title: Global analysis on delay epidemiological dynamic models with nonlinear incidence.
abstract: In this paper, we derive and study the classical SIR, SIS, SEIR and SEI models of epidemiological dynamics with time delays and a general incidence rate. By constructing Lyapunov functionals, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is shown. This analysis extends and develops further our previous results and can be applied to the other biological dynamics, including such as single species population delay models and chemostat models with delay response.
authors.affiliation: Graduate School of Science and Technology, Shizuoka University, Hamamatsu 4328561, Japan. f5845034@ipc.shizuoka.ac.jp
authors.forename: Gang
authors.initials: G
authors.lastname: Huang
authors.forename: Yasuhiro
authors.initials: Y
authors.lastname: Takeuchi
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission; D018562:Disease Transmission, Infectious / Q000706:statistics & numerical data*; D005260:Female; D006801:Humans; D015994:Incidence; D008297:Male; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D012749:Sexually Transmitted Diseases / Q000453:epidemiology / Q000635:transmission