On the Stability Analysis of the Generalized Mathematical Model with Fractional-Order for Mycobacterium Tuberculosis

Year 2019, Volume: 9 Issue: 1, 272 - 287, 01.03.2019

Bahatdin Daşbaşı

https://doi.org/10.21597/jist.450193

Abstract

In this study, the mathematical model, based on the system of fractional-order differential equations and examined the dynamics among concentrations of multiple antibiotic, immune system cells of host and sensitive and resistant bacterial populations to antibiotic in case of bacterial infection, was proposed. The existence and uniqueness of this model solutions were showed. In addition, according to the specific conditions of the parameters used in the model, the existence of disease-free equilibrium point and the stability of this point was examined. The proposed model with numerical simulations by using the parameter values obtained from the literature for Mycobacterium Tuberculosis (Mtb) was supported, which is fully compatible with the recommended treatment method.

Keywords

Fractional-order differential equation, equilibrium point, stability, numerical simulation, mycobacterium tuberculosis

Mycobacterium Tuberculosis için Genelleştirilmiş Kesirsel Mertebeden Matematiksel Modelin Kararlılık Analizi Üzerine

Abstract

Bu çalışmada kesirsel mertebeden diferansiyel denklem sistemi temel alınarak bakteriyel bir enfeksiyon durumunda çoklu antibiyotik konsantrasyonu, bu antibiyotiklere hassas ve dirençli bakteri popülasyonları ve konakçının bağışıklık sistemi hücrelerinin aralarındaki dinamikleri inceleyen bir matematiksel model önerildi. Modelin çözümünün varlığı ve tekliği gösterildi. Ayrıca modelde kullanılan parametrelerin özel durumlarına göre, enfeksiyondan bağımsız denge noktasının varlığı ve bu denge noktasının kararlılığı bulundu. Bunlara ek olarak Mycobacterium Tuberculosis (Mtb) için literatürden elde edilen parametre değerleri kullanılarak önerilen tedavi yöntemiyle bire bir uyumlu Nümerik simülasyonlarla önerilen model desteklendi.

Keywords

Kesirli mertebeden diferansiyel denklem, denge noktası, kararlılık, nümerik simülasyon, mycobacterium tuberculosis

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