{"title":"由潜伏期、感染期和免疫期决定的延迟流行模型","authors":"Masoud Saade , Samiran Ghosh , Malay Banerjee , Vitaly Volpert","doi":"10.1016/j.mbs.2024.109155","DOIUrl":null,"url":null,"abstract":"<div><p>We propose new single and two-strain epidemic models represented by systems of delay differential equations and based on the number of newly exposed individuals. Transitions between exposed, infectious, recovered, and back to susceptible compartments are determined by the corresponding time delays. Existence and positiveness of solutions are proved. Reduction of delay differential equations to integral equations allows the analysis of stationary solutions and their stability. In the case of two strains, they compete with each other, and the strain with a larger individual basic reproduction number dominates the other one. However, if the basic reproduction number exceeds some critical values, stationary solution loses its stability resulting in periodic time oscillations. In this case, both strains are present and their dynamics is not completely determined by the basic reproduction numbers but also by other parameters. The results of the work are illustrated by comparison with data on seasonal influenza.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Delay epidemic models determined by latency, infection, and immunity duration\",\"authors\":\"Masoud Saade , Samiran Ghosh , Malay Banerjee , Vitaly Volpert\",\"doi\":\"10.1016/j.mbs.2024.109155\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose new single and two-strain epidemic models represented by systems of delay differential equations and based on the number of newly exposed individuals. Transitions between exposed, infectious, recovered, and back to susceptible compartments are determined by the corresponding time delays. Existence and positiveness of solutions are proved. Reduction of delay differential equations to integral equations allows the analysis of stationary solutions and their stability. In the case of two strains, they compete with each other, and the strain with a larger individual basic reproduction number dominates the other one. However, if the basic reproduction number exceeds some critical values, stationary solution loses its stability resulting in periodic time oscillations. In this case, both strains are present and their dynamics is not completely determined by the basic reproduction numbers but also by other parameters. The results of the work are illustrated by comparison with data on seasonal influenza.</p></div>\",\"PeriodicalId\":51119,\"journal\":{\"name\":\"Mathematical Biosciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-02-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Biosciences\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0025556424000154\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Biosciences","FirstCategoryId":"99","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0025556424000154","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"BIOLOGY","Score":null,"Total":0}
Delay epidemic models determined by latency, infection, and immunity duration
We propose new single and two-strain epidemic models represented by systems of delay differential equations and based on the number of newly exposed individuals. Transitions between exposed, infectious, recovered, and back to susceptible compartments are determined by the corresponding time delays. Existence and positiveness of solutions are proved. Reduction of delay differential equations to integral equations allows the analysis of stationary solutions and their stability. In the case of two strains, they compete with each other, and the strain with a larger individual basic reproduction number dominates the other one. However, if the basic reproduction number exceeds some critical values, stationary solution loses its stability resulting in periodic time oscillations. In this case, both strains are present and their dynamics is not completely determined by the basic reproduction numbers but also by other parameters. The results of the work are illustrated by comparison with data on seasonal influenza.
期刊介绍:
Mathematical Biosciences publishes work providing new concepts or new understanding of biological systems using mathematical models, or methodological articles likely to find application to multiple biological systems. Papers are expected to present a major research finding of broad significance for the biological sciences, or mathematical biology. Mathematical Biosciences welcomes original research articles, letters, reviews and perspectives.