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Houy N, Flaig J. Value of information dynamics in Disease X vaccine clinical trials. Vaccine 2024; 42:1521-1533. [PMID: 38311534 DOI: 10.1016/j.vaccine.2024.01.063] [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: 06/11/2023] [Revised: 12/29/2023] [Accepted: 01/19/2024] [Indexed: 02/06/2024]
Abstract
BACKGROUND Solutions have been proposed to accelerate the development and rollout of vaccines against a hypothetical disease with epidemic or pandemic potential called Disease X. This may involve resolving uncertainties regarding the disease and the new vaccine. However the value for public health of collecting this information will depend on the time needed to perform research, but also on the time needed to produce vaccine doses. We explore this interplay, and its effect on the decision on whether or not to perform research. METHOD We simulate numerically the emergence and transmission of a disease in a population using a susceptible-infected-recovered (SIR) compartmental model with vaccination. Uncertainties regarding the disease and the vaccine are represented by parameter prior distributions. We vary the date at which vaccine doses are available, and the date at which information about parameters becomes available. We use the expected value of perfect information (EVPI) and the expected value of partially perfect information (EVPPI) to measure the value of information. RESULTS As expected, information has less or no value if it comes too late, or (equivalently) if it can only be used too late. However we also find non trivial dynamics for shorter durations of vaccine development. In this parameter area, it can be optimal to implement vaccination without waiting for information depending on the respective durations of dose production and of clinical research. CONCLUSION We illustrate the value of information dynamics in a Disease X outbreak scenario, and present a general approach to properly take into account uncertainties and transmission dynamics when planning clinical research in this scenario. Our method is based on numerical simulation and allows us to highlight non trivial effects that cannot otherwise be investigated.
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Affiliation(s)
- Nicolas Houy
- University of Lyon, Lyon F-69007, France; CNRS, GATE Lyon Saint-Etienne, F-69007, France.
| | - Julien Flaig
- Epidemiology and Modelling of Infectious Diseases (EPIMOD), Lyon F-69002, France.
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Li W, Cai S, Zhai X, Ou J, Zheng K, Wei F, Mao X. Transmission dynamics of symptom-dependent HIV/AIDS models. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:1819-1843. [PMID: 38454662 DOI: 10.3934/mbe.2024079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/09/2024]
Abstract
In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0^s $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.
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Affiliation(s)
- Wenshuang Li
- School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
| | - Shaojian Cai
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Xuanpei Zhai
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Jianming Ou
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Kuicheng Zheng
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Fengying Wei
- School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
- Center for Applied Mathematics of Fujian Province, Fuzhou University, Fuzhou 350116, Fujian, China
- Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou University, Fuzhou 350116, Fujian, China
| | - Xuerong Mao
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
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Medina-Vásquez P, Romero-Romero R, Mayorga-Zambrano J. A model for the SARS-CoV-2 dynamics in a population lacking herd immunity. BIONATURA 2023. [DOI: 10.21931/rb/2023.08.01.45] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2023] Open
Abstract
We introduced the S-HI model, a generalized SEIR model to describe the dynamics of the SARS-CoV-2 virus in a community without herd immunity and performed simulations for six months. The S- HI model consists of eight equations corresponding to susceptible individuals, exposed, asymptomatic infected, asymptomatic recovered, symptomatic infected, quarantined, symptomatic recovered and dead. We study the dynamics of the infected, asymptomatic. Dead classes in 4 different networks: households, workplaces, agglomeration places and the general community, showing that the dynamics of the three compartments have the exact nature in each layer and that the speed of the disease considerably increases in the networks with the highest weight of contacts. The reproduction number, R0, is greater than 1 in all networks conforming to the theory. The variants of the SARS-Cov-2 virus are not taken into account, so the S-HI model would fit a situation similar to the first wave of contagion after the mandatory lockdown.
Keywords: SARS-Cov-2, mathematical models, SEIR, data-driven networks, simulations, basic reproduction number, lack of herd immunity.
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Catano-Lopez A, Rojas-Diaz D, Lizarralde-Bejarano DP, Puerta Yepes ME. A discrete model for the evaluation of public policies: The case of Colombia during the COVID-19 pandemic. PLoS One 2023; 18:e0275546. [PMID: 36787303 PMCID: PMC9928135 DOI: 10.1371/journal.pone.0275546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 09/19/2022] [Indexed: 02/15/2023] Open
Abstract
In mathematical epidemiology, it is usual to implement compartmental models to study the transmission of diseases, allowing comprehension of the outbreak dynamics. Thus, it is necessary to identify the natural history of the disease and to establish promissory relations between the structure of a mathematical model, as well as its parameters, with control-related strategies (real interventions) and relevant socio-cultural behaviors. However, we identified gaps between the model creation and its implementation for the use of decision-makers for policy design. We aim to cover these gaps by proposing a discrete mathematical model with parameters having intuitive meaning to be implemented to help decision-makers in control policy design. The model considers novel contagion probabilities, quarantine, and diffusion processes to represent the recovery and mortality dynamics. We applied mathematical model for COVID-19 to Colombia and some of its localities; moreover, the model structure could be adapted for other diseases. Subsequently, we implemented it on a web platform (MathCOVID) for the usage of decision-makers to simulate the effect of policies such as lock-downs, social distancing, identification in the contagion network, and connectivity among populations. Furthermore, it was possible to assess the effects of migration and vaccination strategies as time-dependent inputs. Finally, the platform was capable of simulating the effects of applying one or more policies simultaneously.
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Affiliation(s)
| | - Daniel Rojas-Diaz
- Department of Mathematical Sciences, Universidad EAFIT, Medellín, Colombia
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Akinwande N, Ashezua T, Gweryina R, Somma S, Oguntolu F, Usman A, Abdurrahman O, Kaduna F, Adajime T, Kuta F, Abdulrahman S, Olayiwola R, Enagi A, Bolarin G, Shehu M. Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination. Heliyon 2022; 8:e11513. [DOI: 10.1016/j.heliyon.2022.e11513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Revised: 07/22/2022] [Accepted: 11/02/2022] [Indexed: 11/11/2022] Open
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Moore SE, Nyandjo-Bamen HL, Menoukeu-Pamen O, Asamoah JKK, Jin Z. Global stability dynamics and sensitivity assessment of COVID-19 with timely-delayed diagnosis in Ghana. COMPUTATIONAL AND MATHEMATICAL BIOPHYSICS 2022. [DOI: 10.1515/cmb-2022-0134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Abstract
In this paper, we study the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana during its initial phase by using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, ℛ0, for the proposed model is 1.04. One of the main focus of this study is global stability results. Theoretically and numerically, we show that the disease persistence depends on ℛ0. We carry out a local and global sensitivity analysis. The local sensitivity analysis shows that the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility rate from the infectious with delayed diagnosis to the susceptible individuals. And that the most negative sensitive parameters are: self-quarantined, waiting time of the infectious for delayed diagnosis and the proportion of the infectious with timely diagnosis. The global sensitivity analysis using the partial rank correlation coefficient confirms the directional flow of the local sensitivity analysis. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection). Other recommendations for controlling the disease from the proposed model are provided in Section 7.
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Affiliation(s)
- Stephen E. Moore
- Department of Mathematics , University of Cape Coast, Ghana Regional Transport Research and Education Centre Kumasi, Kwame Nkrumah University of Science and Technology , Kumasi , Ghana
| | - Hetsron L. Nyandjo-Bamen
- African Institute for Mathematical Sciences , Ghana; Department of Mathematics, School of Science, College of Science and Technology , University of Rwanda , Rwanda
| | - Olivier Menoukeu-Pamen
- African Institute for Mathematical Sciences , Ghana; IFAM, Department of Mathematical Sciences , University of Liverpool , United Kingdom
| | - Joshua Kiddy K. Asamoah
- Department of Mathematics , Kwame Nkrumah University of Science andTechnology , Kumasi , Ghana
| | - Zhen Jin
- Complex Systems Research Center , Shanxi University , Taiyuan , China
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Nguyen L, Raissi M, Seshaiyer P. Modeling, Analysis and Physics Informed Neural Network approaches for studying the dynamics of COVID-19 involving human-human and human-pathogen interaction. COMPUTATIONAL AND MATHEMATICAL BIOPHYSICS 2022. [DOI: 10.1515/cmb-2022-0001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Abstract
In this work, the dynamics of the spread of COVID-19 is considered in the presence of both human-to-human transmission as well as environment-to-human transmission. Specifically, we expand and modify traditional epidemiological model for COVID-19 by incorporating a compartment to study the dynamics of pathogen concentration in the environmental reservoir, for instance concentration of droplets in closed spaces. We perform a mathematical analysis for the model proposed including an endemic equilibrium analysis as well as a next-generation approach both of which help to derive the basic reproduction number. We also study the e˚cacy of wearing a facemask through this model. Another important contribution of this work is the introduction to physics informed deep learning methods (PINNs) to study the dynamics. We propose this as an alternative to traditional numerical methods for solving system of differential equations used to describe dynamics of infectious diseases. Our results show that the proposed PINNs approach is a reliable candidate for both solving such systems and for helping identify important parameters that control the disease dynamics.
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Affiliation(s)
- Long Nguyen
- George Mason University , Fairfax, Virginia, USA
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Bestehorn M, Riascos AP, Michelitsch TM, Collet BA. A Markovian random walk model of epidemic spreading. CONTINUUM MECHANICS AND THERMODYNAMICS 2021; 33:1207-1221. [PMID: 34776647 PMCID: PMC7811397 DOI: 10.1007/s00161-021-00970-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Accepted: 01/04/2021] [Indexed: 05/07/2023]
Abstract
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time Markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then, we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node, there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations, we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.
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Affiliation(s)
- Michael Bestehorn
- Institut für Physik, Brandenburgische Technische Universität Cottbus-Senftenberg, 03046 Cottbus, Germany
| | - Alejandro P. Riascos
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de Mexico, Mexico
| | - Thomas M. Michelitsch
- Institut Jean le Rond d’Alembert, Sorbonne Université, CNRS UMR 7190, 4 place Jussieu, 75252 Paris, cedex 05 France
| | - Bernard A. Collet
- Institut Jean le Rond d’Alembert, Sorbonne Université, CNRS UMR 7190, 4 place Jussieu, 75252 Paris, cedex 05 France
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