Approximation of the Basic Reproduction Number R 0 for Vector-Borne Diseases with a Periodic Vector Population

Springer Science and Business Media LLC - Tập 69 Số 3 - Trang 1067-1091 - 2007
Nicolas Bacaër1
1INSTITUT DE RECHERCHE POUR LE DEVELOPPEMENT (I.R.D.)

Tóm tắt

Từ khóa


Tài liệu tham khảo

Altizer, S., Dobson, A., Hosseini, P., Hudson, P., Pascual, M., Rohani, P., 2006. Seasonality and the dynamics of infectious diseases. Ecol. Lett. 9, 467–484.

Anderson, R.M., May, R.M., 1991. Infectious Diseases of Humans, Dynamics and Control. Oxford University Press, Oxford.

Anita, S., Iannelli, M., Kim, M.Y., Park E.J., 1998. Optimal harvesting for periodic age-dependent population dynamics. SIAM J. Appl. Math. 58, 1648–1666.

Aron, J.L., Schwartz, I.B., 1984. Seasonality and period-doubling bifurcations in an epidemic model. J. Theor. Biol. 110, 665–679.

Bacaër, N., Guernaoui, S., 2006. The epidemic threshold of vector-borne diseases with seasonality—The case of cutaneous leishmaniasis in Chichaoua, Morocco. J. Math. Biol. 53, 421–436.

Bailey, N.T.J., 1982. The Biomathematics of Malaria. Charles Griffin, London.

Bartlett, M.S., 1960. Stochastic Population Models in Ecology and Epidemiology. Methuen, London.

Coale, A.J., 1972. The Growth and Structure of Human Populations—A Mathematical Investigation. Princeton University Press, Princeton, NJ.

Codeço, C.T., 2001. Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir. BMC Infect. Dis. 289, 2801–2810.

Cohen-Tannoudji, C., Diu, B., Laloë, F., 1986. Mécanique Quantique, 3rd edn. Hermann, Paris.

Cooke, K.L., Kaplan, J.L., 1976. A periodicity threshold theorem for epidemics and population growth. Math. Biosci. 31, 87–104.

Diekmann, O., Heesterbeek, J.A.P., 2000. Mathematical Epidemiology of Infectious Diseases—Model Building, Analysis and Interpretation. Wiley, Chichester, UK.

Dietz, K., 1976. The incidence of infectious diseases under the influence of seasonal fluctuations. In: Berger, J., Bühler, W., Repges, R., Tautu, P. (Eds), Mathematical Modelling in Medicine. Springer, Berlin, pp. 1–15.

Duhamel, G., Gombert, D., Paupy, C., Quatresous, I., 2006. Mission d’appui à la lutte contre l’épidémie de chikungunya à la Réunion. Inspection générale des affaires sociales, Paris. www.invs.sante.fr/publications/2006/chikungunya_janvier_2006/chikungunya.pdf .

Grossman, Z., 1980. Oscillatory phenomena in a model of infectious diseases. Theor. Popul. Biol. 18, 204–243.

Grossman, Z., Gumowski, I., Dietz, K., 1977. The incidence of infectious diseases under the influence of seasonal fluctuations —Analytical approach. In: Lakshmikantham, V. (Ed.), Nonlinear Systems and Applications. Academic, New York, pp. 525–546.

Hale, J.K., 1980. Ordinary Differential Equations. Krieger, New York.

Heesterbeek, J.A.P., 2002. A brief history of R 0 and a recipe for its calculation. Acta Biotheor. 50, 189–204.

Heesterbeek, J.A.P., Roberts, M.G., 1995a. Threshold quantities for helminth infections. J. Math. Biol. 33, 415–434.

Heesterbeek, J.A.P., Roberts, M.G., 1995b. Threshold quantities for infectious diseases in periodic environments. J. Biol. Syst. 3, 779–787.

Hochstadt, H., 1973. Integral Equations. Wiley, New York.

Jagers, P., Nerman, O., 1985. Branching processes in periodically varying environment. Ann. Probl. 13, 254–268.

Kato, T., 1984. Perturbation Theory for Linear Operators, 2nd edn. Springer, Berlin.

Krasnosel’skij, M.A., Lifshits, Je.A., Sobolev, A.V., 1980. Positive Linear Systems: The Method of Positive Operators. Heldermann, Berlin.

Kuznetsov, Yu.A., Piccardi, C., 1994. Bifurcation analysis of periodic SEIR and SIR epidemic models. J. Math. Biol. 32, 109–121.

Ma, J., Ma, Z., 2006. Epidemic threshold conditions for seasonally forced SEIR models. Math. Biosci. Eng. 3, 161–172.

Moneim, I.A., Greenhalgh, D., 2005. Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate. Math. Biosci. Eng. 2, 591–611.

Nussbaum, R.D., 1977. Periodic solutions of some integral equations from the theory of epidemics. In: Lakshmikantham, V. (Ed.), Nonlinear Systems and Applications. Academic, New York, pp. 235–257.

Nussbaum, R.D., 1978. A periodicity threshold theorem for some nonlinear integral equations. SIAM J. Math. Anal. 9, 356–376.

Pierre, V., Thiria, J., Rachou, E., Sissoko, D., Lassalle, C., Renault, P., 2005. Epidémie de dengue 1 à la Réunion en 2004. Journées de veille sanitaire 2005, Poster # 13. www.invs.sante.fr/publications/2005/jvs_2005/poster_13.pdf

Ross, R., 1911. The Prevention of Malaria, 2nd edn. John Murray, London.

Schaefer, H.H., 1974. Banach Lattices and Positive Operators. Springer, New York.

Schwartz, I.B., Smith, H.L., 1983. Infinite subharmonic bifurcation in an SEIR epidemic model. J. Math. Biol. 18, 233–253.

Smith, H.L., 1977, On periodic solutions of a delay integral equation modelling epidemics. J. Math. Biol. 4, 69–80.

Thieme, H.R., 1984. Renewal theorems for linear periodic Volterra integral equations. J. Integr. Equ. 7, 253–277.

Williams, B.G., Dye, C., 1997. Infectious disease persistence when transmission varies seasonally. Math. Biosci. 145, 77–88.