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Li X, Li Z, Ding S. Dynamic properties of deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences. Comput Methods Biomech Biomed Engin 2025; 28:265-291. [PMID: 38017704 DOI: 10.1080/10255842.2023.2286213] [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: 05/29/2023] [Revised: 11/03/2023] [Accepted: 11/11/2023] [Indexed: 11/30/2023]
Abstract
The classical compartment model is often used to study the spread of an epidemic with one virus. However, there are few types of research on epidemic models with multiple viruses. The article aims to propose two new deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences. We obtain asymptotic properties of disease-free and several endemic equilibria for the deterministic model. In the stochastic case, we prove the existence and uniqueness of positive global solutions. The extinction and persistence of diseases are obtained under different threshold conditions. We analyze the existence of stationary distribution through a suitable Lyapunov function. The results indicate that the extinction or persistence of the two viruses is closely related to the intensity of white noise interference. Specifically, considerable white noise is beneficial for the extinction of diseases, while slight one can lead to long-term epidemics of diseases. Finally, numerical simulations illustrate our theoretical results and the effect of essential parameters.
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Affiliation(s)
- Xiaoyu Li
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
| | - Zhiming Li
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
| | - Shuzhen Ding
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
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2
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Guo J, Luo Y, Ma Y, Xu S, Li J, Wang T, Lei L, He L, Yu H, Xie J. Assessing the impact of vaccination and medical resource allocation on infectious disease outbreak management: a case study of COVID-19 in Taiyuan City. Front Public Health 2024; 12:1368876. [PMID: 39185114 PMCID: PMC11344268 DOI: 10.3389/fpubh.2024.1368876] [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] [Indexed: 08/27/2024] Open
Abstract
Introduction Amidst an emerging infectious disease outbreak, the rational allocation of vaccines and medical resources is crucial for controlling the epidemic's progression. Method Analysing COVID-19 data in Taiyuan City from December 2022 to January 2023, this study constructed a S V 1 V 2 V 3 E I Q H R dynamics model to assess the impact of COVID-19 vaccination and resource allocation on epidemic trends. Results Vaccination significantly reduces infection rates, hospitalisations, and severe cases, while also curtailing strain on medical resources by reducing congestion periods. An early and sufficient reserve of medical resources can delay the onset of medical congestion, and with increased maximum capacity of medical resources, the congestion's end can be accelerated. Stronger resource allocation capabilities lead to earlier congestion resolution within a fixed total resource pool. Discussion Integrating vaccination and medical resource allocation can effectively reduce medical congestion duration and alleviate the epidemic's strain on medical resource capacity (CCMR).
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Affiliation(s)
- Jiaming Guo
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Yuxin Luo
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Yifei Ma
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Shujun Xu
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Jiantao Li
- School of Management, Shanxi Medical University, Taiyuan, China
| | - Tong Wang
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Lijian Lei
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Lu He
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Hongmei Yu
- School of Public Health, Shanxi Medical University, Taiyuan, China
- Shanxi Provincial Key Laboratory of Major Diseases Risk Assessment, Shanxi Medical University, Taiyuan, China
- MOE Key Laboratory of Coal Environmental Pathogenicity and Prevention, Shanxi Medical University, Taiyuan, China
| | - Jun Xie
- MOE Key Laboratory of Coal Environmental Pathogenicity and Prevention, Shanxi Medical University, Taiyuan, China
- Department of Biochemistry and Molecular Biology, Shanxi Medical University, Taiyuan, China
- Shanxi Key Laboratory of Birth Defect and Cell Regeneration, Shanxi Medical University, Taiyuan, China
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Yadav SK, Khan SA, Tiwari M, Kumar A, Kumar V, Akhter Y. Taking cues from machine learning, compartmental and time series models for SARS-CoV-2 omicron infection in Indian provinces. Spat Spatiotemporal Epidemiol 2024; 48:100634. [PMID: 38355258 DOI: 10.1016/j.sste.2024.100634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 11/15/2023] [Accepted: 01/15/2024] [Indexed: 02/16/2024]
Abstract
SARS-CoV-2, the virus responsible for COVID-19, posed a significant threat to the world. We analyzed COVID-19 dissemination data in the top ten Indian provinces by infection incidences using the Susceptible-Infectious-Removed (SIR) model, an Autoregressive Integrated Moving Average (ARIMA) time series model, a machine learning model based on the Random Forest, and distribution fitting. Outbreaks are expected to continue if the Basic Reproduction Number (R0) > 1, and infection waves are anticipated to end if the R0 < 1, as determined by the SIR model. Different parametric probability distributions are also fitted. Data collected from December 12, 2021, to March 31, 2022, encompassing data from both before and during the implementation of strict control measures. Based on the estimates of the model parameters, health agencies and government policymakers can develop strategies to combat the spread of the disease in the future, and the most effective technique can be recommended for real-world application for other outbreaks of COVID-19. The best method out of these could be also implemented further on the epidemiological data of other similar infectious agents.
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Affiliation(s)
- Subhash Kumar Yadav
- Department of Statistics, School of Physical and Decision Science, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
| | - Saif Ali Khan
- Department of Statistics, School of Physical and Decision Science, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
| | - Mayank Tiwari
- Department of Statistics, School of Physical and Decision Science, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
| | - Arun Kumar
- Department of Statistics, School of Physical and Decision Science, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
| | - Vinit Kumar
- Department of Library & Information Science, School of Information Science & Technology, Babasaheb Bhimrao Ambedkar University, Lucknow 226025, India
| | - Yusuf Akhter
- Department of Biotechnology, School of Life Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India.
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Lv MM, Sun XD, Jin Z, Wu HR, Li MT, Sun GQ, Pei X, Wu YT, Liu P, Li L, Zhang J. Dynamic analysis of rabies transmission and elimination in mainland China. One Health 2023; 17:100615. [PMID: 37638210 PMCID: PMC10458286 DOI: 10.1016/j.onehlt.2023.100615] [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: 05/25/2023] [Revised: 08/07/2023] [Accepted: 08/15/2023] [Indexed: 08/29/2023] Open
Abstract
Rabies is an acute zoonotic infectious disease caused by rabies virus. In 2015, the World Health Organization proposed the goal of eliminating dog-induced human rabies by 2030. In response to this goal positively, China has been dedicated to the control and elimination of rabies mainly caused by dogs, for nearly 10 years. By applying infectious disease dynamics, in this paper, we establish a dog-human rabies transmission model to forecast future epidemic trends of rabies, assess whether the goal of eliminating dog-induced human rabies cases in China can be achieved in 2030, and further evaluate and suggest the follow-up sustained preventive measures after the elimination of human rabies. By analyzing and simulating above dynamic model, it is concluded that rabies has been well controlled in China in recent years, but dog-induced human rabies cannot be eliminated by 2030 according to current situation. In addition, we propose to improve rabies control efforts by increasing the immunization coverage rate of rural domestic dogs, controlling the number of stray dogs and preventing the import of rabies virus in wild animals. Immunization coverage rate of rural domestic dogs which is currently less than 10% is far from requirement, and it needs to reach 50%-60% to meet the goal of 2030. Since it is difficult to immunize stray dogs, we suggest to control the number of stray dogs below 15.27 million to achieve the goal. If the goal of eliminating human rabies is reached in 2030, the essential immunization coverage needs to be maintained for 18 years to reduce the number of canine rabies cases to zero. Lastly, to prevent transmission of rabies virus from wild animals to dogs, the thresholds of the number of dogs and the immunization coverage rate of dogs after eliminating canine rabies cases are also discussed.
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Affiliation(s)
- Miao-Miao Lv
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
- Complex Systems and Data Science Key Laboratory of Ministry of Education, Taiyuan 030006, China
- School of Mathematical Sciences, Shanxi University, Shanxi, Taiyuan 030006, China
| | - Xiang-Dong Sun
- The Laboratory of Animal Epidemiological Surveillance, China Animal Health and Epidemiology Center, Shandong, Qingdao 266032, China
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
- Complex Systems and Data Science Key Laboratory of Ministry of Education, Taiyuan 030006, China
- School of Mathematical Sciences, Shanxi University, Shanxi, Taiyuan 030006, China
| | - Hai-Rong Wu
- School of Journalism and Communication, Guangxi University, Nanning 530004, China
| | - Ming-Tao Li
- College of Mathematics, Taiyuan University of Technology, Shanxi, Taiyuan 030024, China
| | - Gui-Quan Sun
- School of Mathematics, North University of China, Shanxi, Taiyuan 030051, China
| | - Xin Pei
- College of Mathematics, Taiyuan University of Technology, Shanxi, Taiyuan 030024, China
| | - Yu-Tong Wu
- Beijing University of Civil Engineering and Architecture, Beijing 102616, China
| | - Ping Liu
- The Laboratory of Animal Epidemiological Surveillance, China Animal Health and Epidemiology Center, Shandong, Qingdao 266032, China
| | - Li Li
- School of Computer and Information Technology, Shanxi University, Taiyuan 030006, China
| | - Juan Zhang
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
- Complex Systems and Data Science Key Laboratory of Ministry of Education, Taiyuan 030006, China
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Wei X, Li M, Pei X, Liu Z, Zhang J. Assessing the effectiveness of the intervention measures of COVID-19 in China based on dynamical method. Infect Dis Model 2023; 8:159-171. [PMID: 36624814 PMCID: PMC9812467 DOI: 10.1016/j.idm.2022.12.007] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Revised: 12/29/2022] [Accepted: 12/29/2022] [Indexed: 01/06/2023] Open
Abstract
Normalized interventions were implemented in different cities in China to contain the outbreak of COVID-19 before December 2022. However, the differences in the intensity and timeliness of the implementations lead to differences in final size of the infections. Taking the outbreak of COVID-19 in three representative cities Xi'an, Zhengzhou and Yuzhou in January 2022, as examples, we develop a compartmental model to describe the spread of novel coronavirus and implementation of interventions to assess concretely the effectiveness of Chinese interventions and explore their impact on epidemic patterns. After applying reported human confirmed cases to verify the rationality of the model, we apply the model to speculate transmission trend and length of concealed period at the initial spread phase of the epidemic (they are estimated as 10.5, 7.8, 8.2 days, respectively), to estimate the range of basic reproduction number (2.9, 0.7, 1.6), and to define two indexes (transmission rate v t and controlled rate v c ) to evaluate the overall effect of the interventions. It is shown that for Zhengzhou, v c is always more than v t with regular interventions, and Xi'an take 8 days to achieve v c > v t twice as long as Yuzhou, which can interpret the fact that the epidemic situation in Xi'an was more severe. By carrying out parameter values, it is concluded that in the early stage, strengthening the precision of close contact tracking and frequency of large-scale nucleic acid testing of non-quarantined population are the most effective on controlling the outbreaks and reducing final size. And, if the close contact tracking strategy is sufficiently implemented, at the late stage large-scale nucleic acid testing of non-quarantined population is not essential.
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Affiliation(s)
- Xiaomeng Wei
- Complex Systems Research Center, Shanxi University, 030006, Shanxi, China,Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, 030006, Shanxi, China,School of Mathematical Sciences, Shanxi University, 030006, Shanxi, China
| | - Mingtao Li
- College of Mathematics, Taiyuan University of Technology, 030024, Shanxi, China
| | - Xin Pei
- College of Mathematics, Taiyuan University of Technology, 030024, Shanxi, China
| | - Zhiping Liu
- School of Data Science and Technology, North University of China, 030051, Shanxi, China
| | - Juan Zhang
- Complex Systems Research Center, Shanxi University, 030006, Shanxi, China,Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, 030006, Shanxi, China,Corresponding author. Complex Systems Research Center, Shanxi University, 030006, Shanxi, China
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