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Ladib M, Ouhinou A, Yakubu AA. Mathematical modeling of contact tracing and stability analysis to inform its impact on disease outbreaks; an application to COVID-19. Infect Dis Model 2024; 9:329-353. [PMID: 38371875 PMCID: PMC10867662 DOI: 10.1016/j.idm.2024.01.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2023] [Revised: 01/29/2024] [Accepted: 01/29/2024] [Indexed: 02/20/2024] Open
Abstract
We develop a mathematical model to investigate the effect of contact tracing on containing epidemic outbreaks and slowing down the spread of transmissible diseases. We propose a discrete-time epidemic model structured by disease-age which includes general features of contact tracing. The model is fitted to data reported for the early spread of COVID-19 in South Korea, Brazil, and Venezuela. The calibrated values for the contact tracing parameters reflect the order pattern observed in its performance intensity within the three countries. Using the fitted values, we estimate the effective reproduction number R e and investigate its responses to varied control scenarios of contact tracing. Alongside the positivity of solutions, and a stability analysis of the disease-free equilibrium are provided.
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Affiliation(s)
- Mohamed Ladib
- University of Sultan Moulay Slimane, Faculty of Sciences and Techniques, Team of Mathematics and Interactions, Béni-Mellal, Morocco
| | - Aziz Ouhinou
- University of Sultan Moulay Slimane, Faculty of Sciences and Techniques, Team of Mathematics and Interactions, Béni-Mellal, Morocco
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Rui J, Li K, Wei H, Guo X, Zhao Z, Wang Y, Song W, Abudunaibi B, Chen T. MODELS: a six-step framework for developing an infectious disease model. Infect Dis Poverty 2024; 13:30. [PMID: 38632643 PMCID: PMC11022334 DOI: 10.1186/s40249-024-01195-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 03/11/2024] [Indexed: 04/19/2024] Open
Abstract
Since the COVID-19 pandemic began, a plethora of modeling studies related to COVID-19 have been released. While some models stand out due to their innovative approaches, others are flawed in their methodology. To assist novices, frontline healthcare workers, and public health policymakers in navigating the complex landscape of these models, we introduced a structured framework named MODELS. This framework is designed to detail the essential steps and considerations for creating a dependable epidemic model, offering direction to researchers engaged in epidemic modeling endeavors.
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Affiliation(s)
- Jia Rui
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Kangguo Li
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Hongjie Wei
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Xiaohao Guo
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Zeyu Zhao
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Yao Wang
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Wentao Song
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Buasiyamu Abudunaibi
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China
| | - Tianmu Chen
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen city, China.
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, China.
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Guo X, Guo Y, Zhao Z, Yang S, Su Y, Zhao B, Chen T. Computing R0 of dynamic models by a definition-based method. Infect Dis Model 2022; 7:196-210. [PMID: 35702140 PMCID: PMC9160772 DOI: 10.1016/j.idm.2022.05.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Revised: 05/17/2022] [Accepted: 05/18/2022] [Indexed: 11/22/2022] Open
Abstract
Objectives Computing the basic reproduction number (R0) in deterministic dynamical models is a hot topic and is frequently demanded by researchers in public health. The next-generation methods (NGM) are widely used for such computation, however, the results of NGM are usually not to be the true R0 but only a threshold quantity with little interpretation. In this paper, a definition-based method (DBM) is proposed to solve such a problem. Methods Start with the definition of R0, consider different states that one infected individual may develop into, and take expectations. A comparison with NGM has proceeded. Numerical verification is performed using parameters fitted by data of COVID-19 in Hunan Province. Results DBM and NGM give identical expressions for single-host models with single-group and interactive Rij of single-host models with multi-groups, while difference arises for models partitioned into subgroups. Numerical verification showed the consistencies and differences between DBM and NGM, which supports the conclusion that R0 derived by DBM with true epidemiological interpretations are better. Conclusions DBM is more suitable for single-host models, especially for models partitioned into subgroups. However, for multi-host dynamic models where the true R0 is failed to define, we may turn to the NGM for the threshold R0.
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Affiliation(s)
- Xiaohao Guo
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, 361102, Fujian Province, People's Republic of China
| | - Yichao Guo
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, 361102, Fujian Province, People's Republic of China
| | - Zeyu Zhao
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, 361102, Fujian Province, People's Republic of China
- Université de Montpellier, CIRAD, Intertryp, IES, Université de Montpellier-CNRS, Montpellier, France
| | - Shiting Yang
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, 361102, Fujian Province, People's Republic of China
| | - Yanhua Su
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, 361102, Fujian Province, People's Republic of China
| | - Benhua Zhao
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, 361102, Fujian Province, People's Republic of China
| | - Tianmu Chen
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, 361102, Fujian Province, People's Republic of China
- Corresponding author. State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, 4221-117, South Xiang'an Road, Xiang'an District, Xiamen City, Fujian Province, People's Republic of China.
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