Dynamic analysis of conversion from a drug-sensitivity strain to a drug-resistant strain. (English) Zbl 1407.34074
Summary: In this paper, a mathematical model of conversion from a drug-sensitivity strain to a drug-resistant strain is given to investigate how antibiotic usage may be optimized to preserve or restore antibiotic effectiveness. This novel theoretical framework could result in an optimal criterion on how to reduce the drug resistance to a reasonable range by using the antibiotic dressing strategy. The sufficient conditions of existence of order-1 periodic solution are obtained in view of the geometrical theory of the semi-continuous dynamical system and the qualitative properties of the corresponding continuous system. The stability of the order-1 periodic solution is proved by means of H. Guo et al. [“Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property”, Appl. Math. Comput. 271, 905–922 (2015; doi:10.1016/j.amc.2015.09.046)]. Finally, our results are confirmed by means of numerical simulations.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 92D25 | Population dynamics (general) |
| 34A37 | Ordinary differential equations with impulses |
| 92C50 | Medical applications (general) |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34H05 | Control problems involving ordinary differential equations |
Keywords:
impulsive state feedback control; drug-sensitivity strain; order-1 periodic solution; drug-resistant strainReferences:
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