Dynamics of Japanese encephalitis - A study in mathematical epidemiology

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 16, Issue 1, 1999, Pages 1-27

  Ghosh, Asit K ^a   Tapaswi, P K ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Basic reproduction ratio; Global stability; Japanese encephalitis

Indexed keywords

ARTICLE; CULEX; DYNAMICS; EPIDEMIC ENCEPHALITIS; INFECTION SENSITIVITY; MATHEMATICAL MODEL; POPULATION RESEARCH; VIRUS INFECTIVITY;

ANIMALIA; AVES; BOS TAURUS; CULEX TRITAENIORHYNCHUS; CULEX VISHNUI; JAPANESE ENCEPHALITIS VIRUS;

EID: 0032951676     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb16.1.1     Document Type: Article

References (33)

1. ANDERSON, R. M. & MAY, R. M. 1979 Population biology of infectious diseases I. Nature 180, 361-367.
2. ANDERSON, R. M. & MAY, R. M. 1981 The population dynamics of microparasites and their invertebrate hosts. Trans. R. Soc. Lond. B 291, 451-524.
3. ANDERSON, R. M. & MAY, R. M. 1982 Directly transmitted infectious diseases: Control by vaccination. Science 215, 1053-1060.
4. ARON, J. L. 1988 Acquired immunity dependent upon exposure in an SIRS epidemic model. Math. Biosci. 88, 37-47.
5. BARKER, G. P., BERMAN, A., & PLEMMONS, R. J. 1978 Positive diagonal solutions to the Lyapunov equations. Linear Multilinear Alg. 5, 249-256.
6. BERMAN, A. & HERSHKOWITZ, D. 1983 Matrix diagonal stability and its implications. SIAM J. Alg. Disc. Meth. 4, 377-382.
7. BUSENBERG, S. N. & VAN DEN DRIESSCHE, P. 1990 Analysis of a disease transmission model in a population with varying size. J. Math. Biol. 28, 257-270.
8. CASTILLO-CHAVEZ, C., COOKE, K., HUANG, W., & LEVIN, S. A. 1989 On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1. Single population models. J. Math. Biol. 27, 373-398.
9. CROSS, G. W. 1978 Three types of matrix stability. Lin. Alg. Appl. 20, 253-263.
10. GAO, L. Q. & HETHCOTE, H. W. 1992 Disease transmission models with density-dependent demographics. J. Math. Biol. 30, 717-731.
11. GREENHALGH, D. 1990 An epidemic model with density-dependent death rate. IMA J. Appl. Med. Biol. 7, 1-26.
12. HALE, J. K. 1969 Ordinary Differential Equations. New York: Wiley-Interscience.
13. HETHCOTE, H. W. 1976 Qualitative analysis of communicable disease models. Math. Biosci. 28, 335-356.
14. KODAMA, K., SASAKI, N., & INOUE, Y. K. 1968 Studies of live attenuated Japanese encephalitis vaccine in swine. J. Immunol. 100, 194-200.
15. LANCASTER, P. & TISMENETSKY, M. 1985 The Theory of Matrices. New York: Academic Press.
16. LIU, WEI-MIN, HETHCOTE, H. W., & LEVIN, S. A. 1987 Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Biol. 25, 359-380.
17. LYAPUNOV, A. 1892 Problemes General de la stabilite du mouvment, Communications of the Math. Soc. of Kharkow, republished in Annals of Mathematics Studies, No. 17, 1947, Princeton: Princeton Press.
18. MANI, T. R., MOHAN RAO, C. V. R., RAJENDRAN, R., DEVAPUTRA, M., PRASANNA, Y., HANUMAIAH GAJANANA, A., & REUBEN, R. 1991 Surveillance for Japanese encephalitis in villages near Madurai, Tamil Nandu, India. Trans. R. Soc. Trop. Med. Hyg. 85, 287-291.
19. MENA-LORCA, J. & HETHCOTE, H. W. 1992 Dynamics models of infectious diseases as regulators of population sizes. J. Math. Biol. 30, 693-716.
20. MILLER, R. K. & MICHEL, A. N. 1982 Ordinary Differential Equations. New York: Academic Press.
21. MUKHOPADHYAY, B. B. & TAPASWI, P. K. 1994 An SIRS epidemic model of Japanese encephalitis. Int. J. Math. Math. Sci. 17, 347-356.
22. MUKHOPADHYAY, B. B., TAPASWI, P. K., CHATTERJEE, A., & MUKHERJEE, B. 1993 A mathematical model for the occurrences of Japanese encephalitis. Math. Comput. Modell. 17, 99-103.
23. REDHEFFER, R. 1985 Volterra multipliers II. SIAM J. Alg. Disc. Meth. 6, 612-623.
24. RINALDI, F. 1990 Global stability results for epidemic models with latent period. IMA J. Math. Appl. Med. Biol. 7, 69-75.
25. SADANAND, A. V. 1987 Problems of control of Japanese encephalitis vectors. Proceedings of a Symposium on Alternatives to Synthetic Insecticides in Integrated Pest Management Systems (R. Reuben & P. C. Sundarababu, eds.), pp. 125-133. Madurai: CRME.
26. SCHERER, W. F. et al. 1959 Ecologic studies of Japanese encephalitis virus in Japan (I-IX). Am. J. Trop. Med. Hyg. 8, 644-722.
27. TAPASWI, P. K. & MUKHOPADHYAY, B. B. 1995 An SIRS epidemic model of the spread of Japanese encephalitis. In: Mathematical Population Dynamics: Analysis of Heterogeneity, Vol. 1, Theory of Epidemics (O. Arino, D. Axelrod, M. Kimmel, & M. Langlais, eds.), pp. 367-380. Winnipeg, Canada: Wuerz Publishing.
28. TAPASWI, P. K., GHOSH, ASIT K., & MUKHOPADHYAY, B. B. 1995 Transmission of Japanese encephalitis in a 3-population model. Ecolog. Modell. 83, 295-309.
29. TULJAPURKAR, S. D. & SEMURA, J. S. 1975 Stability of Lotka-Volterra systems. Nature 257, 388-389.
30. VELASCO-HERNANDEZ, J. X. & HSIEH, Y.-H. 1994 Modelling the effects of treatment and behavioral change in HIV transmission dynamics. J. Math. Biol. 32, 233-249.
31. VOLOVSKAYA, M. L. 1990 Epidemiology and Fundamentals of Infectious Diseases (translated from the Russian by A. Rosinkin), p. 237. Moscow: Mir Publishers.
32. WADA, Y. 1972 Theoretical considerations on the effects of pig immunization as preventive measures for Japanese encephalitis. Trop. Med. 14, 151-163.
33. ZHOU, J. & HETHCOTE, H. W. 1994 Population size dependent incidence in models for diseases without immunity. J. Math. Biol. 32, 809-834.