Spatial spread of sexually transmitted diseases within susceptible populations at demographic steady state

Mathematical Biosciences and Engineering

Volumn 5, Issue 4, 2008, Pages 713-727

  Castillo Chavez, Carlos ^a   Li, Bingtuan ^b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF LOUISVILLE   (United States)

Author keywords

Disease spread; Sexually transmitted disease; Spreading speed; Traveling wave

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; DISEASE TRANSMISSION; FEMALE; HETEROSEXUALITY; HUMAN; MALE; POPULATION DYNAMICS; SEXUALLY TRANSMITTED DISEASE;

FEMALE; HETEROSEXUALITY; HUMANS; MALE; MODELS, BIOLOGICAL; POPULATION DYNAMICS; SEXUALLY TRANSMITTED DISEASES;

EID: 58849164152     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2008.5.713     Document Type: Article

References (18)

1. F. Brauer, C. Castillo-Chavez, and J. X. Velasco-Hernandez, Recruitment Effects in Heterosexually Transmitted Disease Models, In: Advances in Mathematical Modeling of Biological Processes, Denise Kirschner (editor), International Journal of Applied Science and Computation, 3 (1996), 78-90.
2. C. Castillo-Chavez, W. Huang, and J. Li, Dynamics of Multiple Pathogen Strains in Heterosexual Epidemiological Models, In: Differential equations and applications to biology and to industry: Proceedings of the June 1-4, 1994, Claremont international conference dedicated to the memory of Stavros Busenberg (1941-1993): 129-298, 1996.
3. C. Castillo-Chavez, W. Huang, and J. Li, Competitive exclusion in gonorrhea models and other sexually transmitted diseases, SIAM. J. Appl. Math., 56 (1996), 494-508
4. C. Castillo-Chavez, W. Huang, and J. Li, The effects of females susceptibility on the coexistence of multiple pathogen strains of sexually-transmitted diseases, Journal of Mathematical Biology, 35 (1997), 503-522.
5. G. Chowell, C. A. Torre, C. Munayco-Escate, L. Suarez-Ognio, R. Lopez-Cruz, J. M. Hyman, and C. Castillo-Chavez, Spatial and temporal dynamics of Dengue fever in Peru: 1994-2006 (preprint).
6. K. L. Cooke and J. A. Yorke, Some equations modelling growth processes and gonorrhea epidemics, Math. Biosciences, 16 (1973), 75-101.
7. H. W. Hethcote and J. A. Yorke, Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics, Vol. 56 (1984), Springer-Verlag, New York.
8. G. T. Kasseem, S. Roudenko, S. Tennenbaum, and C. Castillo-Chavez, The Role of Transactional Sex in Spreading HIV/AIDS in Nigeria: A Modeling Perspective. In: Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges. A. Gumel, C. Castillo-Chavez, D. P. Clemence, and R.E. Mickens, American Mathematical Society, 410 (2006), 367-389.
9. D. Kirschner, A diffusion model for AIDS in a closed, heterosexual populations: Estimating rates of infection, SIAM J. Appl. Math., 56 (1996),143-166.
10. A. Lajmanovich, and J. A. Yorke, A deterministic model for gonorrhea in a non-homogeneous population, Math. Biosciences, 28 (1976), 221-236.
11. M. A. Lewis, B. Li, and H. F. Weinberger, Spreading speeds and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
12. B. Li, H. F. Weinberger, and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosc, 196 (2005), 82-98.
13. R. Lui, Biological growth and spread modeled by system sof recursions, I Mathematical theory, Math. Biosc, 93 (1989), 269-295.
14. J. D. Murray, Mathematical Biology I-II, Springer-Verlag, 2003.
15. R. Ross, The prevention of malaria (2nd ed.), John Murray, London, 1911, p. 667.
16. N. Shigesada and K. Kawasaki, Biological Invasions: Theory and Practice, Oxford University Press, 1997.
17. H. F. Weinberger, M. A. Lewis, and B. Li, Analysis of linear conjecture for spread in cooperative models, J. Math. Biol., 45 (2002), 183-218.
18. H. F. Weinberger, M. A. Lewis, and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.