Geodesic
Asymptotic expansions of solutions in a singularly perturbed model of virus evolution
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 2, pp. 242-252 
A. A. Archibasov; A. Korobeinikov; V. A. Sobolev. Asymptotic expansions of solutions in a singularly perturbed model of virus evolution. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 2, pp. 242-252. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a8/
@article{ZVMMF_2015_55_2_a8,
     author = {A. A. Archibasov and A. Korobeinikov and V. A. Sobolev},
     title = {Asymptotic expansions of solutions in a singularly perturbed model of virus evolution},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {242--252},
     year = {2015},
     volume = {55},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a8/}
}
TY  - JOUR
AU  - A. A. Archibasov
AU  - A. Korobeinikov
AU  - V. A. Sobolev
TI  - Asymptotic expansions of solutions in a singularly perturbed model of virus evolution
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 242
EP  - 252
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a8/
LA  - ru
ID  - ZVMMF_2015_55_2_a8
ER  - 
%0 Journal Article
%A A. A. Archibasov
%A A. Korobeinikov
%A V. A. Sobolev
%T Asymptotic expansions of solutions in a singularly perturbed model of virus evolution
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 242-252
%V 55
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_2_a8/
%G ru
%F ZVMMF_2015_55_2_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

An initial boundary value problem for a singularly perturbed system of partial integro-differential equations involving two small parameters multiplying the derivatives is studied. The problem arises in a virus evolution model. An asymptotic solution of the problem is constructed by the Tikhonov–Vasil’eva method of boundary functions. The analytical results are compared with numerical ones.

[1] Tikhonov A. N., “Sistemy differentsialnykh uravnenii, soderzhaschie malye parametry pri proizvodnykh”, Mat. sb., 31(73):3 (1952), 575–586

[2] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vysshaya shkola, M., 1990

[3] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973

[4] Vasileva A. B., Butuzov V. F., “Asimptotika resheniya integrodifferentsialnogo uravneniya s malym parametrom pri proizvodnoi”, Chislennye metody resheniya differentsialnykh i integralnykh uravnenii i kvadraturnye formuly, Vychislitelnaya matematika i matematicheskaya fizika, 1964, 183–191

[5] Korobeinikov A., Dempsey C., “A continuous phenotype space model of RNA virus evolution within a host”, Math. Biosci. Eng., 11:4 (2014), 919–927 | DOI

[6] Nowak M. A., May R. M., Virus dynamics: mathematical principles of immunology and virology, OUP, Oxford, 2000

[7] Korobeinikov A., “Global properties of basic virus dynamics models”, Bull. Math. Biol., 66:4 (2004), 879–883 | DOI

[8] Korobeinikov A., “Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate”, Math. Med. Biol., 26:3 (2009), 225–239 | DOI

[9] Nefedov N. N., Nikitin A. G., Urazgildina T. A., “Zadacha Koshi dlya singulyarno vozmuschennogo integrodifferentsialnogo uravneniya Volterra”, Zh. vychisl. matem. i matem. fiz., 46:5 (2006), 805–812

[10] Nefedov N. N., Nikitin A. G., “Zadacha Koshi dlya singulyarno vozmuschennogo integrodifferentsialnogo uravneniya Fredgolma”, Zh. vychisl. matem. i matem. fiz., 47:4 (2007), 655–664

[11] Nefedov N. N., Nikitin A. G., “Nachalno-kraevaya zadacha dlya nelokalnogo singulyarno vozmuschennogo uravneniya reaktsiya-diffuziya”, Zh. vychisl. matem. i matem. fiz., 52:6 (2012), 1042–1047

[12] Nefedov N. N., Omelchenko O. E., “Pogransloinye resheniya v kvazilineinykh integrodifferentsialnykh uravneniyakh vtorogo poryadka”, Zh. vychisl. matem. i matem. fiz., 42:4 (2002), 491–503

[13] Vasileva A. B., “Asimptoticheskie formuly dlya reshenii sistem obyknovennykh differentsialnykh uravnenii, soderzhaschikh pri proizvodnykh parametry razlichnykh poryadkov malosti”, Dokl. AN SSSR, 128:6 (1959), 1110–1113

[14] Vasileva A. B., “Asimptoticheskie metody v teorii obyknovennykh differentsialnykh uravnenii s malymi parametrami pri starshikh proizvodnykh”, Zh. vychisl. matem. i matem. fiz., 3:4 (1963), 611–642

[15] Sobolev V. A., Tropkina E. A., “Asimptoticheskie razlozheniya medlennykh invariantnykh mnogoobrazii i reduktsiya modelei khimicheskoi kinetiki”, Zh. vychisl. matem. i matem. fiz., 52:1 (2012), 81–96

[16] Sobolev V. A., Schepakina E. A., Reduktsiya modelei i kriticheskie yavleniya v makrokinetike, Fizmatlit, M., 2010