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COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies

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  • Das, Arghya
  • Dhar, Abhishek
  • Goyal, Srashti
  • Kundu, Anupam
  • Pandey, Saurav

Abstract

The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, R0, to a target value R0target<1, but in distinct ways, which we implement in our model equations. We find that for the same R0target<1, TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

Suggested Citation

  • Das, Arghya & Dhar, Abhishek & Goyal, Srashti & Kundu, Anupam & Pandey, Saurav, 2021. "COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
  • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077920309863
    DOI: 10.1016/j.chaos.2020.110595
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    References listed on IDEAS

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    1. Piovella, Nicola, 2020. "Analytical solution of SEIR model describing the free spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Frank, T.D., 2020. "COVID-19 interventions in some European countries induced bifurcations stabilizing low death states against high death states: An eigenvalue analysis based on the order parameter concept of synergetic," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    Cited by:

    1. Yuan Liu & Chuyao Liao & Li Zhuo & Haiyan Tao, 2022. "Evaluating Effects of Dynamic Interventions to Control COVID-19 Pandemic: A Case Study of Guangdong, China," IJERPH, MDPI, vol. 19(16), pages 1-17, August.
    2. Yu, Zhenhua & Zhang, Jingmeng & Zhang, Yun & Cong, Xuya & Li, Xiaobo & Mostafa, Almetwally M., 2024. "Mathematical modeling and simulation for COVID-19 with mutant and quarantined strategy," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Haiyue Chen & Benedikt Haus & Paolo Mercorelli, 2021. "Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability," Mathematics, MDPI, vol. 9(17), pages 1-25, August.
    4. Castillo, Oscar & Melin, Patricia, 2021. "A new fuzzy fractal control approach of non-linear dynamic systems: The case of controlling the COVID-19 pandemics," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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