Lokal Bakteriyel enfeksiyon durumunda çoklu antibiyotik tedavisine karşı bakteriyel direncin kesirsel mertebeden matematiksel modellemesi
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.
The Fractional-Order mathematical modeling of bacterial resistance against multiple antibiotics in case of local bacterial infection
In this study, it is described the general forms of fractional-order differential equations and asymtotic stability oftheir system’s equilibria. In addition that, the stability analysis of equilibrium points of the local bacterial infectionmodel which is fractional-order differential equation system, is made. Results of this analysis are supported vianumerical simulations drawn by datas obtained from literature for mycobacterium tuberculosis and the antibioticsisoniazid (INH), rifampicin (RIF), streptomycin (SRT) and pyrazinamide (PRZ) used against this bacterial infection.
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