Lyapunov functional and global asymptotic stability for an infection-age model
作者： P. Magal , C.C. McCluskey , G.F. Webb
DOI: 10.1080/00036810903208122
关键词:
摘要: We study an infection-age model of disease transmission, where both the infectiousness and the removal rate may depend on the infection age. In order to study persistence, the system is described using integrated semigroups. If the basic reproduction number R 0< 1, then the disease-free equilibrium is globally asymptotically stable. For R 0> 1, a Lyapunov functional is used to show that the unique endemic equilibrium is globally stable amongst solutions for which disease transmission occurs.
sci-hub.se 参考文章(60)
Herbert W. Hethcote, Three Basic Epidemiological Models Biomathematics. ,vol. 18, pp. 119- 144 ,(1989) , 10.1007/978-3-642-61317-3_5
Vincenzo Capasso, V Capasso, Mathematical structures of epidemic systems ,(1993)
Horst R. Thieme, Mathematics in Population Biology ,(2003)
Horst R. Thieme, Semiflows generated by lipschitz perturbations of non-densely defined operators Differential and Integral Equations. ,vol. 3, pp. 1035- 1066 ,(1990)
Mimmo Iannelli, Mathematical theory of age-structured population dynamics Giardini Editori e Stampatori in Pisa. ,(1995)
Pierre Magal, Shigui Ruan, Erika M. C. D'Agata, Glenn Webb, Asymptotic behavior in nosocomial epidemic models with antibiotic resistance Differential and Integral Equations. ,vol. 19, pp. 573- 600 ,(2006)
Jack K. Hale, Asymptotic Behavior of Dissipative Systems ,(1988)
Klaus-Jochen Engel, Rainer Nagel, One-Parameter Semigroups for Linear Evolution Equations ,(1999)
Robert M. May, Roy M. Anderson, Infectious Diseases of Humans: Dynamics and Control ,(1991)
Global dynamics of a staged progression model for infectious diseases. Mathematical Biosciences and Engineering. ,vol. 3, pp. 513- 525 ,(2006) , 10.3934/MBE.2006.3.513