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González-Parra G, Mahmud MS, Kadelka C. Learning from the COVID-19 pandemic: A systematic review of mathematical vaccine prioritization models. Infect Dis Model 2024; 9:1057-1080. [PMID: 38988830 PMCID: PMC11233876 DOI: 10.1016/j.idm.2024.05.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2024] [Revised: 04/26/2024] [Accepted: 05/10/2024] [Indexed: 07/12/2024] Open
Abstract
As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.
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Affiliation(s)
- Gilberto González-Parra
- Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, València, Spain
- Department of Mathematics, New Mexico Tech, 801 Leroy Place, Socorro, 87801, NM, USA
| | - Md Shahriar Mahmud
- Department of Mathematics, Iowa State University, 411 Morrill Rd, Ames, 50011, IA, USA
| | - Claus Kadelka
- Department of Mathematics, Iowa State University, 411 Morrill Rd, Ames, 50011, IA, USA
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Gonzalez-Parra G, Mahmud MS, Kadelka C. Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2024:2024.03.04.24303726. [PMID: 38496570 PMCID: PMC10942533 DOI: 10.1101/2024.03.04.24303726] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2024]
Abstract
As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.
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Affiliation(s)
- Gilberto Gonzalez-Parra
- Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, València, Spain
- Department of Mathematics, New Mexico Tech, 801 Leroy Place, Socorro, 87801, NM, USA
| | - Md Shahriar Mahmud
- Department of Mathematics, Iowa State University, 411 Morrill Rd, Ames, 50011, IA, USA
| | - Claus Kadelka
- Department of Mathematics, Iowa State University, 411 Morrill Rd, Ames, 50011, IA, USA
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Cuevas-Maraver J, Kevrekidis PG, Chen QY, Kevrekidis GA, Drossinos Y. Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants. Math Biosci 2024; 367:109109. [PMID: 37981262 DOI: 10.1016/j.mbs.2023.109109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Revised: 10/14/2023] [Accepted: 11/14/2023] [Indexed: 11/21/2023]
Abstract
We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant. The first one is for the delta variant, where we do not follow the dynamics of the vaccinated individuals since infections of vaccinated individuals were rare. The second one for the far more contagious omicron variant incorporates the evolution of the infections within the vaccinated cohort. We explore comparisons with available data involving two possible classes of counts, fatalities and hospitalizations. We present our results for two regions, Andalusia and Switzerland (including the Principality of Liechtenstein), where the necessary data are available. In the majority of the considered cases, the models are found to yield good agreement with the data and have a reasonable predictive capability beyond their training window, rendering them potentially useful tools for the interpretation of the COVID-19 and further pandemic waves, and for the design of intervention strategies during these waves.
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Affiliation(s)
- J Cuevas-Maraver
- Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla. Escuela Politécnica Superior, C/ Virgen de África, 7, 41011 Sevilla, Spain; Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012 Sevilla, Spain.
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - Q Y Chen
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
| | - G A Kevrekidis
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA; Los Alamos National Laboratory, Los Alamos, NM, USA; Mathematical Institute for Data Science, Johns Hopkins University, Baltimore MD, USA
| | - Y Drossinos
- Thermal Hydraulics & Multiphase Flow Laboratory, Institute of Nuclear & Radiological Sciences and Technology, Energy & Safety, N.C.S.R. "Demokritos", GR 15341, Agia Paraskevi, Greece
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Wu Y, Zhou W, Tang S, Cheke RA, Wang X. Prediction of the next major outbreak of COVID-19 in Mainland China and a vaccination strategy for it. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230655. [PMID: 37650063 PMCID: PMC10465198 DOI: 10.1098/rsos.230655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2023] [Accepted: 08/14/2023] [Indexed: 09/01/2023]
Abstract
After the widespread prevalence of COVID-19 at the end of 2022 in Mainland China, a major concern is when will the second major outbreak occur and with what prevalence and fatality rates will it be associated with, as peoples' immunity from natural infection subsides. To address this, we established an age-structured model considering vaccine and infection-derived immunity, fitted an immunity-waning curve, and calibrated the model using the epidemic and vaccination data from Hong Kong in 2022. The model and the situation of the first major epidemic in Mainland China were then used to predict the prevalence rate, fatality rate and peak time of the second wave. In addition, the controlling effects of different vaccination strategies on the second major outbreak are discussed. Finally, a characterization indicator for the level of population immunity was provided. We conclude that if the prevalence of the first major epidemic was 80%, the prevalence rate of the second major outbreak would be about 37.64%, and the peak time would have been July 2 2023. Strengthening vaccination can effectively delay the peak of the second wave of the epidemic and reduce the prevalence.
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Affiliation(s)
- Yuanyuan Wu
- School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, People's Republic of China
| | - Weike Zhou
- School of Mathematics, Northwest University, Xi'an 710127, People's Republic of China
| | - Sanyi Tang
- School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, People's Republic of China
| | - Robert A. Cheke
- Natural Resources Institute, University of Greenwich at Medway, Central Avenue, Chatham Maritime, Kent ME4 4TB, UK
- Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, St Mary's Campus, Norfolk Place, London W2 1PG, UK
| | - Xia Wang
- School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, People's Republic of China
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Malek A, Hoque A. Impact of vaccination on the entire population and dose-response relation of COVID-19. VACUNAS 2023:S1576-9887(23)00032-8. [PMID: 37362834 PMCID: PMC10156990 DOI: 10.1016/j.vacun.2023.04.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 04/19/2023] [Indexed: 06/28/2023]
Abstract
Objective The objective of this study is to develop a mathematical model for the COVID-19 pandemic including vaccination, the transmissibility of the virus-pathogen dose-response relationship, vaccine efficiency, and vaccination rate. Methods The Runge-Kutta (RK-45) method was applied to solve the proposed model with MATLAB code and the calculated results show the dynamics of the individuals in each compartment. The data of total death due to the COVID-19 pandemic in the case of the USA were collected from GitHub and the re-use of this data needs no ethical clearance. The control reproduction number was used to assess the dose-response relationship and critical vaccination coverage. Results We have calculated the probability of infection and the infection risk against the different exposure doses and the virus copies, respectively. The results show that the probability of infection increases with the increasing exposure dose for certain virus copies and the risk of infection decreases with the increasing of virus copies for a certain exposure dose. The results also show that the critical vaccination coverage demands increase with an increase in transmission rate and decrease with increasing vaccine efficacy. Conclusions It was seen that the critical vaccination coverage corresponding to an increased transmission rate rise sharply in the beginning and then reached a threshold. Moreover, the real data of the total death cases in the USA were compared with the fitted curved of the model which validated the proposed model. Vaccination against COVID-19 is essential to control the pandemic, and achieving high vaccine uptake in the population can reduce the pandemic as fast as possible.
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Affiliation(s)
- Abdul Malek
- Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
| | - Ashabul Hoque
- Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
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Freiberger M, Grass D, Kuhn M, Seidl A, Wrzaczek S. Chasing up and locking down the virus: Optimal pandemic interventions within a network. JOURNAL OF PUBLIC ECONOMIC THEORY 2022; 24:JPET12604. [PMID: 35942308 PMCID: PMC9350112 DOI: 10.1111/jpet.12604] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Revised: 05/31/2022] [Accepted: 06/13/2022] [Indexed: 05/06/2023]
Abstract
During the COVID-19 pandemic countries invested significant amounts of resources into its containment. In early stages of the pandemic most of the (nonpharmaceutical) interventions can be classified into two groups: (i) testing and identification of infected individuals, (ii) social distancing measures to reduce the transmission probabilities. Furthermore, both groups of measures may, in principle, be targeted at certain subgroups of a networked population. To study such a problem, we propose an extension of the SIR model with additional compartments for quarantine and different courses of the disease across several network nodes. We develop the structure of the optimal allocation and study a numerical example of three symmetric regions that are subject to an asymmetric progression of the disease (starting from an initial hotspot). Key findings include that (i) for our calibrations policies are chosen in a "flattening-the-curve," avoiding hospital congestion; (ii) policies shift from containing spillovers from the hotspot initially to establishing a symmetric pattern of the disease; and (iii) testing that can be effectively targeted allows to reduce substantially the duration of the disease, hospital congestion and the total cost, both in terms of lives lost and economic costs.
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Affiliation(s)
- Michael Freiberger
- Economic Frontiers ProgramInternational Institute for Applied Systems Analysis (IIASA)LaxenburgAustria
| | - Dieter Grass
- Economic Frontiers ProgramInternational Institute for Applied Systems Analysis (IIASA)LaxenburgAustria
| | - Michael Kuhn
- Economic Frontiers ProgramInternational Institute for Applied Systems Analysis (IIASA)LaxenburgAustria
- Vienna Institute of DemographyWittgenstein Centre (IIASA, ÖAW, Universität Wien)ViennaAustria
| | - Andrea Seidl
- Department of Business Decision and AnalyticsUniversity of ViennaViennaAustria
| | - Stefan Wrzaczek
- Economic Frontiers ProgramInternational Institute for Applied Systems Analysis (IIASA)LaxenburgAustria
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