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Pathogen-Immune System Model with Multiple Fractional-Orders

İlhan ÖZTÜRK, Bahatdin DAŞBAŞI

Abstract



In this study, the size of the pathogen and immune system cells in the case of an infection was modelled by fractional differential equation’s system with multi-orders. Parameters consisting of functions expressed the growth rate of immune system cells depending on the age of the individual and the level of aggression of the pathogen,were suggested in the model. These sizes have been tried to predict depending on the time. According to the results of qualitative analysis of the model, the stability of free-infection and positive equilibrium points were found to be dependent on these functions and the other parameters used in the model. In cases of different individuals anddifferent strains of pathogen causing infection,the model was supported by numerical simulations compatible with the results of this analysis to estimate the immune system response and the pathogen size.

Keywords


Fractional-order differential equation, Qualitative analysis, Stability, Numerical simulation.

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