@article{DM_2013_25_4_a9,
author = {Sh. K. Formanov and A. N. Startsev and S. S. Sedov},
title = {Limit theorems for the generalized size of epidemic in {a~Markov} model with immunization},
journal = {Diskretnaya Matematika},
pages = {103--115},
year = {2013},
volume = {25},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2013_25_4_a9/}
}
TY - JOUR AU - Sh. K. Formanov AU - A. N. Startsev AU - S. S. Sedov TI - Limit theorems for the generalized size of epidemic in a Markov model with immunization JO - Diskretnaya Matematika PY - 2013 SP - 103 EP - 115 VL - 25 IS - 4 UR - http://geodesic.mathdoc.fr/item/DM_2013_25_4_a9/ LA - ru ID - DM_2013_25_4_a9 ER -
Sh. K. Formanov; A. N. Startsev; S. S. Sedov. Limit theorems for the generalized size of epidemic in a Markov model with immunization. Diskretnaya Matematika, Tome 25 (2013) no. 4, pp. 103-115. http://geodesic.mathdoc.fr/item/DM_2013_25_4_a9/
[1] Kermack W. O., McKendrick A. G., “Contributions to the mathematical theory of epidemics”, Proc. Roy. Lond. Soc. A, 115 (1927), 700–721 | DOI | Zbl
[2] Bartlett M. S., Vvvedenie v teoriyu sluchainykh protsessov, IL, Moskva, 1958 | MR
[3] Barucha-Rid A. T., Elementy teorii markovskikh protsessov i ikh prilozheniya, Nauka, Moskva, 1969, 512 pp. | MR
[4] Downton F., “The ultimate size of carrier-born epidemic”, Biometrika, 55:2 (1968), 277–289 | DOI | MR | Zbl
[5] Nagaev A. V., Rakhmanina G. I., “Porogovye teoremy dlya stokhasticheskoi modeli s immunizatsiei”, Mat. zametki, 8:3 (1970), 385–392 | MR | Zbl
[6] Gani J., “On the partial differential equation of epidemic theory. I”, Biometrika, 52:3–4 (1965), 617–622 | MR | Zbl
[7] Siskind V., “A solution of general stochastic epidemic”, Biometrika, 52:3–4 (1965), 613–616 | MR | Zbl
[8] Bailey N. T. J., The mathematical theory of epidemic, London, 1957 | MR
[9] Nagaev A. V., Startsev A. N., “Porogovaya teorema dlya odnoi modeli epidemii”, Mat. zametki, 3:2 (1968), 179–185 | MR | Zbl
[10] Nagaev A. V., Startsev A. N., “Asimptoticheskii analiz odnoi stokhasticheskoi modeli epidemii”, Teoriya veroyatnostei i eë prim., 15:1 (1970), 97–105 | MR | Zbl
[11] Nagaev A. V., “Nekotorye predelnye teoremy dlya obschei stokhasticheskoi modeli epidemii”, Matem. zametki, 13:5 (1973), 709–716 | MR | Zbl
[12] Startsev A. N., “Ob odnoi modeli s vzaimodeistviem chastits dvukh tipov, obobschayuschei protsess epidemii Bartletta–MakKendrika”, Teoriya veroyatnostei i eë primeneniya, 46:3 (2001), 463–482 | DOI | MR | Zbl
[13] Startsev A. N., “Asymptotic analysis of the general stochastic epidemic with variable infections periods”, J. Aplied Probablity, 38 (2001), 18–35 | DOI | MR | Zbl
[14] Mirzaev M., Startsev A. N., “Predelnye teoremy dlya odnoi modeli s vzaimodeistviem chastits dvukh tipov, obobschayuschei protsess epidemii Bartletta–MakKendrika”, Teoriya veroyatnostei i eë primeneniya, 51:2 (2006), 385–391 | DOI | MR | Zbl
[15] Foster F. G., “Note on Bailey's and Whitte's treatment of a general stochastic epidemic”, Biometrika, 42 (1955), 123–125 | MR | Zbl
[16] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Moskva, 1965 | Zbl
[17] Takach L., Kombinatornye metody v teorii sluchainykh protsessov, Mir, Moskva, 1974, 264 pp. | MR