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Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study

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  • Ullah, Saif
  • Khan, Muhammad Altaf

Abstract

Coronavirus disease (COVID-19) is the biggest public health challenge the world is facing in recent days. Since there is no effective vaccine and treatment for this virus, therefore, the only way to mitigate this infection is the implementation of non-pharmaceutical interventions such as social-distancing, community lockdown, quarantine, hospitalization or self-isolation and contact-tracing. In this paper, we develop a mathematical model to explore the transmission dynamics and possible control of the COVID-19 pandemic in Pakistan, one of the Asian countries with a high burden of disease with more than 200,000 confirmed infected cases so far. Initially, a mathematical model without optimal control is formulated and some of the basic necessary analysis of the model, including stability results of the disease-free equilibrium is presented. It is found that the model is stable around the disease-free equilibrium both locally and globally when the basic reproduction number is less than unity. Despite the basic analysis of the model, we further consider the confirmed infected COVID-19 cases documented in Pakistan from March 1, till May 28, 2020 and estimate the model parameters using the least square fitting tools from statistics and probability theory. The results show that the model output is in good agreement with the reported COVID-19 infected cases. The approximate value of the basic reproductive number based on the estimated parameters is R0≈1.87. The effect of low (or mild), moderate, and comparatively strict control interventions like social-distancing, quarantine rate, (or contact-tracing of suspected people) and hospitalization (or self-isolation) of testing positive COVID-19 cases are shown graphically. It is observed that the most effective strategy to minimize the disease burden is the implementation of maintaining a strict social-distancing and contact-tracing to quarantine the exposed people. Furthermore, we carried out the global sensitivity analysis of the most crucial parameter known as the basic reproduction number using the Latin Hypercube Sampling (LHS) and the partial rank correlation coefficient (PRCC) techniques. The proposed model is then reformulated by adding the time-dependent control variables u1(t) for quarantine and u2(t) for the hospitalization interventions and present the necessary optimality conditions using the optimal control theory and Pontryagin’s maximum principle. Finally, the impact of constant and optimal control interventions on infected individuals is compared graphically.

Suggested Citation

  • Ullah, Saif & Khan, Muhammad Altaf, 2020. "Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304720
    DOI: 10.1016/j.chaos.2020.110075
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    References listed on IDEAS

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    5. Asamoah, Joshua Kiddy K. & Jin, Zhen & Sun, Gui-Quan & Seidu, Baba & Yankson, Ernest & Abidemi, Afeez & Oduro, F.T. & Moore, Stephen E. & Okyere, Eric, 2021. "Sensitivity assessment and optimal economic evaluation of a new COVID-19 compartmental epidemic model with control interventions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    7. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. 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.
    9. Ojo, Mayowa M. & Benson, Temitope O. & Peter, Olumuyiwa James & Goufo, Emile Franc Doungmo, 2022. "Nonlinear optimal control strategies for a mathematical model of COVID-19 and influenza co-infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    10. 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.
    11. Alberto Olivares & Ernesto Staffetti, 2021. "Optimal Control Applied to Vaccination and Testing Policies for COVID-19," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    12. Yiheng Li, 2024. "Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters," Mathematics, MDPI, vol. 12(10), pages 1-15, May.
    13. Boudaoui, Ahmed & El hadj Moussa, Yacine & Hammouch, Zakia & Ullah, Saif, 2021. "A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Liu, Xuan & Ullah, Saif & Alshehri, Ahmed & Altanji, Mohamed, 2021. "Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    15. Tingting Li & Youming Guo, 2022. "Optimal Control Strategy of an Online Game Addiction Model with Incomplete Recovery," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 780-807, December.
    16. Torsten Thalheim & Tyll Krüger & Jörg Galle, 2022. "Indirect Virus Transmission via Fomites Can Counteract Lock-Down Effectiveness," IJERPH, MDPI, vol. 19(21), pages 1-14, October.
    17. Li, Tingting & Guo, Youming, 2022. "Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    18. Siphokazi Princess Gatyeni & Faraimunashe Chirove & Farai Nyabadza, 2022. "Modelling the Potential Impact of Stigma on the Transmission Dynamics of COVID-19 in South Africa," Mathematics, MDPI, vol. 10(18), pages 1-23, September.
    19. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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