Abstract
A birth and death process with killing and reestablishment of the total population is defined. For the process with constant rates the transient probability distribution can be obtained from a renewal equation. The ideas are applied to a model for parasitic infections.
Keywords
- Parasitic Infection
- Death Process
- Parasite Population
- Immigration Rate
- Renewal Equation
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References
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Hadeler, K.P., Dietz, K.: Population dynamics of killing parasites which reproduce in the host. J. Math. Biol. 21 (1984) 45–65.
Karlin, S., Tavaré, S.: Linear birth and death processes with killing. J. Appl. Prob. 19, 477–487 (1982).
Puri, P.S.: A method for studying the integral functionals of stochastic processes with applications III. Proc. Sixth Berkeley Symp. Math. Stat. Prob. Vol. III, 481–500, UCLA Press (1972).
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© 1986 Springer-Verlag
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Hadeler, K.P. (1986). Birth and death processes with killing and applications to parasitic infections. In: Tautu, P. (eds) Stochastic Spatial Processes. Lecture Notes in Mathematics, vol 1212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076247
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DOI: https://doi.org/10.1007/BFb0076247
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16803-4
Online ISBN: 978-3-540-47053-3
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