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Volumn 31, Issue 3, 1999, Pages 742-757

On the algebraic structure in markovian processes of death and epidemic types

Author keywords

Abel Gontcharoff pseudopolynomials with two indices; Abelian expansions; Bivariate death process; Exact temporal distribution; Markovian SIR epidemic models; Martingales

Indexed keywords


EID: 17744396915     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800009393     Document Type: Article
Times cited : (2)

References (23)
  • 1
    • 0000504567 scopus 로고
    • The final size and severity of a generalised stochastic multitype epidemic model
    • BALL, F. G. AND CLANCY, D. (1993). The final size and severity of a generalised stochastic multitype epidemic model. Adv. Appl. Prob. 25, 721-736.
    • (1993) Adv. Appl. Prob. , vol.25 , pp. 721-736
    • Ball, F.G.1    Clancy, D.2
  • 2
    • 0002756353 scopus 로고
    • A modification of the general stochastic epidemic motivated by AIDS modelling
    • BALL, F. G. AND O'NEILL, P. D. (1993). A modification of the general stochastic epidemic motivated by AIDS modelling. Adv. Appl. Prob. 25, 39-62.
    • (1993) Adv. Appl. Prob. , vol.25 , pp. 39-62
    • Ball, F.G.1    O'Neill, P.D.2
  • 5
    • 0008844345 scopus 로고
    • Factorial moments and probabilities for the general stochastic epidemic
    • BILLARD, L. (1973). Factorial moments and probabilities for the general stochastic epidemic. J. Appl. Prob. 10, 277-288.
    • (1973) J. Appl. Prob. , vol.10 , pp. 277-288
    • Billard, L.1
  • 6
    • 0343382646 scopus 로고
    • Competition between two species
    • BILLARD, L. (1974). Competition between two species. Stoch. Proc. Appl. 2, 391-398.
    • (1974) Stoch. Proc. Appl. , vol.2 , pp. 391-398
    • Billard, L.1
  • 7
    • 0017585572 scopus 로고
    • The transition probabilities of a bounded bivariate pure death process
    • BILLARD, L. AND KRYSCIO, R. J. (1977). The transition probabilities of a bounded bivariate pure death process. Math. Biosci. 37, 205-221.
    • (1977) Math. Biosci. , vol.37 , pp. 205-221
    • Billard, L.1    Kryscio, R.J.2
  • 10
    • 77957175122 scopus 로고
    • Some population and epidemic models revisited. 1MA J
    • GANI, J. (1984). Some population and epidemic models revisited. 1MA J. Math. Appl. Med. Biol. 1, 277-287.
    • (1984) Math. Appl. Med. Biol. , vol.1 , pp. 277-287
    • Gani, J.1
  • 11
    • 0343382643 scopus 로고
    • The transition probabilities of the extended simple stochastic epidemic model and the Haskey model. 7
    • KRYSCIO, R. J. (1972). The transition probabilities of the extended simple stochastic epidemic model and the Haskey model. 7. Appl. Prob. 9, 471-185.
    • (1972) Appl. Prob. , vol.9 , pp. 471-1185
    • Kryscio, R.J.1
  • 12
    • 0008844346 scopus 로고
    • The transition probabilities of the general stochastic epidemic model
    • KRYSCIO, R. J. (1975). The transition probabilities of the general stochastic epidemic model. J. Appl. Prob. 12, 415-124.
    • (1975) J. Appl. Prob. , vol.12 , pp. 415-1124
    • Kryscio, R.J.1
  • 13
    • 0016519036 scopus 로고
    • Computational and estimation procedures in multidimensional rightshift processes and some applications
    • KRYSCIO, R. J. AND SEVERO, N. C. (1975). Computational and estimation procedures in multidimensional rightshift processes and some applications. Adv. Appl. Prob, l, 349-382.
    • (1975) Adv. Appl. Prob, L , pp. 349-382
    • Kryscio, R.J.1    Severo, N.C.2
  • 14
    • 0002708819 scopus 로고
    • A non standard family of polynomials and the final size distribution of Reed-Frost epidemic processes
    • LEFèVRE CL. AND PICARD, PH. (1990). A non standard family of polynomials and the final size distribution of Reed-Frost epidemic processes. Adv. Appl. Prob. 22, 25-48.
    • (1990) Adv. Appl. Prob. , vol.22 , pp. 25-48
    • Lefèvre, C.L.1    Picard, P.H.2
  • 15
    • 0027172362 scopus 로고
    • An epidemic model with fatal risk
    • LEFèVRE CL. AND PICARD, Pu. (1993). An epidemic model with fatal risk. Math. Biosci. 117, 127-145.
    • (1993) Math. Biosci. , vol.117 , pp. 127-145
    • Lefèvre, C.L.1    Picard, P.2
  • 16
    • 0009123751 scopus 로고    scopus 로고
    • Abelian-type expansions and non-linear death processes (II)
    • LEFÈVRE CL. AND PICARD, PH. (1996). Abelian-type expansions and non-linear death processes (II). Adv. Appl. Prob. 28, 877-894.
    • (1996) Adv. Appl. Prob. , vol.28 , pp. 877-894
    • Lefèvre, C.L.1    Picard, P.H.2
  • 17
    • 0343810514 scopus 로고    scopus 로고
    • Abel-Gontcharoff pseudopolynomials and the exact final outcome of SIR epidemic models (III)
    • LEFÈVRE CL. AND PICARD, PH. (1999). Abel-Gontcharoff pseudopolynomials and the exact final outcome of SIR epidemic models (III). Adv. Appl. Prob. 31, 530-547.
    • (1999) Adv. Appl. Prob. , vol.31 , pp. 530-547
    • Lefèvre, C.L.1    Picard, P.H.2
  • 18
    • 0002035606 scopus 로고
    • Applications of martingale theory to some epidemic models
    • PICARD, PH. (1980). Applications of martingale theory to some epidemic models. J. Appl. Prob. 17, 583-599.
    • (1980) J. Appl. Prob. , vol.17 , pp. 583-599
    • Picard, P.H.1
  • 19
    • 0001285449 scopus 로고
    • Applications of martingale theory to some epidemic models, II
    • PICARD, PH. (1984). Applications of martingale theory to some epidemic models, II. J. Appl. Prob. 21, 677-684.
    • (1984) J. Appl. Prob. , vol.21 , pp. 677-684
    • Picard, P.H.1
  • 20
    • 0000729953 scopus 로고
    • A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes
    • PICARD, PH. AND LEFèVRE CL. (1990). A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes. Adv. Appl. Prob. 22, 269-294.
    • (1990) Adv. Appl. Prob. , vol.22 , pp. 269-294
    • Picard, P.H.1    Lefèvre, C.L.2
  • 21
    • 0000827499 scopus 로고    scopus 로고
    • First crossing of basic counting processes with lower non-linear boundaries: A unified approach through pseudopolynomials (I)
    • PICARD, PH. AND LEFèVRE CL. (1996). First crossing of basic counting processes with lower non-linear boundaries: a unified approach through pseudopolynomials (I). Adv. Appl. Prob. 28, 853-876.
    • (1996) Adv. Appl. Prob. , vol.28 , pp. 853-876
    • Picard, P.H.1    Lefèvre, C.L.2
  • 22
    • 0008864518 scopus 로고
    • A recursive theorem on solving differential-difference equations and applications to some stochastic processes./ Appl
    • SEVERO, N. C. (1969a). A recursive theorem on solving differential-difference equations and applications to some stochastic processes./ Appl. Prob. 6, 673-681.
    • (1969) Prob. , vol.6 , pp. 673-681
    • Severo, N.C.1
  • 23
    • 0343382642 scopus 로고
    • The probabilities of some epidemic models
    • SEVERO, N. C. (1969b). The probabilities of some epidemic models. Biometrika 56, 197-201.
    • (1969) Biometrika , vol.56 , pp. 197-201
    • Severo, N.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.