Incorporating immunological ideas in epidemiological models

Journal of Theoretical Biology

Volumn 180, Issue 3, 1996, Pages 181-187

  Dushoff, Jonathan ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; EPIDEMIOLOGY; HOST PARASITE INTERACTION; IMMUNOLOGY; INFECTION; MATHEMATICAL MODEL; PRIORITY JOURNAL;

EID: 0030573518     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1996.0094     Document Type: Article

References (21)

1. ANDERSON, R. M. (1982). The population dynamics and control of hook-worm and roundworm infections. In: Population Dynamics of Infectious Disease: Theory and Applications (Anderson, R. M., ed.) pp. 67-108. London: Chapman and Hall.
2. ARON, J. L. (1983). The dynamics of immunity boosted by exposure to infection. Math. Biosci., 64, 249-259.
3. ARON, J. L. & MAY, R. M. (1982). The population dynamics of malaria. In : Population Dynamics of Infectious Disease: Theory and Applications (Anderson, R. M., ed.) pp. 139-179. London: Chapman and Hall.
4. CASTILLO-CHAVEZ, C., COOKE, K., HUANG, W. & LEVIN, S. A. (1989). The role of long incubation periods in the dynamics of HIV/AIDS. part 2: Multiple group models. In: Mathematical and Statistical Approaches to AIDS Epidemiology (Castillo-Chavez, C., ed.) pp. 200-217. Lecture Notes in Biomathematics, vol. 83. Berlin: Springer-Verlag.
5. CORNILLE BRÖGGER, R., MATTHEWS, H. M., STOREY, J., ASHKAR, T. S., BRÖGGER, S. & MOLINEAUX, L. (1978). Changing patterns in the humoral immune response to malaria before, during, and after the application of control measures: a longitudinal study in the West African savanna. Bull. World Health Org., 56, 579-600.
6. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365-382.
7. DIETZ, K., MOLINEAUX, L. & THOMAS, A. (1974). A malaria model tested in the African savannah. Bull. World Health Org., 50, 347-357.
8. DUSHOFF, J., HUANG, W. & CASTILLO-CHAVEZ, C. (1996). Backwards Bifurcations and Catastrophe in Simple Models of Fatal Diseases. J. Math. Biol. (submitted).
9. ELDERKIN, R. H., BERKOWITZ, D. P., FARRIS, F. A., GUNN, C. F., HICKERNELL, F. J., KASS S. N. et al. (1977). On the steady state of an age dependent model for malaria. In: Nonlinear Systems and Application: An International Conference (Lakshmikantham, V., ed.) pp. 491-512. New York: Academic Press.
10. FULFORD, A. J. C., BUTTERWORTH, A. E., STURROCK, R. F. & OUMA, J. H. (1992). On the use of age-intensity data to detect immunity to parasitic infections, with special reference to Schistosoma mansoni in Kenya. Parasitology, 105, 219-227.
11. GUCKENHEIMER, J. & HOLMES, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Berlin: Springer-Verlag.
12. HADELER, K. P. & CASTILLO-CHAVEZ, C. (1995). A core group model for disease transmission. Math. Biosci., 128, 41-55.
13. HUANG, W., COOKE, K. & CASTILLO-CHAVEZ, C. (1992). Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appl. Math., 52, 835-854.
14. LAJMANOVICH, A. & YORKE, J. A. (1976). A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci., 28, 221-236.
15. LUDWIG, D., JONES, D. D. & HOLLING, C. S. (1978). Qualitative analysis of insect outbreak systems: The spruce budworm and forest. Journal of Animal Ecology, 47, 315-332.
16. MAY, R. M. (1977). Togetherness among schistosomes: Its effects on the dynamics of the infection. Math. Biosci., 35, 301-343.
17. PACALA, S. W. & DOBSON, A. P. (1988). The relation between the number of parasites/host and host age: Population dynamic causes and maximum likelihood estimation. Parasitology, 96, 197-210.
18. + T-cell dynamics and host predisposition to infection. Infection and Immunity, 61(4), 1516-1522.
19. + T-cells and parasitic helminths: Mathematical models of heterogeneity in outcome. Parasitology, 105, 513-522.
20. SIMON, C. P. & JACQUEZ, J. A. (1992). Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations. SIAM J. Appl. Math., 52, 541-576.
21. WAKELIN, D. (1988). Helminth infections. In: Genetics of Resistance to Bacterial and Parasitic Infection (Wakelin, D. & Blackwell, J. M., eds) pp. 153-225. London: Taylor & Francis.