Endemic threshold results in an age-duration-structured population model for HIV infection

Mathematical Biosciences

Volumn 201, Issue 1-2, 2006, Pages 15-47

  Inaba, Hisashi ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Basic reproduction ratio; Bifurcation; Endemic state; HIV AIDS epidemic; Structured population; Threshold condition

Indexed keywords

BIFURCATION (MATHEMATICS); DISEASES; STABILITY;

BASIC REPRODUCTION RATIO; ENDEMIC STATE; HIV/AIDS EPIDEMIC; STRUCTURED POPULATION; THRESHOLD CONDITION;

MATHEMATICAL MODELS;

ACQUIRED IMMUNE DEFICIENCY SYNDROME; EPIDEMIC; HUMAN IMMUNODEFICIENCY VIRUS;

ACQUIRED IMMUNE DEFICIENCY SYNDROME; ARTICLE; DISEASE PREDISPOSITION; ENDEMIC DISEASE; EPIDEMIC; HIGH RISK POPULATION; HOMOSEXUALITY; HUMAN; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; MATHEMATICAL COMPUTING; POPULATION MODEL; STEADY STATE;

AGE FACTORS; BASIC REPRODUCTION NUMBER; DISEASE OUTBREAKS; HIV; HIV INFECTIONS; HOMOSEXUALITY; HUMANS; MALE; MODELS, BIOLOGICAL; POPULATION DYNAMICS; SEXUAL BEHAVIOR;

EID: 33646824718     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2005.12.017     Document Type: Article

References (26)

1. Britton N.F. Reaction-Diffusion Equations and their Applications to Biology (1986), Academic Press, London
2. Busenberg S., Iannelli M., and Thieme H. Global behaviour of an age-structured S-I-S epidemic model. SIAM J. Math. Anal. 22 (1991) 1065
3. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990) 365
4. Diekmann O., and Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (2000), Wiley, Chichester
5. Hadeler K.P., and van den Driessche P. Backward bifurcation in epidemic control. Math. Biosci. 146 (1997) 15
6. Heijmans H.J.A.M. The dynamical behaviour of the age-size-distribution of a cell population. In: Metz J.A.J., and Diekmann O. (Eds). The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics vol. 68 (1986), Springer, Berlin 185
7. Huang W., Cooke K.L., and Castillo-Chavez C. Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appl. Math. 52 3 (1992) 835
8. Iannelli M. Mathematical Theory of Age-Structured Population Dynamics (1995), Giardini Editori e Stampatori, Pisa
9. Inaba H. Threshold and stability results for an age-structured epidemic model. J. Math. Biol. 28 (1990) 411
10. 0 for HIV infection via pair formation. In: Arino O., Axelrod D., and Kimmel M. (Eds). Advances in Mathematical Population Dynamics - Molecules, Cells and Man (1997), World Scientific, Singapore 355
11. Inaba H. Persistent age distributions for an age-structured two-sex population model. Math. Popul. Studies 7 4 (2000) 365
12. Krasnoselskii M.A. Positive Solutions of Operator Equations (1964), Noordhoff, Groningen
13. Kribs-Zaleta C.M., and Velasco-Hernández J.X. A simple vaccination model with multiple endemic states. Math. Biosci. 164 (2000) 183
14. Kribs-Zaleta C.M., and Martcheva M. Vaccination strategies and backward bifurcation in an age-since-infection structured model. Math. Biosci. 177/178 (2002) 317
15. Marek I. Frobenius theory of positive operators: comparison theorems and applications. SIAM J. Appl. Math. 19 (1970) 607
16. Martcheva M., and Thieme H.R. Progression age enhanced backward bifurcation in an epidemic model with super-infection. J. Math. Biol. 46 (2003) 385
17. Metz J.A.J., and Diekmann O. The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics vol. 68 (1986), Springer, Berlin
18. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer, Berlin
19. Sawashima I. On spectral properties of some positive operators. Nat. Sci. Rep. Ochanomizu Univ. 15 (1964) 53
20. In: Temme N.M. (Ed). Nonlinear Analysis, vol. 2, MC Syllabus 26.2 (1978), Mathematisch Centrum, Amsterdam
21. Thieme H.R. Semiflows generated by Lipschitz perturbations of non-densely defined operators. Diff. Integr. Eqs. 3 6 (1990) 1035
22. Thieme H.R., and Castillo-Chavez C. How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS?. SIAM J. Appl. Math. 53 5 (1993) 1447
23. Thieme H.R. Quasi-compact semigroups via bounded perturbation. In: Arino O., Axelrod D., and Kimmel M. (Eds). Advances in Mathematical Population Dynamics - Molecules, Cells and Man (1997), World Scientific, Singapore 691
24. van den Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29
25. Webb G.F. Theory of Nonlinear Age-Dependent Population Dynamics (1985), Marcel Dekker, New York/Basel
26. Yosida K. Functional Analysis. sixth ed. (1980), Springer, Berlin