doiSerbia

On conformable mathematical model of immune system coupled with intestinal microbiome

Waheed Asif (Department of Mathematics, COMSATS University Islamabad, Attock Campus, Islamabad, Pakistan)
Nazir Aqsa (Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan)
Ahmed Sohail (Department of Mathematics, COMSATS University Islamabad, Attock Campus, Islamabad, Pakistan)
Zeb Muhammad (Department of Mathematics, COMSATS University Islamabad, Attock Campus, Islamabad, Pakistan)
Ahmed Naveed (Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan)
Khan Umar (Department of Mathematics and Statistics, Hazra University, Mansehra, Pakistan)
Tauseef Mohyud-Din Syed (Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan)

Sometimes, an increased reaction is caused by an immune system of the body to a non-toxic agent (e. g. eggs, dust, pollens or some drugs). This is called allergy or hypersensitivity. The regulatory T cells decrease these allergic reactions. Nowadays, it is noticed that immune system has a deep relationship with micro-organism present in the intestine, that can be explained by the example, that some bacteria of intestine increase production of Treg cells by producing butyric acid like fatty acids. This can also understand that sufficiently different types of T cell receptors of Treg cells are needed to stop the inflammatory response produced by intestinal bacteria. In this study, the dynamic relation of T helper cells, intestinal bacteria and Treg cells are illustrated by a conformable mathematical model. Memory effects are figured out and displayed through graphs. Different plots also show the effects of increasing/decreasing amount of Treg induction efficiency on the whole system.

Keywords: intestinal microbiome, conformable derivative, immune system, initial value problem, non-linear differential equations