Open Access Open Access  Restricted Access Subscription or Fee Access

Pathogen-Immune System Model with Multiple Fractional-Orders

İlhan ÖZTÜRK, Bahatdin DAŞBAŞI


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.


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

Full Text:



  • There are currently no refbacks.

Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.