, D., Supriatna, A. K., An analysis of Covid-19 transmission in Indonesia and Saudi Arabia, Communication in Biomathematical Scieces, 3(1), pp. 19-27, 2020.
Khoshnaw, S. H., Salih, R. H., and Sulaimany, S., Mathematical modelling for coronavirus disease (COVID-19) in predicting future behaviours and sensitivity analysis, Mathematical Modelling of Natural Phenomena, 15, p. 33, 2020.
Shahzad, M., Abdel-Aty, A. H., Attia, R. A., Khoshnaw, S. H., Aldila, D., Ali, M., Sultan, F., Dynamics models for identifying the key transmission parameters of the COVID-19 disease, Alexandria Engineering Journal, 60(1), pp. 757-765, 2021. doi: https://doi.org/10.1016/j.aej.2020.10.006
Khoshnaw, S. H., Shahzad, M., Ali, M., Sultan, F., A Quantitative and Qualitative Analysis of the COVID-19 Pandemic Model, Chaos, Solitons Fractals, 138, p. 109932, 2020. https://doi.org/10.1016/j.chaos.2020.109932
Aldila, D., Samiadji, B.M., Simorangkir, G.M., Khosnaw, S.H.A., and Shahzad, M., Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia, BMC Res Notes, 14(1), pp. 1-7, 2021.
Logeswari, K., Ravichandran, C., Nisar, K. S., Mathematical model for spreading of COVID-19 virus with the Mittag?Leffler kernel, Wiley: Numerical Methods for Partial Differential Equations, 2020. DOI: 10.1002/num.22652
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, 20(5), pp. 553-558, 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.
Vaishya, R., Javaid, M., Khan, I. H., Haleem, A., Artificial Intelligence applications for COVID-19 pandemic, Diabetes and Metabolic Syndrome: Clinical Research and Reviews, 14(4), pp. 337-339, 2020.
Chee, M. L., Ong, M. E. H., Siddiqui, F. J., Zhang, Z., Lim, S. L., Ho, A. F. W., Liu, N., Artificial Intelligence Applications for COVID-19 in Intensive Care and Emergency Settings: A Systematic Review, International journal of environmental research and public health, 18(9), p. 4749, 2021.
Wang, X., Studying social awareness of physical distancing in mitigating COVID-19 transmission, Mathematical Biosciences and Engineering, 17(6), pp. 7428-7441, 2020.
Khajanchi, S., Sarkar, K., Mondal, J., Nisar, K. S., Abdelwahab. S. F., Mathematical modeling of the COVID-19 pandemic with intervention strategies, ScienceDirect: Results in Physics Volume 25, p. 104285, 2021. https://doi.org/10.1016/j.rinp.2021.104285
Sasmita, N. R., Ikhwan, M., Suyanto, S., Chongsuvivatwong, V., Optimal control on a mathematical model to pattern the progression of coronavirus disease 2019 (COVID-19) in Indonesia, Global Health Research and Policy, 5(1), p. 1-12 2020. https://doi.org/10.1186/s41256-020-00163-2.
Anderson, R. M., Heesterbeek, H., Klinkenberg, D., and Hollingsworth, T. D., How will country-based mitigation measures influence the course of the COVID-19 epidemic?, The lancet, 395(10228), 931-934, 2020. .
World Health Organization. Coronavirus disease 2019 (COVID-19): situation report, 46, WHO. 2020.
Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., Tong, Y., et al., Early transmission dynamics in Wuhan, China, of novel coronavirusinfected pneumonia, New Engl. J. Med., 382, p. 1199-1207, 2020.
Lauer, S. A., Grantz, K. H., Bi, Q., Jones, F. K., Zheng, Q., Meredith, H. R., et al., The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: Estimation and application, Ann. Int. Med., 172 (9), pp. 577-582, 2020.
Lai, C. C., Shih, T. P., Ko, W. C., Tang, H. J., and Hsueh, P. R., Severe acute respiratory syndrome coronavirus 2 (SARS-cov-2) and corona virus disease-2019 (COVID-19): The epidemic and the challenges, Int. J. Antimicrob. Ag., 55 (3), p. 105924, 2020.
Del Rio, C., and Malani, P. N., COVID-19-new insights on a rapidly changing epidemic, JAMA, 323(14), 1339-1340, 2020.
Feng, Z., and Velasco-Hernandez, J. X., (1997). Competitive exclusion in a vector-host model for the dengue fever, Journal of mathematical biology, 35(5), pp. 523-544, 1997.
Aldila, D., Cost-effectiveness and backward bifurcation analysis on COVID-19 transmission model considering direct and indirect transmission, Communications in Mathematical Biology and Neuroscience, 49, pp.1-28 , 2020.
Castillo-Chavez, C., and Song, B, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1(2), p. 361-404, 2004.
Aldila, D., and Angelina, M. (2021). Optimal control problem and backward bifurcation on malaria transmission with vector bias, Heliyon, 7(4), e06824, 2021.
Pan, D., Sze, S., Martin, C. A., Nevill, C. R., Minhas, J. S., Divall, P., et al., COVID-19 and the new variant strain in England?What are the implications for those from ethnic minority groups?, EClinicalMedicine, 33 100805(1)-2, 2021.
Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., Mishchenko, E. F., The mathematical theory of optimal processes, New York/London, John Wiley Sons, 1962.
