V. V. Malygina, M. V. Mulyukov, N. V. Pertsev, “On local asymptotic stability of a model of epidemic process”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>1301

Differentical equations, dynamical systems and optimal control

On local asymptotic stability of a model of epidemic process

V. V. Malygina^a, M. V. Mulyukov^a, N. V. Pertsev^b

^a Perm National Research Polytechnic University, Komsomolskiy pr., 29, 614990, Perm, Russia
^b Sobolev Institute of Mathematics SB RAS, Omsk Division, Pevtsova street 13, 644033,Omsk, Russia

Abstract: We consider a model of the epidemic process, and use a system of differential equations with retarded argument for the description of the model. We obtain a number of stability tests for the nontrivial equilibrium point and construct stability regions in the parameter space of the original problem.

Keywords: epidemic process, mathematical model, delay differential equation, stability, stability region.

UDC: 517.929

MSC: 34K06,34K20

Received August 23, 2018, published October 30, 2018

DOI: 10.17377/semi.2018.15.106