Qualitative analyses of SIS epidemic model with vaccination and varying total population size

✍ Scribed by Jianquan Li; Zhien Ma

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 764 KB
• Volume: 35
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(02)00082-1

✦ Synopsis

SIS epidemic model with vaccination, temporary immunity, and varying total population size is studied. Three threshold parameters R.e, Ri, and Ra are identified. The disesss free equilibrium is globally stable if Rc 5 1 and unstable if Ro > 1, the endemic equilibrium is globally stable if Rc > 1. The disease cannot break out if R1 < 1, the disesse may break out when the fractions of the susceptible and the infectious satisfy some condition if R1 > 1 and Rc 5 1. The population becomes extinct ultimately and the disesse always exists in the population if Rc > 1 and R2 5 1. There is a really endemic disease if Re > 1 and Rz > 1. The global stability of the disease-free equilibrium and the existence and global stability of the endemic equilibrium are proved by means of LaSalle's invariance principle, the method of estimating values and Stokes' theorem, respectively. The results with vaccination and without vaccination are compared, the measures and effects of vaccination are discussed.