{"title":"在异质环境中对具有多种传播途径、普遍发病率和不完全免疫力的霍乱扩散模型进行全球分析。","authors":"Shengfu Wang, Linfei Nie","doi":"10.3934/mbe.2024218","DOIUrl":null,"url":null,"abstract":"<p><p>With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \\mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \\mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \\mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \\mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \\mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global analysis of a diffusive Cholera model with multiple transmission pathways, general incidence and incomplete immunity in a heterogeneous environment.\",\"authors\":\"Shengfu Wang, Linfei Nie\",\"doi\":\"10.3934/mbe.2024218\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \\\\mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \\\\mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \\\\mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \\\\mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \\\\mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.</p>\",\"PeriodicalId\":49870,\"journal\":{\"name\":\"Mathematical Biosciences and Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Biosciences and Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.3934/mbe.2024218\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Biosciences and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mbe.2024218","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Global analysis of a diffusive Cholera model with multiple transmission pathways, general incidence and incomplete immunity in a heterogeneous environment.
With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.
期刊介绍:
Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing.
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