The Stability of a Tumor-Macrophages Model with Caputo Fractional Operator

被引:3
|
作者
Dehingia, Kaushik [1 ,2 ]
Boulaaras, Salah [3 ]
机构
[1] Sonari Coll, Dept Math, Sonari 785690, Assam, India
[2] Near East Univ, Math Res Ctr, Mersin 10, TR-99318 Nicosia, Turkiye
[3] Qassim Univ, Coll Sci, Dept Math, Buraydah 52571, Saudi Arabia
关键词
fractional derivatives; mathematical operators; tumor; macrophages; stability; numerical study; IMMUNE-SYSTEM; MATHEMATICAL-MODEL; CANCER; DYNAMICS; GROWTH;
D O I
10.3390/fractalfract8070394
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This study proposes a fractional-order model in the Caputo sense to describe the interaction between tumor and immune macrophages by assuming that the pro-tumor macrophages induce a Holling type-II response to the tumor. Then, the basic properties of the solutions to the model are studied. Local stability analysis is conducted at each of the equilibria in the model, and a numerical study is performed with varying activation rates of type-II or pro-tumor macrophages and the order of the fractional operator. The numerical findings suggest that type-I or anti-tumor macrophages can stabilize the system if the activation rate of type-II or pro-tumor macrophages is low. Still, for a higher value of the activation rate for type-II or pro-tumor macrophages, the proliferation of tumor cells is uncontrollable and the system becomes unstable. Furthermore, the stability of the system decreases as the order of the fractional operator increases.
引用
收藏
页数:15
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