{"title":"论具有大规模传播机制和非对称散布模式的流行病斑块模型的动力学特征","authors":"Rachidi B. Salako, Yixiang Wu","doi":"10.1111/sapm.12674","DOIUrl":null,"url":null,"abstract":"<p>This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic equilibrium (EE) solutions are obtained. In particular, we show that when the basic reproduction number <span></span><math>\n <semantics>\n <msub>\n <mi>R</mi>\n <mn>0</mn>\n </msub>\n <annotation>$\\mathcal {R}_0$</annotation>\n </semantics></math> is less than one and the dispersal rate of the susceptible population <span></span><math>\n <semantics>\n <msub>\n <mi>d</mi>\n <mi>S</mi>\n </msub>\n <annotation>$d_S$</annotation>\n </semantics></math> is large, the population would eventually stabilize at the disease-free equilibrium. However, the disease may persist if <span></span><math>\n <semantics>\n <msub>\n <mi>d</mi>\n <mi>S</mi>\n </msub>\n <annotation>$d_S$</annotation>\n </semantics></math> is small, even if <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>R</mi>\n <mn>0</mn>\n </msub>\n <mo><</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$\\mathcal {R}_0&lt;1$</annotation>\n </semantics></math>. In such a scenario, explicit conditions on the model parameters that lead to the existence of multiple EE are identified. These results provide new insights into the dynamics of infectious diseases in multipatch environments. Moreover, results in Li and Peng (<i>Stud Appl Math</i>. 2023;150(3):650-704), which is for the same model but with symmetric connectivity matrix, are generalized and improved.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"152 4","pages":"1208-1250"},"PeriodicalIF":2.6000,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the dynamics of an epidemic patch model with mass-action transmission mechanism and asymmetric dispersal patterns\",\"authors\":\"Rachidi B. Salako, Yixiang Wu\",\"doi\":\"10.1111/sapm.12674\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic equilibrium (EE) solutions are obtained. In particular, we show that when the basic reproduction number <span></span><math>\\n <semantics>\\n <msub>\\n <mi>R</mi>\\n <mn>0</mn>\\n </msub>\\n <annotation>$\\\\mathcal {R}_0$</annotation>\\n </semantics></math> is less than one and the dispersal rate of the susceptible population <span></span><math>\\n <semantics>\\n <msub>\\n <mi>d</mi>\\n <mi>S</mi>\\n </msub>\\n <annotation>$d_S$</annotation>\\n </semantics></math> is large, the population would eventually stabilize at the disease-free equilibrium. However, the disease may persist if <span></span><math>\\n <semantics>\\n <msub>\\n <mi>d</mi>\\n <mi>S</mi>\\n </msub>\\n <annotation>$d_S$</annotation>\\n </semantics></math> is small, even if <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>R</mi>\\n <mn>0</mn>\\n </msub>\\n <mo><</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$\\\\mathcal {R}_0&lt;1$</annotation>\\n </semantics></math>. In such a scenario, explicit conditions on the model parameters that lead to the existence of multiple EE are identified. These results provide new insights into the dynamics of infectious diseases in multipatch environments. Moreover, results in Li and Peng (<i>Stud Appl Math</i>. 2023;150(3):650-704), which is for the same model but with symmetric connectivity matrix, are generalized and improved.</p>\",\"PeriodicalId\":51174,\"journal\":{\"name\":\"Studies in Applied Mathematics\",\"volume\":\"152 4\",\"pages\":\"1208-1250\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-01-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studies in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12674\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12674","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
On the dynamics of an epidemic patch model with mass-action transmission mechanism and asymmetric dispersal patterns
This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic equilibrium (EE) solutions are obtained. In particular, we show that when the basic reproduction number is less than one and the dispersal rate of the susceptible population is large, the population would eventually stabilize at the disease-free equilibrium. However, the disease may persist if is small, even if . In such a scenario, explicit conditions on the model parameters that lead to the existence of multiple EE are identified. These results provide new insights into the dynamics of infectious diseases in multipatch environments. Moreover, results in Li and Peng (Stud Appl Math. 2023;150(3):650-704), which is for the same model but with symmetric connectivity matrix, are generalized and improved.
期刊介绍:
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.