Advertisement

Bulletin of Mathematical Biology

, Volume 68, Issue 8, pp 1945–1974 | Cite as

A Stochastic Population Dynamics Model for Aedes Aegypti: Formulation and Application to a City with Temperate Climate

  • Marcelo Otero
  • Hernán G. Solari
  • Nicolás Schweigmann
Original Article

Abstract

Aedes aegypti is the main vector for dengue and urban yellow fever. It is extended around the world not only in the tropical regions but also beyond them, reaching temperate climates. Because of its importance as a vector of deadly diseases, the significance of its distribution in urban areas and the possibility of breeding in laboratory facilities, Aedes aegypti is one of the best-known mosquitoes. In this work the biology of Aedes aegypti is incorporated into the framework of a stochastic population dynamics model able to handle seasonal and total extinction as well as endemic situations. The model incorporates explicitly the dependence with temperature. The ecological parameters of the model are tuned to the present populations of Aedes aegypti in Buenos Aires city, which is at the border of the present day geographical distribution in South America. Temperature thresholds for the mosquito survival are computed as a function of average yearly temperature and seasonal variation as well as breeding site availability. The stochastic analysis suggests that the southern limit of Aedes aegypti distribution in South America is close to the 15^∘C average yearly isotherm, which accounts for the historical and current distribution better than the traditional criterion of the winter (July) 10°C isotherm.

Keywords

Mathematical ecology Population dynamics Aedes aegypti Stochastic model Temperate climate 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersson, H., Britton, T., 2000. Stochastic epidemic models and their statistical analysis. Volume 151 of Lecture Notes in Statistics. Springer-Verlag, Berlin.Google Scholar
  2. Aparicio, J.P., Solari, H.G., 2001. Population dynamics: A poissonian approximation and its relation to the langevin process. Phys. Rev. Lett. 86, 4183–4186.CrossRefGoogle Scholar
  3. Arrivillaga, J., Barrera, R., 2004. Food as a limiting factor for aedes aegypti in water-storage containers. J. Vector Ecol. 29, 11–20.Google Scholar
  4. Bar-Zeev, M., 1957. The effect of density on the larvae of a mosquito and its influence on fecundity. Bull. Res. Council Israel 6B, 220–228.Google Scholar
  5. Bar-Zeev, M., 1958. The effect of temperature on the growth rate and survival of the immature stages of aedes aegypti. Bull. Entomol. Res. 49, 157–163.CrossRefGoogle Scholar
  6. Campos, R.E., Macia, A., 1996. Observaciones biologicas de una poblacion natural de aedes aegypti (diptera: culicidae) en la provincia de buenos aires, argentina. Rev. Soc. Entomol. Argent. 55(1–4), 67–72.Google Scholar
  7. Carbajo, A.E., Schweigmann, N., Curto, S.I., de Garín, A., Bejarán, R., 2001. Dengue transmission risk maps of argentina. Trop. Med. Int. Health 6(3), 170–183.Google Scholar
  8. Carter, H.R., 1931. Yellow Fever: An Epidemiological and Historical Study of Its Place of Origin. The Williams & Wilkins Company, Baltimore.Google Scholar
  9. Christophers, R., 1960. Aedes aegypti (L.), The Yellow Fever Mosquito. Cambridge Univ. Press., Cambridge.Google Scholar
  10. de Garín, A.B., Bejarán, R.A., Carbajo, A.E., de Casas, S.C., Schweigmann, N.J., 2000. Atmospheric control of aedes aegypti populations in buenos aires (argentina) and its variability. Int. J. Biometerol. 44, 148–156.CrossRefGoogle Scholar
  11. Depinay, J.-M.O., Mbogo, C.M., Killeen, G., Knols, B., Beier, J., Carlson, J., Dushoff, J., Billingsley, P., Mwambi, H., Githure, J., Toure, A.M., McKenzie, F.E., 2004. A simulation model of african anopheles ecology and population dynamics for the analysis of malaria transmision. Malaria J. 3(29), 1–21.Google Scholar
  12. Domínguez, C., Almeida, F.F.L., Almirón, W., 2000. Dinámica poblacional de aedes aegypti (diptera: Culicidae) en córdoba capital. Revista de la Sociedad Entomológica de Argentina 59, 41–50.Google Scholar
  13. Dye, C., 1982. Intraspecific competition amongst larval aedes aegypti: Food exploitation or chemical interference. Ecol. Entomol. 7, 39–46.Google Scholar
  14. Ethier, S.N., Kurtz, T.G., 1986. Markov Processes. John Wiley and Sons, New York.Google Scholar
  15. Fay, R.W., 1964. The biology and bionomics of aedes aegypti in the laboratory. Mosq. News. 24, 300–308.Google Scholar
  16. Focks, D.A., Haile, D.C., Daniels, E., Moun, G.A., 1993a. Dynamics life table model for aedes aegypti: Analysis of the literature and model development. J. Med. Entomol. 30, 1003–1018.Google Scholar
  17. Focks, D.A., Haile, D.C., Daniels, E., Mount, G.A., 1993b. Dynamic life table model for aedes aegypti: Simulations results. J. Med. Entomol. 30, 1019–1029.Google Scholar
  18. FUNCEI, 1998. Dengue enfermedad emergente. Fundación de estudios infectológicos 1(1), 1–6, http://www.funcei.org.ar.
  19. FUNCEI, 1999a. Dengue enfermedad emergente. Fundación de estudios infectológicos 2(2), 1–8, http://www.funcei.org.ar.
  20. FUNCEI, 1999b. Dengue enfermedad emergente. Fundación de estudios infectológicos 2(1), 1–12, http://www.funcei.org.ar.
  21. Gleiser, R.M., Urrutia, J., Gorla, D.E., 2000. Effects of crowding on populations of aedes albifasciatus larvae under laboratory conditions. Entomologia Experimentalis et Applicata 95, 135–140.CrossRefGoogle Scholar
  22. Hill, G.W., 1877. On the part of motion of the lunar perigee which is function of the mean motions of the sun and moon. Acta Math. 8, 1.Google Scholar
  23. Horsfall, W.R., 1955. Mosquitoes: Their Bionomics and Relation to Disease. Ronald, New York, USA.Google Scholar
  24. Király, A., Jánosi, I. M., 2002. Stochastic modelling of daily temperature fluctuations. Phys. Rev. E 65, 051102.Google Scholar
  25. Kurtz, T.G., 1970. Solutions of ordinary differential equations as limits of pure jump markov processes. J. Appl. Prob. 7, 49–58.zbMATHCrossRefMathSciNetGoogle Scholar
  26. Kurtz, T.G., 1971. Limit theorems for sequences of jump processes approximating ordinary differential equations. J. Appl. Prob. 8, 344–356.zbMATHCrossRefMathSciNetGoogle Scholar
  27. Legates, D.R., Willmott, C.J., 1990. Mean seasonal and spatial variability in global surface air temperature. Theor. Appl. Climatology 41, 11–21.CrossRefGoogle Scholar
  28. Livdahl, T.P., Koenekoop, R.K., Futterweit, S.G., 1984. The complex hatching response of aedes eggs to larval density. Ecol. Entomol. 9, 437–442.Google Scholar
  29. Ministerio de Asistencia Social y Salud Publica, A., 1964. Campaña de erradicacion del Aedes aegypti en la Republica Argentina. Informe final. Buenos Aires.Google Scholar
  30. Morales, M.A., Monteros, M., Fabbri, C.M., Garay, M.E., Introini, V., Ubeid, M.C., Baroni, P.G., Rodriguez, C., Ranaivoarisoa, M.I., Lanfri, M., Scavuzzo, M., Gentile, A., Zaidemberg, M., Ripoll, C. M., Fernandez, H., Blanco, S., Enria, D.A., 2004. Riesgo de aparicin de dengue hemorrágico en la argentina. In: II Congreso Internacional Dengue y Fiebre Amarilla. La Habana, Cuba, http://www.cidfa2004.sld.cu.
  31. Nayar, J.K., Sauerman, D.M., 1975. The effects of nutrition on survival and fecundity in florida mosquitoes. part 3. utilization of bood and sugar for fecundity. J. Med. Entomol. 12, 220–225.Google Scholar
  32. Perillo, G.M.E., Piccolo, M.C., 2004. quées el estuario de bahía blanca? Ciencia Hoy 14(81), 8–15, on line at http://www.ciencia-hoy.retina.ar.Google Scholar
  33. Powell, J.A., Jenkis, J.L., 2000. Seasonal temperature alone can synchronize life cycles. Bull. Math. Biol. 62, 977–998.CrossRefGoogle Scholar
  34. Rueda, L.M., Patel, K.J., Axtell, R.C., Stinner, R.E., 1990. Temperature-dependent development and survival rates of culex quinquefasciatus and aedes aegypti (diptera: Culicidae). J. Med. Entomol. 27, 892–898.Google Scholar
  35. Schoofield, R.M., Sharpe, P.J.H., Magnuson, C.E., 1981. Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. J. Theor. Biol. 88, 719–731.CrossRefGoogle Scholar
  36. Schuster, H.G., 1984. Deterministic Chaos. Physik Verlag, Weinheim.Google Scholar
  37. Schweigmann, N., Boffi, R., 1998. Aedes aegypti y aedes albopictus: Situación entomológica en la región. In: Temas de Zoonosis y Enfermedades Emergentes, Segundo Cong. Argent. de Zoonosis y Primer Cong. Argent. y Lationoamer. de Enf. Emerg. y Asociación Argentina de Zoonosis. Buenos Aires, pp. 259–263.Google Scholar
  38. Sharpe, P.J.H., DeMichele, D.W., 1977. Reaction kinetics of poikilotherm development. J. Theor. Biol. 64, 649–670.CrossRefGoogle Scholar
  39. Solari, H., Natiello, M., Mindlin, B., 1996. Nonlinear Dynamics: A Two-way Trip from Physics to Math. Institute of Physics, Bristol.Google Scholar
  40. Solari, H., Natiello, M., 2003a. Poisson approximation to density dependent stochastic processes: A numerical implementation and test. In: Khrennikov, A. (Ed.), Mathematical Modelling in Physics, Engineering and Cognitive Sciences. Proceedings of the Workshop Dynamical Systems from Number Theory to Probability–2, vol. 6.Växjö University Press, Växjö, pp. 79–94.Google Scholar
  41. Solari, H.G., Natiello, M.A., 2003b. Stochastic population dynamics: the poisson approximation. Phys. Rev. E 67, 031918.Google Scholar
  42. Southwood, T.R.E., Murdie, G., Yasuno, M., Tonn, R.J., Reader, P.M., 1972. Studies on the life budget of aedes aegypti in wat samphaya bangkok thailand. Bull. W.H.O. 46, 211–226.Google Scholar
  43. Subra, R., Mouchet, J., 1984. The regulation of preimaginal populations of aedes aegypti (l.) (diptera: Culicidae) on the kenya coast. ii. food as a main regulatory fa ctor. Ann. Trop. Med. Parasitol. 78, 63–70.Google Scholar
  44. Trpis, M., 1972. Dry season survival of aedes aegypti eggs in various breeding sites in the dar salaam area, tanzania. Bull. WHO 47, 433–437.Google Scholar
  45. Vezzani, C., Velázquez, S.T., Schweigmann, N., 2004. Seasonal pattern of abundance of aedes aegypti (diptera: Culicidae) in buenos aires city, argentina. Memor Inst Oswaldo Cruz 99, 351–356.Google Scholar
  46. WHO, 1998. Dengue Hemorrhagic Fever. Diagnosis, Treatment, Prevention and Control. World Health Organization, Ginebra, Suiza.Google Scholar
  47. Wiggins, S., 1988. Global Bifurcations and Chaos. No. 73. Applied Mathematical Science.Google Scholar
  48. Wiggins, S., 1990. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, New York.zbMATHGoogle Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  • Marcelo Otero
    • 1
  • Hernán G. Solari
    • 1
  • Nicolás Schweigmann
    • 2
  1. 1.Department of Physics, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.Department of Genetics and Ecology, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina

Personalised recommendations