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Modeling the Influence of Lockdown on Epidemic Progression and Economy

Author

Listed:
  • Anastasia Mozokhina

    (S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Ivan Popravka

    (S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Masoud Saade

    (S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Vitaly Volpert

    (S.M. Nikol’skii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia
    Institut Camille Jordan, UMR 5208 CNRS, University of Lyon 1, 69622 Villeurbanne, France)

Abstract

The COVID-19 pandemic has underscored the necessity of implementing non-pharmaceutical interventions such as lockdowns to mitigate the spread of infectious diseases. This study aims to model the impact of lockdown measures on the progression of an epidemic. Using a combination of compartmental models, specifically a novel delay model, we analyze the effects of varying lockdown intensities and durations on disease transmission dynamics. The results highlight that timely and stringent lockdowns can significantly reduce the peak number of infections and delay the epidemic’s peak, thereby alleviating pressure on healthcare systems. Moreover, our models demonstrate the importance of appropriate lifting of lockdowns to prevent a resurgence of cases. Analytical and numerical results reveal critical thresholds for lockdown efficacy from the epidemiological point of view, which depend on such factors as the basic reproduction number ( ℜ 0 ), disease duration, and immunity waning. In the case of a single outbreak with permanent immunity, we analytically determine the optimal proportion of isolated people which minimizes the total number of infected. While in the case of temporary immunity, numerical simulations show that the infectious cases decrease with respect to the proportion of isolated people during lockdowns; as we increase the proportion of isolated people, we have to increase the duration of lockdowns to obtain periodic outbreaks. Further, we assess the influence of epidemic with or without lockdown on the economy and evaluate its economical efficacy by means of the level of population wealth. The percentage of productive individuals among isolated people influences the wealth state of the population during lockdowns. The latter increases with the rise of the former for fixed epidemic parameters. This research provides valuable insights for policymakers in designing effective lockdown strategies to control future epidemics.

Suggested Citation

  • Anastasia Mozokhina & Ivan Popravka & Masoud Saade & Vitaly Volpert, 2024. "Modeling the Influence of Lockdown on Epidemic Progression and Economy," Mathematics, MDPI, vol. 12(19), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3106-:d:1492056
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    References listed on IDEAS

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    1. Loayza,Norman V., 2020. "Costs and Trade-Offs in the Fight Against the COVID-19 Pandemic : A Developing Country Perspective," Research and Policy Briefs 148535, The World Bank.
    2. Masoud Saade & Sebastian Aniţa & Vitaly Volpert, 2023. "Dynamics of Persistent Epidemic and Optimal Control of Vaccination," Mathematics, MDPI, vol. 11(17), pages 1-15, September.
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