{"title":"异质群体si -流行病模型的聚集和渐近分析","authors":"V. M. Veliov;A. Widder","doi":"10.1093/imammb/dqv018","DOIUrl":null,"url":null,"abstract":"The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficient in order to determine the long-run outcome of the disease. Numerical simulation is used to emphasize that, for a given level of prevalence, the evolution of the disease under the influence of heterogeneity may in the long run qualitatively differ from the one ‘predicted’ by the homogeneous model. Furthermore, it is shown that, in a closed population, the indicator for the survival of the population is in the presence of heterogeneity distinct from the basic reproduction number.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 3","pages":"295-318"},"PeriodicalIF":0.0000,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv018","citationCount":"4","resultStr":"{\"title\":\"Aggregation and asymptotic analysis of an SI-epidemic model for heterogeneous populations\",\"authors\":\"V. M. Veliov;A. Widder\",\"doi\":\"10.1093/imammb/dqv018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficient in order to determine the long-run outcome of the disease. Numerical simulation is used to emphasize that, for a given level of prevalence, the evolution of the disease under the influence of heterogeneity may in the long run qualitatively differ from the one ‘predicted’ by the homogeneous model. Furthermore, it is shown that, in a closed population, the indicator for the survival of the population is in the presence of heterogeneity distinct from the basic reproduction number.\",\"PeriodicalId\":94130,\"journal\":{\"name\":\"Mathematical medicine and biology : a journal of the IMA\",\"volume\":\"33 3\",\"pages\":\"295-318\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1093/imammb/dqv018\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical medicine and biology : a journal of the IMA\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/8189473/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical medicine and biology : a journal of the IMA","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/8189473/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Aggregation and asymptotic analysis of an SI-epidemic model for heterogeneous populations
The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficient in order to determine the long-run outcome of the disease. Numerical simulation is used to emphasize that, for a given level of prevalence, the evolution of the disease under the influence of heterogeneity may in the long run qualitatively differ from the one ‘predicted’ by the homogeneous model. Furthermore, it is shown that, in a closed population, the indicator for the survival of the population is in the presence of heterogeneity distinct from the basic reproduction number.