The minimum effort required to eradicate infections in models with backward bifurcation

Journal of Mathematical Biology

Volumn 53, Issue 4, 2006, Pages 703-718

  Safan, Muntaser ^a,b   Heesterbeek, Hans ^c   Dietz, Klaus ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b Mansoura University   (Egypt)

^c UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Backward bifurcation; Epidemic model; Eradication effort; Reproduction numbers

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; DISEASE TRANSMISSION; HUMAN; IMMUNOLOGY; INFECTION CONTROL; METHODOLOGY; MORTALITY; SURVIVAL RATE;

ALGORITHMS; ANIMALS; COMMUNICABLE DISEASE CONTROL; COMMUNICABLE DISEASES; DISEASE TRANSMISSION; DISEASE TRANSMISSION, INFECTIOUS; HUMANS; MODELS, BIOLOGICAL; SURVIVAL RATE;

EID: 33748286842     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-006-0028-8     Document Type: Article

References (18)

1. Brauer, F.: Backward bifurcations in simple vaccination models. J. Math. Anal. Appl. 298, 418-431 (2004)
2. van Boven, M., Mooi, ER., Schellekens, J.F.P., de Melker, H.E., Kretzschmar, M.: Pathogen adaptation under imperfect vaccination: implications for pertussis. Proc. R. Soc. Lond. B 272, 1617-1624 (2005)
3. Castillo-Chavez, C., Song, B.: Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1, 361-404 (2004)
4. Diekmann, O., Heesterbeek, J.A.P.: Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, Chichester (2000)
5. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365-382 (1990)
6. van den Driessche, P., Watmough, J.: A simple SIS epidemic model with a backward bifurcation. J. Math. Biol. 40, 525-540 (2000)
7. Hadeler, K.P., Castillo-Chavez, C: A core group model for disease transmission. Math. Biosci. 128, 41-55 (1995)
8. Hadeler, KP., van den Driessche, P.: Backward bifurcation in epidemic control. Math. Biosci. 146, 15-35 (1997)
9. Hadeler, K.P., Liberman, U.: Selection models with fertility differences. J. Math. Biol. 2, 19-32 (1975)
10. Greenhalgh, D., Diekmann, O., de Jong, M.C.M.: Subcritical endemic steady states in mathematical models for animal infections with incomplete immunity. Math. Biosci. 165, 1-25 (2000)
11. Ineichen, R., Batschelet, E.: Genetic selection and de Finetti diagrams. J. Math. Biol. 2, 33-39 (1975)
12. Kribs-Zaleta, CM.: Center manifold and normal forms in epidemic models. In: C. Castillo-Chavez et al. (eds.) Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods and Theory, IMA 125, Springer pp. 269-286, New York (2002)
13. Kribs-Zaleta, C.M., Martcheva, M.: Vaccination strategies and backward bifurcation in an age-since-infection structured model. Math. Biosci. 177, 178, 317-332 (2002)
14. Kribs-Zaleta, C.M., Velasco-Hernandez, J.X.: A simple vaccination model with multiple endemic states. Math. Biosci. 164, 183-201 (2000)
15. Moghadas, S.M.: Analysis of an epidemic model with bistable equilibria using the Poincaré index. Appl. Math. Comput. 149, 689-702 (2004)
16. Moghadas, S.M.: Modelling the effect of imperfect vaccines on disease epidemiology. Discret Contin Dyn Syst-Ser B4, 999-1012 (2004)
17. Safan, M.: Spread of infectious diseases: impact on demography, and the eradication effort in models with backward bifurcation. Dissertation, University of Tuebingen, Germany (2006)
18. Seydel, R.: From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis. Elsvier, Amesterdam (1988)