## Attainable set of a SIR epidemiological model with constraints on vaccination and treatment stocks.(English)Zbl 1441.92043

Summary: In this paper the controllable spread of some infectious disease is considered. The evolution model of the disease is described by the 3-dimensional nonlinear ordinary differential equations system. Vaccination and treatment are accepted as control parameters of the system. It is assumed that the stocks of vaccination and treatment is limited. Attainable sets of the system are approximately calculated for different control stocks. Graphical results are presented and possible biological applications are discussed.

### MSC:

 92D30 Epidemiology 92C60 Medical epidemiology 93B03 Attainable sets, reachability 93B05 Controllability 93C15 Control/observation systems governed by ordinary differential equations

### Keywords:

SIR model; attainable set; control system; integral constraint
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### References:

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