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Matematicheskie Zametki, 1970, Volume 8, Issue 3, Pages 385–392
(Mi mzm9573)
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This article is cited in 1 scientific paper (total in 1 paper)
Threshold theorems for a stochastic model of an epidemic with natural immunization
A. V. Nagaev, G. I. Rakhmanina V. I. Romanovskii Mathematics Institute, Academy of Sciences of the Uzbekistan SSR
Abstract:
A stochastic model of an epidemic is investigated, taking account of the removal of ill members of the population (by death, by recovery with immunization, by isolation) and natural immunization. Limiting distributions are found for the size $\nu$ of the epidemic, the number immunized $\nu_1$, and their sum, under the assumption that the original number of susceptible individuals $n\to\infty$ and the number of ill individuals $m\to\infty$, while $\lambda n\to1$, $\mu n\leqslant\alpha_0<\infty$,, where $\lambda$ and $\mu$ are the coefficients for the contraction of the disease and of immunization respectively.
Received: 26.03.1969
Citation:
A. V. Nagaev, G. I. Rakhmanina, “Threshold theorems for a stochastic model of an epidemic with natural immunization”, Mat. Zametki, 8:3 (1970), 385–392; Math. Notes, 8:3 (1970), 686–690
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https://www.mathnet.ru/eng/mzm9573 https://www.mathnet.ru/eng/mzm/v8/i3/p385
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Abstract page: | 140 | Full-text PDF : | 70 | First page: | 1 |
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