The complete classification for dynamics of an SIS STD model in terms of four parameters
✍ Scribed by Zhipeng Qiu
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 509 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1468-1218
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✦ Synopsis
In this paper, a nine-dimensional sexually transmitted disease model proposed by Castillo-Chavez et al. [C. Castillo-Chavez, Wenzhang Huang and Jia Li, The effects of female's susceptibility on coexistence of multiple pathogen strains of sexually transmitted diseases, J. Math. Biol. 35 (1996) 503-522] is studied. The model involves two competing strains 1 and 2 in a two-sex heterosexually active population that includes a single group of males and two different groups of females. The first and second reproduction numbers R i , R i are defined for strain i, i = 1, 2 respectively. By applying the theory of type-K monotone dynamical systems, a complete classification for the dynamics of this model is presented in terms of the first and second reproduction numbers R i , R i , i = 1, 2. The classification not only is different to the complete classification given by Castillo-Chavez et al. [C. Castillo-Chavez, Wenzhang Huang and Jia Li, Competitive exclusion and coexistence of multiple strains in an SIS STD model, SIAM J. Appl. Math. 59 (1999Math. 59 ( ) 1790Math. 59 ( -1811]], but also can be easily explained in biology. Our results also show that the dynamics of the model is completely determined by the ubiety of two functions.