The Fractional-Order mathematical modeling of bacterial resistance against multiple antibiotics in case of local bacterial infection

Abstract

In this study, it is described the general forms of fractional-order differential equations and asymtotic stability of their system’s equilibria. In addition that, the stability analysis of equilibrium points of the local bacterial infection model which is fractional-order differential equation system, is made. Results of this analysis are supported via numerical simulations drawn by datas obtained from literature for mycobacterium tuberculosis and the antibiotics isoniazid (INH), rifampicin (RIF), streptomycin (SRT) and pyrazinamide (PRZ) used against this bacterial infection.

Keywords

• Fractional-order differential equation system,Mathematical model,Stability analysis,Equilibrium points,Multiple antibiotics

Lokal Bakteriyel enfeksiyon durumunda çoklu antibiyotik tedavisine karşı bakteriyel direncin kesirsel mertebeden matematiksel modellemesi

Abstract

Bu çalışmada kesirsel mertebeden diferansiyel denklemlerin genel biçimi ve bu denklemlerin sistemlerinin
dengelerinin asimptotik kararlılıkları tanımlandı. Ayrıca kesirsel mertebeden diferansiyel denklem sistemi şeklinde
ifade edilen lokal bir bakteriyel enfeksiyon modelinin denge noktalarının kararlılık analizi yapıldı. Bu analizin
sonuçları mycobacterium tuberculosis bakterisi ve bu bakterinin neden olduğu enfeksiyona karşı kullanılan isoniazid
(INH), rifampicin (RIF), streptomycin (SRT) ve pyrazinamide (PRZ) antibiyotikleri için literatürden elde edilen
veriler kullanılarak çizilen nümerik simülasyonlar vasıtasıyla desteklendiler.  

Keywords

• Kesirsel mertebeden diferansiyel denklem sistemi,Matematiksel model,Kararlılık analizi,Denge noktaları,Çoklu antibiyotik tedavisi

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