{"title":"饱和处理流行病模型的随机持久性与消亡","authors":"Prasenjit Mahato, Subhashis Das, S. Mahato","doi":"10.1142/s0218339023500249","DOIUrl":null,"url":null,"abstract":"We propose and study the transmission dynamics of susceptible-exposed-infected-recovered [Formula: see text] epidemic model with saturated treatment function. We consider saturated treatment function in the epidemic system to understand the effect of delayed treatment on the disease transmission. The indiscriminately perturbation which is considered as a type of white noise is proportional to the distance of state variables from the values of endemic equilibria. Choosing the suitable Lyapunov function and using the It[Formula: see text]’s formula, the existence and the uniqueness of the positive solution of the system are examined. Stochastic boundedness, permanence and extinction of the epidemic model are investigated with proper conditions. Numerical simulations are performed to illustrate our results. The sensitivity analysis of the basic reproduction number is performed. The effect of control parameter is determined on the model dynamics. It is our main finding that the different intensities of white noises can fluctuate the susceptible, exposed, infected, recovered individuals around its equilibrium points.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"STOCHASTIC PERMANENCE AND EXTINCTION OF AN EPIDEMIC MODEL WITH SATURATED TREATMENT\",\"authors\":\"Prasenjit Mahato, Subhashis Das, S. Mahato\",\"doi\":\"10.1142/s0218339023500249\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose and study the transmission dynamics of susceptible-exposed-infected-recovered [Formula: see text] epidemic model with saturated treatment function. We consider saturated treatment function in the epidemic system to understand the effect of delayed treatment on the disease transmission. The indiscriminately perturbation which is considered as a type of white noise is proportional to the distance of state variables from the values of endemic equilibria. Choosing the suitable Lyapunov function and using the It[Formula: see text]’s formula, the existence and the uniqueness of the positive solution of the system are examined. Stochastic boundedness, permanence and extinction of the epidemic model are investigated with proper conditions. Numerical simulations are performed to illustrate our results. The sensitivity analysis of the basic reproduction number is performed. The effect of control parameter is determined on the model dynamics. It is our main finding that the different intensities of white noises can fluctuate the susceptible, exposed, infected, recovered individuals around its equilibrium points.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218339023500249\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1142/s0218339023500249","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
STOCHASTIC PERMANENCE AND EXTINCTION OF AN EPIDEMIC MODEL WITH SATURATED TREATMENT
We propose and study the transmission dynamics of susceptible-exposed-infected-recovered [Formula: see text] epidemic model with saturated treatment function. We consider saturated treatment function in the epidemic system to understand the effect of delayed treatment on the disease transmission. The indiscriminately perturbation which is considered as a type of white noise is proportional to the distance of state variables from the values of endemic equilibria. Choosing the suitable Lyapunov function and using the It[Formula: see text]’s formula, the existence and the uniqueness of the positive solution of the system are examined. Stochastic boundedness, permanence and extinction of the epidemic model are investigated with proper conditions. Numerical simulations are performed to illustrate our results. The sensitivity analysis of the basic reproduction number is performed. The effect of control parameter is determined on the model dynamics. It is our main finding that the different intensities of white noises can fluctuate the susceptible, exposed, infected, recovered individuals around its equilibrium points.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.