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Zhang F, Zhang J, Li M, Jin Z, Wen Y. Assessing the impact of different contact patterns on disease transmission: Taking COVID-19 as a case. PLoS One 2024; 19:e0300884. [PMID: 38603698 PMCID: PMC11008907 DOI: 10.1371/journal.pone.0300884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 03/02/2024] [Indexed: 04/13/2024] Open
Abstract
Human-to-human contact plays a leading role in the transmission of infectious diseases, and the contact pattern between individuals has an important influence on the intensity and trend of disease transmission. In this paper, we define regular contacts and random contacts. Then, taking the COVID-19 outbreak in Yangzhou City, China as an example, we consider age heterogeneity, household structure and two contact patterns to establish discrete dynamic models with switching between daytime and nighttime to depict the transmission mechanism of COVID-19 in population. We studied the changes in the reproduction number with different age groups and household sizes at different stages. The effects of the proportion of two contacts patterns on reproduction number were also studied. Furthermore, taking the final size, the peak value of infected individuals in community and the peak value of quarantine infected individuals and nucleic acid test positive individuals as indicators, we evaluate the impact of the number of random contacts, the duration of the free transmission stage and summer vacation on the spread of the disease. The results show that a series of prevention and control measures taken by the Chinese government in response to the epidemic situation are reasonable and effective, and the young and middle-aged adults (aged 18-59) with household size of 6 have the strongest transmission ability. In addition, the results also indicate that increasing the proportion of random contact is beneficial to the control of the infectious disease in the phase with interventions. This work enriches the content of infectious disease modeling and provides theoretical guidance for the prevention and control of follow-up major infectious diseases.
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Affiliation(s)
- Fenfen Zhang
- College of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, Shanxi, China
- Shanxi College of Technology, Shuozhou, Shanxi, China
- Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi, China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, Shanxi, China
- Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan, Shanxi, China
| | - Juan Zhang
- Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi, China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, Shanxi, China
- Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan, Shanxi, China
| | - Mingtao Li
- School of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, China
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi, China
- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, Shanxi, China
- Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan, Shanxi, China
| | - Yuqi Wen
- School of Materials Science & Engineering, Beijing Institute of Technology, Beijing, China
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Han Z, Wang Y, Gao S, Sun G, Wang H. Final epidemic size of a two-community SIR model with asymmetric coupling. J Math Biol 2024; 88:51. [PMID: 38551684 DOI: 10.1007/s00285-024-02073-0] [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: 05/08/2023] [Revised: 02/11/2024] [Accepted: 02/29/2024] [Indexed: 04/02/2024]
Abstract
Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number R 0 , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between R 0 and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on R 0 . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, R 0 does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase R 0 . We further demonstrate that network contacts within communities have a greater effect on R 0 than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger R 0 .
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Affiliation(s)
- Zhimin Han
- School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, Hubei, China
| | - Yi Wang
- School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, Hubei, China
| | - Shan Gao
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
- Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB, T6G 2G1, Canada
| | - Guiquan Sun
- School of Mathematics, North University of China, Taiyuan, 030051, Shanxi, China
| | - Hao Wang
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
- Interdisciplinary Lab for Mathematical Ecology and Epidemiology, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
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Zang H, Liu S, Lin Y. Evaluations of heterogeneous epidemic models with exponential and non-exponential distributions for latent period: the Case of COVID-19. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:12579-12598. [PMID: 37501456 DOI: 10.3934/mbe.2023560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Most of heterogeneous epidemic models assume exponentially distributed sojourn times in infectious states, which may not be practical in reality and could affect the dynamics of the epidemic. This paper investigates the potential discrepancies between exponential and non-exponential distribution models in analyzing the transmission patterns of infectious diseases and evaluating control measures. Two SEIHR models with multiple subgroups based on different assumptions for latency are established: Model Ⅰ assumes an exponential distribution of latency, while Model Ⅱ assumes a gamma distribution. To overcome the challenges associated with the high dimensionality of GDM, we derive the basic reproduction number ($ R_{0} $) of the model theoretically, and apply numerical simulations to evaluate the effect of different interventions on EDM and GDM. Our results show that considering a more realistic gamma distribution of latency can change the peak numbers of infected and the timescales of an epidemic, and GDM may underestimate the infection eradication time and overestimate the peak value compared to EDM. Additionally, the two models can produce inconsistent predictions in estimating the time to reach the peak. Our study contributes to a more accurate understanding of disease transmission patterns, which is crucial for effective disease control and prevention.
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Affiliation(s)
- Huiping Zang
- School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
| | - Shengqiang Liu
- School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
| | - Yi Lin
- School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
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Xu W, Shu H, Wang L, Wang XS, Watmough J. The importance of quarantine: modelling the COVID-19 testing process. J Math Biol 2023; 86:81. [PMID: 37097481 PMCID: PMC10127192 DOI: 10.1007/s00285-023-01916-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Revised: 02/12/2023] [Accepted: 04/05/2023] [Indexed: 04/26/2023]
Abstract
We incorporate the disease state and testing state into the formulation of a COVID-19 epidemic model. For this model, the basic reproduction number is identified and its dependence on model parameters related to the testing process and isolation efficacy is discussed. The relations between the basic reproduction number, the final epidemic and peak sizes, and the model parameters are further explored numerically. We find that fast test reporting does not always benefit the control of the COVID-19 epidemic if good quarantine while awaiting test results is implemented. Moreover, the final epidemic and peak sizes do not always increase along with the basic reproduction number. Under some circumstances, lowering the basic reproduction number increases the final epidemic and peak sizes. Our findings suggest that properly implementing isolation for individuals who are waiting for their testing results would lower the basic reproduction number as well as the final epidemic and peak sizes.
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Affiliation(s)
- Wanxiao Xu
- School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, China
| | - Hongying Shu
- School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710062, China.
| | - Lin Wang
- Department of Mathematics and Statistics, University of New Brunswick, Fredericton, E3B 5A3, Canada
| | - Xiang-Sheng Wang
- Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70503, USA
| | - James Watmough
- Department of Mathematics and Statistics, University of New Brunswick, Fredericton, E3B 5A3, Canada
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Sheng Y, Cui JA, Guo S. The modeling and analysis of the COVID-19 pandemic with vaccination and isolation: a case study of Italy. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:5966-5992. [PMID: 36896559 DOI: 10.3934/mbe.2023258] [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: 06/18/2023]
Abstract
The global spread of COVID-19 has not been effectively controlled. It poses a significant threat to public health and global economic development. This paper uses a mathematical model with vaccination and isolation treatment to study the transmission dynamics of COVID-19. In this paper, some basic properties of the model are analyzed. The control reproduction number of the model is calculated and the stability of the disease-free and endemic equilibria is analyzed. The parameters of the model are obtained by fitting the number of cases that were detected as positive for the virus, dead, and recovered between January 20 and June 20, 2021, in Italy. We found that vaccination better controlled the number of symptomatic infections. A sensitivity analysis of the control reproduction number has been performed. Numerical simulations demonstrate that reducing the contact rate of the population and increasing the isolation rate of the population are effective non-pharmaceutical control measures. We found that if the isolation rate of the population is reduced, a short-term decrease in the number of isolated individuals can lead to the disease not being controlled at a later stage. The analysis and simulations in this paper may provide some helpful suggestions for preventing and controlling COVID-19.
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Affiliation(s)
- Yujie Sheng
- School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
| | - Jing-An Cui
- School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
| | - Songbai Guo
- School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
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Duan M, Jin Z. The heterogeneous mixing model of COVID-19 with interventions. J Theor Biol 2022; 553:111258. [PMID: 36041504 PMCID: PMC9420055 DOI: 10.1016/j.jtbi.2022.111258] [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: 06/30/2022] [Revised: 08/17/2022] [Accepted: 08/18/2022] [Indexed: 12/15/2022]
Abstract
The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number Rc of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p3 plays a key role in Rc. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.
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Affiliation(s)
- Moran Duan
- School of Data Science and Technology, North University of China, Taiyuan 030051, Shanxi, China; Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China; Shanxi Key Laboratory of Mathematical Technique and Big Data Analysis on Disease Control and Prevention, Taiyuan 030006, Shanxi, China.
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