{"title":"Complex dynamics of an SIHR epidemic model with variable hospitalization rate depending on unoccupied hospital beds","authors":"Chunping Jia , Xia Wang , Yuming Chen","doi":"10.1016/j.matcom.2024.10.023","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we propose an <strong>susceptible–infectious–hospitalized–recovered</strong> (SIHR) epidemic model with a nonlinear hospitalization rate depending on the number of unoccupied hospital beds. Note that the number of all hospital beds is used as a measure of all available medical resources. The basic reproduction number is calculated using the next-generation matrix method. We analyze the existence of endemic equilibria and discuss the global stability of the disease-free equilibrium. Existence and stability of endemic equilibria indicate possible occurrences of bifurcations. We confirm the appearance of backward bifurcation, saddle–node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation using normal form theory and central manifold theory. Numerical simulations show that the dynamic behavior of the model undergoes a transition from forward bifurcation to backward bifurcation and saddle–node bifurcation when the number of total hospital beds is reduced. Our findings suggest that when the number of total hospital beds falls below a threshold, backward bifurcation will occur, meaning that the disease cannot be eliminated even if the basic reproduction number is below unity. Therefore, the number of hospital beds should be increased beyond the bed threshold during an outbreak of a disease, which has important implications for disease control.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 706-724"},"PeriodicalIF":4.4000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378475424004130","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose an susceptible–infectious–hospitalized–recovered (SIHR) epidemic model with a nonlinear hospitalization rate depending on the number of unoccupied hospital beds. Note that the number of all hospital beds is used as a measure of all available medical resources. The basic reproduction number is calculated using the next-generation matrix method. We analyze the existence of endemic equilibria and discuss the global stability of the disease-free equilibrium. Existence and stability of endemic equilibria indicate possible occurrences of bifurcations. We confirm the appearance of backward bifurcation, saddle–node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation using normal form theory and central manifold theory. Numerical simulations show that the dynamic behavior of the model undergoes a transition from forward bifurcation to backward bifurcation and saddle–node bifurcation when the number of total hospital beds is reduced. Our findings suggest that when the number of total hospital beds falls below a threshold, backward bifurcation will occur, meaning that the disease cannot be eliminated even if the basic reproduction number is below unity. Therefore, the number of hospital beds should be increased beyond the bed threshold during an outbreak of a disease, which has important implications for disease control.
期刊介绍:
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
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