Worm’s sexuality and special function theory

  • J. P. Gabriel
  • Herman Hanisch
  • Warren M. Hirsch
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 86)

Abstract

The work described here concerns some mathematical questions related to parasitology. It has its roots in a paper by Macdonald (1965) on helminthic infections where the author stresses the importance of the parasite’s sexuality in its transmission dynamics. Anyone who wants to capture quantitatively the life-cycle of a parasite has to deal, at some point, with its reproductive strategy. More precisely, it is impossible to avoid computation of the number of fertilized eggs if one wants to get an estimate of the parasite’s progeny. Assuming homogeneity, in the case of helminthic infections the quantity of interest will be proportional to the number of ovipositing worms.

Keywords

Trop Schistosomiasis cosB 

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References

  1. Abramowitz, M. and Stegun, I.A., "Handbook of Mathematical Functions," Dover, New York, 1972.Google Scholar
  2. Bradley, D.J. and May, R.M., Consequences of helminth aggregation for the dynamics of schistosomiasis, Transac. R.y. Soc. Tropical Medicine & Hygiene 72 (1978), 262 - 273.CrossRefGoogle Scholar
  3. Comtet, L., "Advanced Combinatorics," D. Reidel Publishing Company, Dordrecht-Holland, 1974.CrossRefMATHGoogle Scholar
  4. Gabriel, J.P., Hanisch, H. and Hirsch, W.M., Dynamic Equilibria of Helminthic Infections? Quantitative Population Dynamics; D.G. Chapman and V.F. Galluci (eds.), Statistical Ecology Series13 (1981), 84-104, International Cooperative Pub!. House, Maryland.Google Scholar
  5. Gabriel, J.P., Hanisch, H. and Hirsch, W.M, W.M., “Prepatency and sexuality of parasitic worms: the hermaphroditic case,” CERFIM Research Center, Locamo, 1989.Google Scholar
  6. Hirsch, W.M., Hanisch, H. and Gabriel, J.P., The notion of oviposition function in mathematical parasitology, Statistics & Decisions, Supplement Issue No. 2 (1985), 351-360.MathSciNetGoogle Scholar
  7. Hirsch, W.M., Hanisch, H. and Gabriel, J.P., Differential equation Models of Some Parasitic Infections: Methods for the Study of Asymptotic Behavior, Comm. Pure Appl. Math. 38 (1985), 733-753.MATHMathSciNetGoogle Scholar
  8. Macdonald, G., The dynamics of helminth infections, with special reference to schistosomes, Transac. Roy. Soc. Trop. Medicine & Hygiene 59 (1965), 489-506.CrossRefGoogle Scholar
  9. Nasell, I. Mating models for schistosomes, J. Math. Bioi. 6 (1978), 21-35.CrossRefMathSciNetGoogle Scholar
  10. Nasell, I. and Hirsch, W.M., A mathematical model of some helminth infections, Comm. Pure Appl. Math. 25 (1972), 459-477.CrossRefMATHMathSciNetGoogle Scholar
  11. Nasell, I. and Hirsch, W.M., The transmission dynamics of schistosomiasis, Comm. Pure Appl. Math. 26 (1973), 395-453.CrossRefMATHMathSciNetGoogle Scholar
  12. Pellegrinelli, A., Reproduction des vers parasites: le gonochorisme parfait pour Ia loi biniimiale, Cahier de l'Universite de Geneve (janvier 1989 ).Google Scholar
  13. Titchmarsh, E.C., “The theory of functions,” 2nd edition, Oxford University Press, 1968. -Young, W.H., “The fundamental theorems of the differential calculus,” Hafner Publishing Co, New York, 1971.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J. P. Gabriel
    • 1
  • Herman Hanisch
    • 2
  • Warren M. Hirsch
    • 3
    • 4
  1. 1.Institute of MathematicsUniversity of FribourgFribourgSwitzerland
  2. 2.City CollegeCity University of New YorkNew YorkUSA
  3. 3.The Mount Sinai Medical CenterMount Sinai School of Medicine Department of Biomathematical SciencesNew YorkUSA
  4. 4.Courant InstituteNew York UniversityNew YorkUSA

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