A nonlinear control model of a firm describing the change of production and accumulated R&D investment is investigated. An optimal control problem with R&D investment rate as a control parameter isâ€¦ (More)

Biological treatment of waste water involves bacteria, which remove waste products from the treated water and kill pathogens. Thus, this problem is closely linked to both the population dynamics andâ€¦ (More)

A SEIR control model describing the Ebola epidemic in a population of a constant size is considered over a given time interval. It contains two intervention control functions reflecting efforts toâ€¦ (More)

Abstract. We consider a controlled system of differential equations modeling a firm that takes a loan in order to expand its production activities. The objective is to determine the optimal loanâ€¦ (More)

A two-dimensional microeconomic model with three bounded controls is created and investigated. The model describes a manufacturer producing a consumer good and a retailer that buys this product inâ€¦ (More)

An activated sludge process (ASP) is a biochemical process employed for treating sewage and industrial waste-water, which uses microorganisms and air (or oxygen) to biologically oxidize organicâ€¦ (More)

A nonlinear controlled system of differential equations has been constructed to describe the process of production and sales of a consumer good. This model can be controlled either by the rate ofâ€¦ (More)

In this paper, we study a three-dimensional nonlinear model of a controllable reaction [X]+[Y]+[Z]â†’[Z], where the reaction rate is given by a unspecified nonlinear function. A model of this typeâ€¦ (More)

A SEIR type model for the spread of Ebola epidemic in a population of constant size is considered. In order to control the spread of infection and prevent such epidemics, we add to the model fourâ€¦ (More)