Strain replacement in an epidemic model with super-infection and perfect vaccination

Mathematical Biosciences

Volumn 195, Issue 1, 2005, Pages 23-46

  Iannelli, Mimmo ^a   Martcheva, Maia ^b   Li, Xue Zhi ^c  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY OF FLORIDA   (United States)

^c XINYANG NORMAL UNIVERSITY   (China)

Author keywords

Class age structure; Coexistence; Equilibria; Multiple strains; Stability; Strain replacement; Subthreshold coexistence; Super infection; Vaccination

Indexed keywords

BIOMEDICAL ENGINEERING; DISEASE CONTROL; MATHEMATICAL MODELS; MICROORGANISMS; VACCINES;

EPIDEMICS; STRAIN REPLACEMENT; SUPER-INFECTION; VACCINATION;

MEDICAL PROBLEMS;

VACCINATION;

ARTICLE; HUMAN; MOLECULAR DYNAMICS; POPULATION DYNAMICS; SUPERINFECTION; VACCINATION; VIRUS STRAIN;

ALGORITHMS; BACTERIA; COMMUNICABLE DISEASES; DISEASE OUTBREAKS; HUMANS; MODELS, THEORETICAL; SUPERINFECTION; VACCINATION; VIRUSES;

EID: 19444383278     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2005.01.004     Document Type: Article

References (32)

1. A. Ackleh, and L. Allen Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size J. Math. Biol. 47 2003 153
2. V. Andreasen, J. Lin, and S. Levin The dynamics of cocirculating influenza strains conferring partial cross-immunity J. Math. Biol. 35 1997 825
3. V. Andreasen, and A. Pugliese Pathogen coexistence induced by density dependent host mortality J. Theor. Biol. 177 1995 159
4. S. Blower, T. Porco, and T. Lietman Tuberculosis: the evolution of antibiotic resistance and the design of epidemic control strategies A. Horn G. Simonett G.F. Webb Mathematical models in medical and health sciences 1998 Vanderbilt University 1
5. S. Bonhoeffer, and M. Nowak Mutation and the evolution of virulence Proc. Roy. Soc. London B 258 1994 133
6. H.-J. Bremermann, and H.R. Thieme A competitive exclusion principle for pathogen virulence J. Math. Biol. 27 1989 179
7. C. Castillo-Chavez, and Z. Feng To treat or not to treat: the case of tuberculosis J. Math. Biol. 35 1997 629
8. C. Castillo-Chavez, H. Hethcote, V. Andreasen, S. Levin, and W.M. Liu Cross-immunity in the dynamics of homogeneous and heterogeneous populations Mathematical Ecology (Trieste, 1986) 1988 World Sci. Publ. Teaneck, NJ 303
9. C. Castillo-Chavez, H. Hethcote, V. Andreasen, S. Levin, and W.M. Liu Epidemiological models with age structure, proportionate mixing, and cross-immunity J. Math. Biol. 27 1989 233
10. 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
11. C. Castillo-Chavez, W. Huang, and J. Li Competitive exclusion and coexistence of multiple strains in an SIS STD model SIAM J. Appl. Math. 59 1999 1790
12. L. Esteva, and C. Vargas Coexistence of different serotypes of dengue virus J. Math. Biol. 46 2003 31
13. Z. Feng, M. Iannelli, and F. Milner A two-strain tuberculosis model with age of infection SIAM J. Appl. Math. 62 2002 1634
14. Z. Feng, and J. Velasco-Hernándes Competitive exclusion in a vector-host model for the dengue fever J. Math. Biol. 35 1997 523
15. S. Levin, and D. Pimentel Selection of intermediate rates of increase in parasite-host systems Am. Natur. 117 1981 308
16. J. Lin, V. Andreasen, and S. Levin Dynamics of influenza a drift: the linear three-strain model Math. Biosci. 162 1999 33
17. J. Lin, V. Andreasen, R. Casagrandi, and S. Levin Traveling waves in a model of influenza a drift J. Theor. Biol. 222 2003 427
18. M. Lipsitch Vaccination against colonizing bacteria with multiple serotypes Proc. Natl. Acad. Sci. USA 94 1997 6571
19. M. Lipsitch Bacterial vaccines and serotype replacement: lessons from Haemophilus influenzae and prospects for Streptococcus pneumoniae Emerg. Infect. Diseases 5 1999 336
20. M. Lipsitch, and M. Nowak The evolution of virulence in sexually transmitted HIV/AIDS J. Theor. Biol. 174 1995 427
21. R. May, and M. Nowak Superinfection, metapopulation dynamics, and the evolution of diversity J. Theor. Biol. 170 1994 95
22. R. May, and M. Nowak Coinfection and the evolution of parasite virulence Proc. Roy. Soc. London B 261 1995 209
23. A.R. McLean Vaccination, evolution and changes in efficacy of vaccines: a theoretical framework Proc. Roy. Soc. London B 261 1995 389
24. R.K. Miller Nonlinear Volterra integral equations Mathematics lecture note series 1971 W.A. Benjamin Inc. Menlo Park, CA
25. F. Mooi, I. van Loo, and A. King Adaptation of Bordella pertussis to vaccination: a cause for its reemergence? Emerg. Infect. Diseases 7 2001 526
26. M. Nowak, and R. May Superinfection and the evolution of parasite virulence Proc. Roy. Soc. London B 255 1994 81
27. D. Perdue, L. Bulkow, B. Gellin, M. Davidson, K. Petersen, R. Singleton, and A. Perkinson Invasive Haemophilus influenzae disease in Alaskan residents aged 10 years and older before and after infant vaccine programs JAMA 283 2000 3089
28. T. Porco, and S. Blower HIV vaccines: the effect of the mode of action on the coexistence of HIV subtypes Math. Popul. Studies 8 2000 205
29. T. Porco, and S. Blower Designing HIV vaccination polices: subtypes and cross-immunity Interfaces 28 1998 167
30. A. Rodriguez, F. Dickinson, A. Baly, R. Martinez, The Epidemiological impact of antimeningococcal B vaccination in Cuba, Mem. Inst. Oswaldo Cruz, Rio de Jeneiro, vol. 94, 1999, p. 433
31. H.R. Thieme Persistence under relaxed point-dissipativity (with applications to an endemic model) SIAM J. Math. Anal. 24 1993 407
32. L.J. White, M.J. Cox, and G.F. Medley Cross immunity and vaccination against multiple microparasite strains IMA J. Math. Appl. Med. Biol. 15 1998 211