Mathematical Modelling of Bacterial Competition with Multiple Antibiotics and it's Stability Analysis

Bahatdin Daşbaşı, İlhan Öztürk, Fatma Özköse

Abstract


Bacteria affecting organisms in different ways  appear to have many different characteristics such as these compete with their neighbors for space and resources in nature. There is always the need to develop various therapeutic strategies to combat many fatal diseases  such as pneumonia, bloodstream infections, meningitis, urinary tract infection and tuberculosis caused by bacteria such as Acinetobacter baumannii, Escherichia coli, Helicobacter pyroli and Mycobacterium tuberculosis. Among these therapeutic strategies, the theraphy of  special multiple antibiotics against the bacteria that cause disease is the most common one in the world. In general, the bacterial infection is a complex process for not only the infectious bacteria but also the host. This process in experimental studies is very complex because of interactions between the bacteria causing the infections. Hence, It has led to the need to interpret the process by methods such as statistical analysis of the data and mathematical modeling. In this way, it has proposed a mathematical model describing population dynamics in  two species bacteria competing each others and exposed to multiple antibiotics simultaneously. Qualitative analysis revealed of the equilibrium points at which  only one species of bacteria exist, both species of bacteria exist and  both species of bacteria do not exist. In addition, the results of the analysis that consistent with datas obtained from experimental studies have supported by numerical simulations.

Keywords


Ordinary differential equations system; Equilibrium point; Qualitative analysis

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DOI: http://dx.doi.org/10.7212%2Fzkufbd.v6i2.260

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