Global Stability Analysis of a Metapopulation SIS Epidemic Model

Mathematical Population Studies

Volumn 19, Issue 3, 2012, Pages 115-129

  Iggidr, Abderrahman ^a,b   Sallet, Gauthier ^a,b,c   Tsanou, Berge ^a,b,d,e  

^a INRIA   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

^c UNIVERSITÉ GASTON BERGER   (Senegal)

^d University of Daschang   (Cameroon)

^e Université Pierre et Marie Curie   (Cameroon)

Author keywords

global stability; metapopulation models; monotone systems; nonlinear dynamical systems; SIS models

Indexed keywords

METAPOPULATION; NONLINEARITY; NUMERICAL MODEL;

EID: 84864601349     PISSN: 08898480     EISSN: 1547724X     Source Type: Journal    
DOI: 10.1080/08898480.2012.693844     Document Type: Article

References (21)

1. Arino, J., Davis, J.-R., et al. (2005). A multi-species epidemic model with spatial dynamics. Mathematical Medicine and Biology, 22 (2): 129-142.
2. Arino, J., Jordan, R., and van den Driessche, P. (2007). Quarantine in a multi-species epidemic model with spatial dynamics. Mathematical Biosciences, 206 (1): 46-60.
3. Arino, J. and van den Driessche, P. (2003). A multi-city epidemic model. Mathematical Population Studies, 10 (3): 175-193.
4. Artzrouni, M. (2009). Transmission probabilities and reproduction numbers for sexually transmitted infections with variable infectivity: Application to the spread of HIV between low- and high-activity populations. Mathematical Populations Studies, 16 (4): 266-287.
5. Auger, P., Kouokam, E., et al. (2008). The Ross-Macdonald model in a patchy environment. Mathematical Biosciences, 216(2): 123-131.
6. Berman, A. and Plemmons, R. J. (1994). Nonnegative Matrices in the Mathematical Sciences: Classics in Applied Mathematics. 9. Philadelphia, PA: SIAM.
7. Castillo-Chavez, C. and Thieme, H. R. (1995). Asymptotically autonomous epidemic models. In O. Arino, D. Axelrod, M. Kimmel, M. Langlais (Eds.), Mathematical Population Dynamics: Analysis of heterogeneity, Vol. One: Theory of Epidemics. Winnipeg, Canada: Wuerz, 33-50.
8. 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28 (4): 365-382.
9. Diekmann, O. and Heesterbeek, J. (1999). Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation. Wiley Series in Mathematical and Computational Biology. Chichester: Wiley.
10. van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180 (1-2): 29-48.
11. Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42 (4): 599-653.
12. Hirsch, M. W. (1984). The dynamical systems approach to differential equations. Bulletin (New Series) of The American Mathematical Society, 11 (1): 1-64.
13. Iggidr, A., Niri, K. and Sallet, G. (2010). Analysis of a patchy sis epidemic model. Manuscript in preparation.
14. Jacquez, J. A. and Simon, C. P. (1993). Qualitative theory of compartmental systems. SIAM Review, 35 (1): 43-79.
15. Jin, Y. and Wang, W. (2005). The effect of population dispersal on the spread of a disease. Journal of Mathematical Analysis and Applications, 308 (1): 343-364.
16. de Jong, M. C., Diekmann, O., and Heesterbeek, H. (1995). How does transmission of infection depend on population size? In D. Mollison (Ed.), Epidemic Models: Their Structure and Relation to Data. Cambridge, England: Cambridge University Press, 85-94.
17. Norman, R. and Bowers, R. G. (2007). A host-host-pathogen model with vaccination and its application to target and reservoir hosts. Mathematical Populations Studies, 14 (1): 31-56.
18. Sattenspiel, L. and Dietz, K. (1995). A structured epidemic model incorporating geographic mobility among regions. Mathematical Biosciences, 128 (1-2): 71-91.
19. Varga, R. (1962). Matrix Iterative Analysis (Prentice-Hall Series in Automatic Computation). Englewood Cliffs, NJ: Prentice-Hall, Inc.
20. Vidyasagar, M. (1980). Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability. IEEE Transactions on Automatic Control, 25: 773-779.
21. Wang, W. and Zhao, X.-Q. (2004). An epidemic model in a patchy environment. Mathematical Biosciences, 190 (1): 97-112.