Vaccination, Booster Doses and Social Constraints: A Steady State and an Optimal Transient Approaches to Epidemics Containment
Tóm tắt
The problem of the definition of control actions to contain epidemic diseases is crucial in case of high infectivity, dangerous or fatal consequences, large inhabited areas involved. Unfortunately, during the last three years, the COVID-19 pandemic has represented a critical situation all over the world. On the basis of the experiences for known diseases and the literature on the epidemic modeling, various strategies have been proposed and applied in different countries, someone using all the possible efforts, some others just maintaining the global health compact within acceptable levels. The effectiveness of the approaches has been always measured on the basis of the reproduction number
$${\mathcal {R}}_t$$
, which is intrinsically a steady-state evaluation, since it does not takes into account the control variations. In the present paper, with reference to a mathematical model which takes into account the different level of vaccination in the population, an optimal condition based approach is adopted to define the actions of intervention, bringing to a switching optimal control scheme based on the time by time evolution of the disease. The two approaches are developed and compared, showing that the use of partial information can bring to counter-intuitive situations and supporting the necessity of a feedback action to better adapt the containment measure to the situation. Numerical simulations are performed to better show the claimed results.
Tài liệu tham khảo
AlSayegh MAK, Iqbal A. The impact of the vaccination and booster shots in containing the covid-19 epidemic in bahrain: a game theory approach. In: 2021 Third International Sustainability and Resilience Conference: Climate Change, 2021. p. 264–269
Anderson R, Donnelly C, Hollingsworth T, et al. Reproduction number (R) and growth rate (r) of the COVID-19 epidemic in the UK: methods of estimation, data sources, causes of heterogeneity, and use as a guide in policy formulation. R Soc. 2020;24:1–86.
Chang HJ. Evaluation of the basic reproduction number of mers-cov during the 2015 outbreak in South Korea. In: 2016 16th International Conference on Control, Automation and Systems (ICCAS), 2016. p. 981–984, https://doi.org/10.1109/ICCAS.2016.7832428
Dan JM, Mateus J, Kato Y, et al. Immunological memory to SARS-CoV-2 assessed for up to 8 months after infection. Science. 2021;371(6529):1–15.
Di Giamberardino P, Iacoviello D. Optimal control of SIR epidemic model with state dependent switching cost index. Biomed Signal Process Control. 2017;31:377–80.
Di Giamberardino P, Iacoviello D. A control based mathematical model for the evaluation of intervention line in epidemic spreads without vaccination: the covid-19 case study. IEEE J Biomed Health Inf. 2020;13:890.
Di Giamberardino P, Iacoviello D. Evaluation of the effect of different policies in the containment of epidemic spreads for the COVID-19 case. Biomed Signal Process Control. 2021;65(102325):1–15.
Di Giamberardino P, Compagnucci L, Giorgi CD, et al. Modeling the effects of prevention and early diagnosis on hiv/aids infection diffusion. IEEE Trans Systems Man Cybern Syst. 2019;49(10):2119–30.
Di Giamberardino P, Iacoviello D, Papa F, et al. Dynamical evolution of COVID-19 in Italy with an evaluation of the size of the asymptomatic infective population. IEEE J Biomed Health Inf. 2021;25(4):1326–32.
Diagne ML, Rwezaura H, Tchoumi SY, et al. A mathematical model of COVID-19 with vaccination and treatment. Comput Math Methods Med. 2021;1250129:1–16.
Giordano G, Blanchini F, Bruno R, et al. Modeling the COVID-19 epidemic and implementation of population wide interventions in Italy. Nat Med. 2020;26:855.
Glizer VY, Turetsky V. Optimal time-sampling problem in a statistical control with a quadratic cost functional. In: Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, INSTICC. SciTePress; 2018. p. 21–32, https://doi.org/10.5220/0006829000210032
Liu Z, Omayrat M, Stursberg O. A study on model-based optimization of vaccination strategies against epidemic virus spread. In: Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO, INSTICC. SciTePress; 2021. p. 630–637, https://doi.org/10.5220/0010604006300637
Nishiura H, Chowell G. The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends. Math Stat Estim Approaches. 2009
Olivares A, Staffetti E. Optimal control-based vaccination and testing strategies for COVID-19. Comput Methods Progr Biomed. 2021;211(106411):1–9.
Pereira Barros G, Pereira Barros R, Souza de Oliveira E, et al. Estimation of reproduction number for COVID-19 with statistical correction of notifications delay. IEEE Latin Am Trans. 2022;20(7):1085–91. https://doi.org/10.1109/TLA.2021.9827471.
Radulescu A, Williams C, Cavanagh K. Management strategies in a SEIR-type model of COVID-19 community spread. Nat Sci Rep. 2020;10:21256.
Rui J, Zheng J, Chen J. Optimal control strategies of SARS-CoV-2 Omicron supported by invasive and dynamic models. Infect Dis Poverty. 2022;11:115.
Rzymski P, Camargo CA, Fal A, et al. COVID-19 vaccine boosters: the good, the bad, and the ugly. Vaccines. 2021;9(11):1299. https://doi.org/10.3390/vaccines9111299.
Silva CJ, Cruz C, Torres DFM, et al. Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal. Sci Rep. 2021;11(3451):1–15.
Tang B, Bragazzi NL, Li Q, et al. An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infect Dis Model. 2020;5:248–55.
Van Den Driessche P. Reproduction numbers of infectious disease models. Infect Dis Models. 2017;2:288–303.
Zhao S, Lin Q, Ran J, et al. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: a data-driven analysis in the early phase of the outbreak. Int J Infect Dis. 2020;92:214–7.