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A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia

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  • Aldila, Dipo
  • Khoshnaw, Sarbaz H.A.
  • Safitri, Egi
  • Anwar, Yusril Rais
  • Bakry, Aanisah R.Q.
  • Samiadji, Brenda M.
  • Anugerah, Demas A.
  • GH, M. Farhan Alfarizi
  • Ayulani, Indri D.
  • Salim, Sheryl N.

Abstract

The aim of this study is to investigate the effects of rapid testing and social distancing in controlling the spread of COVID-19, particularly in the city of Jakarta, Indonesia. We formulate a modified susceptible exposed infectious recovered compartmental model considering asymptomatic individuals. Rapid testing is intended to trace the existence of asymptomatic infected individuals among the population. This asymptomatic class is categorized into two subclasses: detected and undetected asymptomatic individuals. Furthermore, the model considers the limitations of medical resources to treat an infected individual in a hospital. The model shows two types of equilibrium point: COVID-19 free and COVID-19 endemic. The COVID-19-free equilibrium point is locally and asymptotically stable if the basic reproduction number (R0)is less than unity. In contrast, COVID-19-endemic equilibrium always exists when R0>1. The model can also show a backward bifurcation at R0=1whenever the treatment saturation parameter, which describes the hospital capacity, is larger than a specific threshold. To justify the model parameters, we use the incidence data from the city of Jakarta, Indonesia. The data pertain to infected individuals who self-isolate in their homes and visit the hospital for further treatment. Our numerical experiments indicate that strict social distancing has the potential to succeed in reducing and delaying the time of an outbreak. However, if the strict social distancing policy is relaxed, a massive rapid-test intervention should be conducted to avoid a large-scale outbreak in the future.

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  • Aldila, Dipo & Khoshnaw, Sarbaz H.A. & Safitri, Egi & Anwar, Yusril Rais & Bakry, Aanisah R.Q. & Samiadji, Brenda M. & Anugerah, Demas A. & GH, M. Farhan Alfarizi & Ayulani, Indri D. & Salim, Sheryl N, 2020. "A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304367
    DOI: 10.1016/j.chaos.2020.110042
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    References listed on IDEAS

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    1. Chakraborty, Tanujit & Ghosh, Indrajit, 2020. "Real-time forecasts and risk assessment of novel coronavirus (COVID-19) cases: A data-driven analysis," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Mandal, Manotosh & Jana, Soovoojeet & Nandi, Swapan Kumar & Khatua, Anupam & Adak, Sayani & Kar, T.K., 2020. "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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    Cited by:

    1. Zhang, Ge & Li, Zhiming & Din, Anwarud & Chen, Tao, 2024. "Dynamic analysis and optimal control of a stochastic COVID-19 model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 498-517.
    2. Usama H. Issa & Ashraf Balabel & Mohammed Abdelhakeem & Medhat M. A. Osman, 2021. "Developing a Risk Model for Assessment and Control of the Spread of COVID-19," Risks, MDPI, vol. 9(2), pages 1-15, February.
    3. Nur Hannani Bi Rahman & Shazmin Shareena A. Azis & Ibrahim Sipan, 2021. "COVID-19: Standard Operating Procedure Improvement For Green Office Building Using Indoor Environmental Quality," LARES lares-2021-4dqg, Latin American Real Estate Society (LARES).
    4. Yang, Chao & Wan, Zhiyang & Yuan, Quan & Zhou, Yang & Sun, Maopeng, 2023. "Travel before, during and after the COVID-19 pandemic: Exploring factors in essential travel using empirical data," Journal of Transport Geography, Elsevier, vol. 110(C).
    5. Md Arif Billah & Md Mamun Miah & Md Nuruzzaman Khan, 2020. "Reproductive number of coronavirus: A systematic review and meta-analysis based on global level evidence," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-17, November.
    6. Sara K Al-Harbi & Salma M Al-Tuwairqi, 2022. "Modeling the effect of lockdown and social distancing on the spread of COVID-19 in Saudi Arabia," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-40, April.
    7. Nadim, Sk Shahid & Ghosh, Indrajit & Chattopadhyay, Joydev, 2021. "Short-term predictions and prevention strategies for COVID-19: A model-based study," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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