Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness

1 Department of Mathematics, Universitas Indonesia, Depok 16424, Indonesia
2 Department of Mathematics, University of Nusa Cendana, Kupang-NTT 85361, Indonesia

Special Issues: Modeling the Biological, Epidemiological, Immunological, Molecular, Virological Aspects of COVID-19

A total of more than 27 million confirmed cases of the novel coronavirus outbreak, also known as COVID-19, have been reported as of September 7, 2020. To reduce its transmission, a number of strategies have been proposed. In this study, mathematical models with nonpharmaceutical and pharmaceutical interventions were formulated and analyzed. The first model was formulated without the inclusion of community awareness. The analysis focused on investigating the mathematical behavior of the model, which can explain how medical masks, medical treatment, and rapid testing can be used to suppress the spread of COVID-19. In the second model, community awareness was taken into account, and all the interventions considered were represented as time-dependent parameters. Using the center-manifold theorem, we showed that both models exhibit forward bifurcation. The infection parameters were obtained by fitting the model to COVID-19 incidence data from three provinces in Indonesia, namely, Jakarta, West Java, and East Java. Furthermore, a global sensitivity analysis was performed to identify the most influential parameters on the number of new infections and the basic reproduction number. We found that the use of medical masks has the greatest effect in determining the number of new infections. The optimal control problem from the second model was characterized using the well-known Pontryagin’s maximum principle and solved numerically. The results of a cost-effectiveness analysis showed that community awareness plays a crucial role in determining the success of COVID-19 eradication programs.
  Figure/Table
  Supplementary
  Article Metrics

Keywords COVID-19; community awareness; medical mask; rapid testing; hospitalization; quarantine; basic reproduction number; forward bifurcation; optimal control

Citation: Dipo Aldila, Meksianis Z. Ndii, Brenda M. Samiadji. Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness. Mathematical Biosciences and Engineering, 2020, 17(6): 6355-6389. doi: 10.3934/mbe.2020335

References

  • 1. WorldMeter, COVID-19 CORONAVIRUS PANDEMIC, available from: https://www.worldometers.info/coronavirus/#countries, accessed 02 July 2020.
  • 2. Kementerian Kesehatan Republik Indonesia, Data Sebaran, available from: https://covid19.go.id/, accessed 02 July 2020.
  • 3. A. Abidemi, M. I. Abd. Aziz, R. Ahmad, Vaccination and vector control effect on dengue virus transmission dynamics: Modelling and simulation, Chaos Solitons Fractals, 133 (2020), 109648.
  • 4. N. Ganegoda, T. Gotz, K. P. Wijaya, An age-dependent model for dengue transmission: Analysis and comparison to field data, Appl. Math. Comput., 388 (2021), 125538.
  • 5. A. Bustamam, D. Aldila, A. Yuwanda, Understanding Dengue Control for Short- and Long-Term Intervention with a Mathematical Model Approach, J. Appl. Math., 2018 (2018), 9674138.
  • 6. J. Mohammad-Awel, A. B. Gumel, Mathematics of an epidemiology-genetics model for assessing the role of insecticides resistance on malaria transmission dynamics, Math. Biosci., 312 (2019), 33-49.
  • 7. F. B. Agusto, S. Y. D. Valle, K. W. Blayneh, C. N. Ngonghala, M. J. Goncalves, N. Li, et al., The impact of bed-net use on malaria prevalence, J. Theor. Biol., 320 (2013), 58-65.    
  • 8. L. Cai, X. Li, N. Tuncer, M. Martcheva, A. A. Lashari, Optimal control of a malaria model with asymptomatic class and superinfection, Math. Biosci., 288 (2017), 94-108.
  • 9. S. Kim, A. Aurelio, E. Jung, Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines, J Theor Biol., 443 (2018), 100-112.
  • 10. D. K. Das, S. Khajanci, T. K. Kar, The impact of the media awareness and optimal strategy on the prevalence of tuberculosis, Appl. Math. Comput., 366 (2020), 124732.
  • 11. G. O. Agaba, Y. N. Kyrychko, K. B. Blyuss, Mathematical model for the impact of awareness on the dynamics of infectious diseases, Math. Biosci., 286 (2017), 22-30.
  • 12. R. K. Rai, A. K. Misra, Y. Takeuchi, Modeling the impact of sanitation and awareness on the spread of infectious diseases, Math. Biosci. Eng., 16 (2019), 667-700.
  • 13. A. K. Misra, R. K. Rai, Y. Takeuchi, Modeling the control of infectious diseases: Effects of TV and social media advertisements, Math. Biosci. Eng., 15 (2018), 1315-1343.
  • 14. K. Leung, J. T. Wu, D. Liu, G. M. Leung, First-wave covid-19 transmissibility and severity in china outside hubei after control measures, and second-wave scenario planning: a modelling impact assessment, The Lancet, 395 (2020), 1382-1393.
  • 15. A. J. Kucharski, T. W. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, et al., Early dynamics of transmission and control of covid-19: a mathematical modelling study, Lancet Infect. Dis., 20 (2020), 553-558.
  • 16. K. Prem, Y. Liu, T. W. Russell, A. J. Kucharski, R. M. Eggo, N. Davies, et al., The effect of control strategies to reduce social mixing on outcomes of the covid-19 epidemic in wuhan, china: a modelling study, Lancet Public Health, 5 (2020), e261-e270.
  • 17. E. Soewono, On the analysis of covid-19 transmission in wuhan, diamond princess and jakartacluster, Commun. Biomath. Sci., 3 (2020), 9-18.
  • 18. M. Z. Ndii, P. Hadisoemarto, D. Agustian, A. Supriatna, An analysis of covid-19 transmission in indonesia and saudi arabia, Commun. Biomath. Sci., 3 (2020), 19-27.
  • 19. S. E. Eikenberry, M. Mancuso, E. Iboi, T. Phan, K. Eikenberry, Y. Kuang, et al., To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the covid-19 pandemic, Infect. Disease Model., 5 (2020), 293-308.
  • 20. G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo, et al., Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy, Nat. Med., 26 (2020), 855-860.
  • 21. D. Aldila, S. H. Khoshnaw, E. Safitri, Y. R. Anwar, A. R. Bakry, B. M. Samiadji, et al., A mathematical study on the spread of covid-19 considering social distancing and rapid assessment: The case of jakarta, indonesia, Chaos Solitons Fractals, 139 (2020), 110042.
  • 22. R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang, et al., Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2), Science, 368 (2020), 489-493.
  • 23. The world bank: Awareness Campaigns Help Prevent Against COVID-19 in Afghanistan. Available from: https://www.worldbank.org/en/news/feature/2020/06/28/awareness-campaigns-help-prevent-against-covid-19-in-afghanistan. (Accessed 15 July 2020).
  • 24. M. S. Wolf, M. Serper, L. Opsasnick, R. M. O'Conor, L. M. Curtis, J. Y. Benavente, et al., Awareness, Attitudes, and Actions Related to COVID-19 Among Adults With Chronic Conditions at the Onset of the U.S. Outbreak: A Cross-sectional Survey, Ann. Intern. Med., 173 (2020), 100-109.
  • 25. Worldometer, COVID-19 CORONAVIRUS PANDEMIC, available from: https://www.worldometers.info/coronavirus/#countries (Accessed 25 August 2020).
  • 26. Z. Feng, J. X. Velasco-Hernández, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol., 35 (1997), 523-544.
  • 27. A. Davies, K. A. Thompson, K. Giri, G. Kafatos, J. Walker, A. Bennett, Testing the efficacy of homemade masks: would they protect in an influenza pandemic?, Disaster. Med. Public Health Prep., 7 (2013), 413-418.
  • 28. N. M. Ferguson, D. Laydon, G. Nedjati-Gilani, N. Imai, K. Ainslie, M. Baguelin, et al., Impact of Non-Pharmaceutical Interventions (NPIs) to Reduce COVID-19 Mortality and Healthcare Demand, vol. 16, Imperial College COVID-19 Response Team, London, 2020.
  • 29. R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang, et al., Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-cov2), Science, 368 (2020), 489-493.
  • 30. Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, et al., Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia, New Engl. J. Med., 382 (2020), 1199-1207.
  • 31. S. A. Lauer, K. H. Grantz, Q. Bi, F. K. Jones, Q. Zheng, H. R. Meredith, et al., The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: Estimation and application, Ann. Int. Med., 172 (2020), 577-582.
  • 32. C.-C. Lai, T.-P. Shih, W.-C. Ko, H.-J. Tang, P.-R. Hsueh, 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 (2020), 105924.
  • 33. C. del Rio, P. N. Malani, COVID-19-new insights on a rapidly changing epidemic, JAMA, 323 (2020), 1339-1340.
  • 34. R. M. Anderson, H. Heesterbeek, D. Klinkenberg, T. D. Hollingsworth, How will country-based mitigation measures influence the course of the COVID-19 epidemic?, Lancet, 395 (2020), 931-934.
  • 35. World Health Organization, Coronavirus disease 2019 (COVID-19): Situation report, 46, WHO (2020).
  • 36. B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Tang, Y. Xiao, et al., Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions, J. Clin. Med., 9 (2020), 462.
  • 37. L. Zou, F. Ruan, M. Huang, L. Liang, H. Huang, Z. Hong, et al., SARS-CoV-2 viral load in upper respiratory specimens of infected patients, New Engl. J. Med., 382 (2020), 1177-1179.
  • 38. G. Grasselli, A. Pesenti, M. Cecconi, Critical care utilization for the COVID-19 outbreak in Lombardy, Italy: early experience and forecast during an emergency response, JAMA, 323 (2020), 1545-1546.
  • 39. C. N. Ngonghala, E. Iboi, S. Eikenberry, M. Scotch, C. R. Maclntyre, M. H. Bonds, et al., Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus, Math. Biosci., 325 (2020), 108364.
  • 40. O. Diekmann, J. A. Heesterbeek, M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, J. R. Soc. Interface, 4 (2010), 873-885.
  • 41. P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
  • 42. O. Diekmann, J. A. Heesterbeek, J. A. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
  • 43. K. P. Wijaya, J. P. Chavez, D. Aldila, An epidemic model highlighting humane social awareness and vector-host lifespan ratio variation, Commun. Nonlinear Sci. Numer. Simulat., 90 (2020), 105389.
  • 44. B. D. Handari, F. Vitra, R. Ahya, D. Aldila, Optimal control in a malaria model: intervention of fumigation and bed nets, Adv. Differ. Equations, 497 (2019), 497.
  • 45. D. Aldila, T. Götz, E. Soewono, An optimal control problem arising from a dengue disease trans-mission model, Math. Biosci., 242 (2013), 9-16.
  • 46. D. Aldila, H. Seno, A Population Dynamics Model of Mosquito-Borne Disease Transmission, Focusing on Mosquitoes' Biased Distribution and Mosquito Repellent Use, Bull. Math. Biol., 81 (2020), 4977-5008.
  • 47. S. M. Garba, A. B. Gumel, M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 11-25.
  • 48. T. C. Reluga, J. Medlock, A. S. Perelson, Backward bifurcations and multiple equilibria in epidemic models with structured immunity, J. Theor. Biol., 252 (2008), 155-165.
  • 49. D. H. Knipl, G. Röst, Backward bifurcation in SIVS Model with immigration of Non-infectives, Biomath., 2 (2013), 1-14.
  • 50. C. Castillo-Chavez, B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361-404.
  • 51. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The mathematical theory of optimal processes, New York/London 1962. John Wiley & Sons.
  • 52. F. B. Agusto, I. M. Elmojtaba, Optimal control and cost-effective analysis of malaria/visceral leishmaniasis co-infection,PLoS One, 12 (2017), e0171102.
  • 53. A. Kumar, P. K. Srivastava, Y. Dong, Y. Takeuchi, Optimal control of infectious disease: Information-induced vaccination and limited treatment, Physica A, 542 (2020), 123196.
  • 54. H. R. Joshi, S. Lenhart, S. Hota, F. Agusto, Optimal control of an SIR model with changing behavior through an education campaign, Electron. J. Differ. Eq., 50 (2015), 1-14.
  • 55. M. Z. Ndii, F. R. Berkanis, D. Tambaru, M. Lobo, B. S. Djahi, Optimal control strategy for the effects of hard water consumption on kidney-related diseases, BMC Res. Notes, 13 (2020), 201.
  • 56. Jakarta responses to COVID-19 official website. Available from: https://corona.jakarta.go.id/id
  • 57. East Java responses to COVID-19 official website. Available from: http://infocovid19.jatimprov.go.id
  • 58. Information center and coordination for COVID-19, West Java, official website. Available from: https://pikobar.jabarprov.go.id
  • 59. S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178-196.
  • 60. M. Z. Ndii, B. S. Djahi, N. D. Rumlaklak, A. K. Supriatna, Determining the important parameters of mathematical models of the propagation of malware, in: M. A. Othman, M. Z. A. Abd Aziz, M. S. Md Saat, M. H. Misran (Eds.), Proceedings of the 3rd International Symposium of Information and Internet Technology (SYMINTECH 2018), Springer International Publishing, Cham, 2019, pp. 1-9.
  • 61. S. Lenhart, J. T.& Workman Optimal control applied to biological models. CRC Press, 2007.

 

This article has been cited by

  • 1. Dipo Aldila, Analyzing the impact of the media campaign and rapid testing for COVID-19 as an optimal control problem in East Java, Indonesia, Chaos, Solitons & Fractals, 2020, 110364, 10.1016/j.chaos.2020.110364

Reader Comments

your name: *   your email: *  

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved