The stochastic SI model with recruitment and deaths. I. Comparison with the closed SIS model.

[1]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[2]  P. Whittle THE OUTCOME OF A STOCHASTIC EPIDEMIC—A NOTE ON BAILEY'S PAPER , 1955 .

[3]  Mark Bartlett,et al.  Deterministic and Stochastic Models for Recurrent Epidemics , 1956 .

[4]  On a stochastic model of an epidemic , 1967 .

[5]  T. Kurtz Solutions of ordinary differential equations as limits of pure jump markov processes , 1970, Journal of Applied Probability.

[6]  George H. Weiss,et al.  On the asymptotic behavior of the stochastic and deterministic models of an epidemic , 1971 .

[7]  T. Kurtz Limit theorems for sequences of jump Markov processes approximating ordinary differential processes , 1971, Journal of Applied Probability.

[8]  Trevor Williams,et al.  An algebraic proof of the threshold theorem for the general stochastic epidemic , 1971, Advances in Applied Probability.

[9]  Norman T. J. Bailey,et al.  The Mathematical Theory of Infectious Diseases , 1975 .

[10]  D. Stirzaker,et al.  A Perturbation Method for the Stochastic Recurrent Epidemic , 1975 .

[11]  George H. Weiss,et al.  Stochastic theory of nonlinear rate processes with multiple stationary states , 1977 .

[12]  R. H. Norden On the distribution of the time to extinction in the stochastic logistic population model , 1982, Advances in Applied Probability.

[13]  J. Gani,et al.  Matrix-geometric methods for the general stochastic epidemic. , 1984, IMA journal of mathematics applied in medicine and biology.

[14]  Lisa Sattenspiel,et al.  Modeling and analyzing HIV transmission: the effect of contact patterns , 1988 .

[15]  Richard J. Kryscio,et al.  On the Extinction of the S–I–S stochastic logistic epidemic , 1989 .

[16]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[17]  J A Jacquez,et al.  Reproduction numbers and thresholds in stochastic epidemic models. I. Homogeneous populations. , 1991, Mathematical biosciences.

[18]  John A. Jacquez,et al.  Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations , 1992 .

[19]  P Picard,et al.  An epidemic model with fatal risk. , 1993, Mathematical biosciences.

[20]  John A. Jacquez,et al.  Qualitative Theory of Compartmental Systems , 1993, SIAM Rev..

[21]  A modification of the general stochastic epidemic motivated by AIDS modelling , 1993, Advances in Applied Probability.