Infectious Disease Modelling最新文献

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Application of multiple linear regression model and long short-term memory with compartmental model to forecast dengue cases in Selangor, Malaysia based on climate variables 基于气候变量的多元线性回归模型和长短期记忆分区模型在马来西亚雪兰莪州登革热病例预测中的应用
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-10-28 DOI: 10.1016/j.idm.2024.10.007
{"title":"Application of multiple linear regression model and long short-term memory with compartmental model to forecast dengue cases in Selangor, Malaysia based on climate variables","authors":"","doi":"10.1016/j.idm.2024.10.007","DOIUrl":"10.1016/j.idm.2024.10.007","url":null,"abstract":"<div><div>Despite the implementation of various initiatives, dengue remains a significant public health concern in Malaysia. Given that dengue has no specific treatment, dengue prediction remains a useful early warning mechanism for timely and effective deployment of public health preventative measures. This study aims to develop a comprehensive approach for forecasting dengue cases in Selangor, Malaysia by incorporating climate variables. An ensemble of Multiple Linear Regression (MLR) model, Long Short-Term Memory (LSTM), and Susceptible-Infected mosquito vectors, Susceptible-Infected-Recovered human hosts (SI-SIR) model were used to establish a relation between climate variables (temperature, humidity, precipitation) and mosquito biting rate. Dengue incidence subject to climate variability can then be projected by SI-SIR model using the forecasted mosquito biting rate. The proposed approach outperformed three alternative approaches and expanded the temporal horizon of dengue prediction for Selangor with the ability to forecast approximately 60 weeks ahead with a Mean Absolute Percentage Error (MAPE) of 13.97 for the chosen prediction window before the implementation of the Movement Control Order (MCO) in Malaysia. Extended validation across subsequent periods also indicates relatively satisfactory forecasting performance (with MAPE ranging from 13.12 to 17.09). This research contributed to the field by introducing a novel framework for the prediction of dengue cases over an extended temporal range.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Network-based virus dynamic simulation: Evaluating the fomite disinfection effectiveness on SARS-CoV-2 transmission in indoor environment 基于网络的病毒动态模拟:评估室内环境中飞沫消毒对 SARS-CoV-2 传播的有效性
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-10-22 DOI: 10.1016/j.idm.2024.10.004
{"title":"Network-based virus dynamic simulation: Evaluating the fomite disinfection effectiveness on SARS-CoV-2 transmission in indoor environment","authors":"","doi":"10.1016/j.idm.2024.10.004","DOIUrl":"10.1016/j.idm.2024.10.004","url":null,"abstract":"<div><div>Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is involved in aerosol particles and droplets excreted from a coronavirus disease 2019 (COVID-19) patient. Such aerosol particles or droplets including infectious virions can be attached on fomite, so fomite is not a negligible route for SARS-CoV-2 transmission within a community, especially in indoor environment. This necessarily evokes a need of fomite disinfection to remove virions, but the extent to which fomite disinfection breaks off virus transmission chain in indoor environment is still elusive. In this study, we evaluated the fomite disinfection effectiveness on COVID-19 case number using network analysis that reproduced the reported indoor outbreaks. In the established network, virus can move around not only human but also air and fomite while growing in human and decaying in air and on fomite, and infection success was determined based on the exposed virus amount and the equation of probability of infection. The simulation results have demonstrated that infectious virions on fomite should be kept less than a hundred to sufficiently reduce COVID-19 case, and every-hour disinfection was required to avoid stochastic increase in the infection case. This study gives us a practical disinfection manner for fomite to control SARS-CoV-2 transmission in indoor environment.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142539544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of an SVEIR transmission model with protection awareness and two strains 具有保护意识和两种菌株的 SVEIR 传播模型的动态变化
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-10-10 DOI: 10.1016/j.idm.2024.10.001
{"title":"Dynamics of an SVEIR transmission model with protection awareness and two strains","authors":"","doi":"10.1016/j.idm.2024.10.001","DOIUrl":"10.1016/j.idm.2024.10.001","url":null,"abstract":"<div><div>As of May 2024, the main strains of COVID-19 caused hundreds of millions of infection cases and millions of deaths worldwide. In this study, we consider the COVID-19 epidemics with the main strains in the Chinese mainland. We study complex interactions among hosts, non-pharmaceutical interventions, and vaccinations for the main strains by a differential equation model called SVEIR. The disease transmission model incorporates two strains and protection awareness of the susceptible population. Results of this study show that the protection awareness plays a crucial role against infection of the population, and that the vaccines are effective against the circulation of the earlier strains, but ineffective for emerging strains. By using the next generation matrix method, the basic reproduction number of the SVEIR model is firstly obtained. Our analysis by Hurwitz criterion and LaSalle's invariance principle shows that the disease free-equilibrium point is locally and globally asymptotically stable when the threshold value is below one. The existences of endemic equilibrium points are also established, and the global asymptotic stabilities are analyzed using the Lyapunov function method. Further, the SVEIR model is confirmed to satisfy the principle of competitive exclusion, of which the strain with the larger value of the basic reproduction number is dominant. Numerically, the surveillance data with the Omicron strain and the XBB strain are split by the cubic spline interpolation method. The fitting curves against the surveillance data are plotted using the least-squares method from MATLAB. The results indicate that the XBB strain dominates in this study. Moreover, a global sensitivity analysis of the key parameters is performed by using of PRCC. The numerical simulations imply that combination control strategy positively impacts on the infection scale than what separate control strategy does, and that the earlier time producing protection awareness for the public creates less infection scale, further that the increment of protection awareness also reduces the infection scale. Therefore, the policymakers of the local government are suggested to concern the changes of protection awareness of the public.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A tentative exploration for the association between influenza virus infection and SARS-CoV-2 infection in Shihezi, China: A test-negative study 中国石河子市流感病毒感染与 SARS-CoV-2 感染关系的初步探索:一项检测阴性的研究
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-10-09 DOI: 10.1016/j.idm.2024.10.002
{"title":"A tentative exploration for the association between influenza virus infection and SARS-CoV-2 infection in Shihezi, China: A test-negative study","authors":"","doi":"10.1016/j.idm.2024.10.002","DOIUrl":"10.1016/j.idm.2024.10.002","url":null,"abstract":"<div><div>The outbreak of respiratory diseases, such as COVID-19 and influenza, has drawn global attention. However, it remains unclear whether the risk of influenza A infection may be affected by the history of SARS-CoV-2 infection. In this study, we conducted a test-negative case-control study, and utilized a logistic regression model to analyze the relationship between SARS-CoV-2 and influenza A infections. Among 258 eligible patient samples with influenza-like illness (ILI), we did not detect a statistically significant association between the history of SARS-CoV-2 infection and the risk of influenza A infection. These findings might indicate that antibodies against COVID-19 acquired through vaccination or natural immunity have not protected against influenza.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modelling and investigating memory immune responses in infectious disease. Application to influenza a virus and sars-cov-2 reinfections 模拟和研究传染病中的记忆免疫反应。应用于甲型流感病毒和 sars-cov-2 再感染
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-10-08 DOI: 10.1016/j.idm.2024.09.009
{"title":"Modelling and investigating memory immune responses in infectious disease. Application to influenza a virus and sars-cov-2 reinfections","authors":"","doi":"10.1016/j.idm.2024.09.009","DOIUrl":"10.1016/j.idm.2024.09.009","url":null,"abstract":"<div><div>Understanding effector and memory immune responses against influenza A virus (IAV) and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections and re-infections is extremely important, given that they are now endemic in the community. The goal of this study is to investigate the role of memory cells and antibodies in the immune responses against IAV and SARS-CoV-2 re-infections. To this end, we adapt a previously-published within-host mathematical model (Sadria &amp; Layton, 2021) for the primary immune response against SARS-CoV-2 infections, by including two types of memory immune cells, i.e., memory CD8<sup>+</sup> T-cells and memory B-cells, and by parametrising the new model with values specific to the two viruses. We first investigate the long-term dynamics of the model by identifying the virus-free steady states and studying the conditions that ensure the stability of these states. Then, we investigate the transient dynamics of this in-host model by simulating different viral reinfection times: 20 days, 60 days and 400 days after the first encounter with the pathogen. This allows us to highlight which memory immune components have the greatest impact on the viral elimination depending on the time of reinfection. Our results suggest that memory immune responses have a greater impact in the case of IAV infections compared to SARS-CoV-2 infections. Moreover, we observe that the immune response after a secondary infection is more efficient when the reinfection occurs at a shorter time.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gradient boosting: A computationally efficient alternative to Markov chain Monte Carlo sampling for fitting large Bayesian spatio-temporal binomial regression models 梯度提升:马尔科夫链蒙特卡罗抽样的高效计算替代方案,用于拟合大型贝叶斯时空二项式回归模型
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-10-04 DOI: 10.1016/j.idm.2024.09.008
{"title":"Gradient boosting: A computationally efficient alternative to Markov chain Monte Carlo sampling for fitting large Bayesian spatio-temporal binomial regression models","authors":"","doi":"10.1016/j.idm.2024.09.008","DOIUrl":"10.1016/j.idm.2024.09.008","url":null,"abstract":"<div><div>Disease forecasting and surveillance often involve fitting models to a tremendous volume of historical testing data collected over space and time. Bayesian spatio-temporal regression models fit with Markov chain Monte Carlo (MCMC) methods are commonly used for such data. When the spatio-temporal support of the model is large, implementing an MCMC algorithm becomes a significant computational burden. This research proposes a computationally efficient gradient boosting algorithm for fitting a Bayesian spatio-temporal mixed effects binomial regression model. We demonstrate our method on a disease forecasting model and compare it to a computationally optimized MCMC approach. Both methods are used to produce monthly forecasts for Lyme disease, anaplasmosis, ehrlichiosis, and heartworm disease in domestic dogs for the contiguous United States. The data have a spatial support of 3108 counties and a temporal support of 108–138 months with 71–135 million test results. The proposed estimation approach is several orders of magnitude faster than the optimized MCMC algorithm, with a similar mean absolute prediction error.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonlinear mixed models and related approaches in infectious disease modeling: A systematic and critical review 传染病建模中的非线性混合模型和相关方法:系统性和批判性综述
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-09-18 DOI: 10.1016/j.idm.2024.09.001
{"title":"Nonlinear mixed models and related approaches in infectious disease modeling: A systematic and critical review","authors":"","doi":"10.1016/j.idm.2024.09.001","DOIUrl":"10.1016/j.idm.2024.09.001","url":null,"abstract":"<div><div>The level of surveillance and preparedness against epidemics varies across countries, resulting in different responses to outbreaks. When conducting an in-depth analysis of microinfection dynamics, one must account for the substantial heterogeneity across countries. However, many commonly used statistical model specifications lack the flexibility needed for sound and accurate analysis and prediction in such contexts. Nonlinear mixed effects models (NLMMs) constitute a specific statistical tool that can overcome these significant challenges. While compartmental models are well-established in infectious disease modeling and have seen significant advancements, Nonlinear Mixed Models (NLMMs) offer a flexible approach for handling heterogeneous and unbalanced repeated measures data, often with less computational effort than some individual-level compartmental modeling techniques. This study provides an overview of their current use and offers a solid foundation for developing guidelines that may help improve their implementation in real-world situations. Relevant scientific databases in the <em>Research4life</em> Access initiative programs were used to search for papers dealing with key aspects of NLMMs in infectious disease modeling (IDM). From an initial list of 3641 papers, 124 were finally included and used for this systematic and critical review spanning the last two decades, following the PRISMA guidelines. NLMMs have evolved rapidly in the last decade, especially in IDM, with most publications dating from 2017 to 2021 (83.33%). The routine use of normality assumption appeared inappropriate for IDM, leading to a wealth of literature on NLMMs with non-normal errors and random effects under various estimation methods. We noticed that NLMMs have attracted much attention for the latest known epidemics worldwide (COVID-19, Ebola, Dengue and Lassa) with the robustness and reliability of relaxed propositions of the normality assumption. A case study of the application of COVID-19 data helped to highlight NLMMs’ performance in modeling infectious diseases. Out of this study, estimation methods, assumptions, and random terms specification in NLMMs are key aspects requiring particular attention for their application in IDM.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2468042724001003/pdfft?md5=a1cfb322095780bbffb2c061082d891e&pid=1-s2.0-S2468042724001003-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Impact of vaccination on Omicron's escape variants: Insights from fine-scale modelling of waning immunity in Hong Kong 疫苗接种对 Omicron 逃逸变种的影响:从香港免疫力下降的精细模型中获得的启示
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-09-16 DOI: 10.1016/j.idm.2024.09.006
{"title":"Impact of vaccination on Omicron's escape variants: Insights from fine-scale modelling of waning immunity in Hong Kong","authors":"","doi":"10.1016/j.idm.2024.09.006","DOIUrl":"10.1016/j.idm.2024.09.006","url":null,"abstract":"<div><div>COVID-19 vaccine-induced protection declines over time. This waning of immunity has been described in modelling as a lower level of protection. This study incorporated fine-scale vaccine waning into modelling to predict the next surge of the Omicron variant of the SARS-CoV-2 virus. In Hong Kong, the Omicron subvariant BA.2 caused a significant epidemic wave between February and April 2022, which triggered high vaccination rates. About half a year later, a second outbreak, dominated by a combination of BA.2, BA.4 and BA.5 subvariants, began to spread. We developed mathematical equations to formulate continuous changes in vaccine boosting and waning based on empirical serological data. These equations were incorporated into a multi-strain discrete-time Susceptible-Exposed-Infectious-Removed model. The daily number of reported cases during the first Omicron outbreak, with daily vaccination rates, the population mobility index and daily average temperature, were used to train the model. The model successfully predicted the size and timing of the second surge and the variant replacement by BA.4/5. It estimated 655,893 cumulative reported cases from June 1, 2022 to 31 October 2022, which was only 2.69% fewer than the observed cumulative number of 674,008. The model projected that increased vaccine protection (by larger vaccine coverage or no vaccine waning) would reduce the size of the second surge of BA.2 infections substantially but would allow more subsequent BA.4/5 infections. Increased vaccine coverage or greater vaccine protection can reduce the infection rate during certain periods when the immune-escape variants co-circulate; however, new immune-escape variants spread more by out-competing the previous strain.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2468042724001118/pdfft?md5=2e0c58621546ee3ac3d0fbd14dfae520&pid=1-s2.0-S2468042724001118-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Predicting influenza in China from October 1, 2023, to February 5, 2024: A transmission dynamics model based on population migration 2023 年 10 月 1 日至 2024 年 2 月 5 日中国流感预测:基于人口迁移的传播动态模型
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-09-16 DOI: 10.1016/j.idm.2024.09.007
{"title":"Predicting influenza in China from October 1, 2023, to February 5, 2024: A transmission dynamics model based on population migration","authors":"","doi":"10.1016/j.idm.2024.09.007","DOIUrl":"10.1016/j.idm.2024.09.007","url":null,"abstract":"<div><h3>Introduction</h3><div>Since November 2023, influenza has ranked first in reported cases of infectious diseases in China, with the outbreak in both northern and southern provinces exceeding the levels observed during the same period in 2022. This poses a serious health risk to the population. Therefore, short to medium-term influenza predictions are beneficial for epidemic assessment and can reduce the disease burden.</div></div><div><h3>Methods</h3><div>A transmission dynamics model considering population migration, encompassing susceptible-exposed-infectious-asymptomatic-recovered (SEIAR) was used to predict the dynamics of influenza before the Spring Festival travel rush.</div></div><div><h3>Results</h3><div>The overall epidemic shows a declining trend, with the peak expected to occur from week 47 in 2023 to week 1 in 2024. The number of cases of A (H3N2) is greater than that of influenza B, and the influenza situation is more severe in the southern provinces compared to the northern ones.</div></div><div><h3>Conclusion</h3><div>Our method is applicable for short-term and medium-term influenza predictions. As the spring festival travel rush approaches. Therefore, it is advisable to advocate for nonpharmaceutical interventions (NPIs), influenza vaccination, and other measures to reduce healthcare and public health burden.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S246804272400112X/pdfft?md5=f4e1aab3693ea3714a8aa47f1dc204af&pid=1-s2.0-S246804272400112X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A heterogeneous continuous age-structured model of mumps with vaccine 使用疫苗的流行性腮腺炎异质性连续年龄结构模型
IF 8.8 3区 医学
Infectious Disease Modelling Pub Date : 2024-09-13 DOI: 10.1016/j.idm.2024.09.004
{"title":"A heterogeneous continuous age-structured model of mumps with vaccine","authors":"","doi":"10.1016/j.idm.2024.09.004","DOIUrl":"10.1016/j.idm.2024.09.004","url":null,"abstract":"<div><p>In classical mumps models, individuals are generally assumed to be uniformly mixed (homogeneous), ignoring population heterogeneity (preference, activity, etc.). Age is the key to catching mixed patterns in developing mathematical models for mumps. A continuous heterogeneous age-structured model for mumps with vaccines has been developed in this paper. The stability of age-structured models is a difficult question. An explicit formula of <em>R</em><sub>0</sub> was defined for the various mixing modes (isolation, proportional and heterogeneous mixing) with or without the vaccine. The results show that the endemic steady state is unique and locally stable if <em>R</em><sub>0</sub> &gt; 1 without any additional conditions. A number of numerical examples are given to support the theory.</p></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2468042724001039/pdfft?md5=cc9d975dffe62e46b221b254e4d36443&pid=1-s2.0-S2468042724001039-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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