S. I. Kabanikhin, O. I. Krivorot'ko, V. A. Latyshenko, D. V. Yermolenko, V. N. Kashtanova, “Inverse problems of immunology and epidemiology”, Eurasian Journal of Mathematical and Computer Applications, 2017, Volume 5, Issue 2,Pages <nobr>14

Inverse problems of immunology and epidemiology

S. I. Kabanikhin^ab, O. I. Krivorot'ko^ba, V. A. Latyshenko^b, D. V. Yermolenko^ab, V. N. Kashtanova^b

^a Institute of Computational Mathematics and Mathematical Geophysics SB RAS Prospekt Akad. Lavrentyeva 6, Novosibirsk, 630090, Russia
^b Novosibirsk State University Pirogova str. 2, Novosibirsk, 630090, Russia

Abstract: A parameter identification problem (inverse problem) for some mathematical models of HIV dynamics and tuberculosis epidemics with experimental observations is investigated. The inverse problems are reduced to a minimization problem. The optimization problem is solved with the help of stochastic methods: a genetic algorithm and fast simulated annealing. The results of numerical calculations are presented.

Keywords: Inverse problem, ordinary differential equations, optimization problem, parameter identification, genetic algorithm, simulated annealing.

MSC: 49M30, 65L09, 92B05.

Received: 22.02.2017

Language: English