The analysis of a new fractional model to the Zika virus infection with mutant

被引:3
|
作者
Zafar, Zain Ul Abadin [1 ]
Khan, Muhammad Altaf [2 ]
Inc, Mustafa [3 ,4 ,11 ]
Akgul, Ali [5 ,6 ,7 ]
Asiri, Mohammed [8 ]
Riaz, Muhammad Bilal [9 ,10 ]
机构
[1] Univ Cent Punjab, Fac Sci & Technol, Dept Math, Lahore, Pakistan
[2] Univ Free State, Inst Ground Water Studies, Fac Nat & Agr Sci, Bloemfontein, South Africa
[3] Firat Univ, Sci Fac, Dept Math, Elazig, Turkiye
[4] China Med Univ, Dept Med Res, Taichung, Taiwan
[5] Lebanese Amer Univ, Dept Comp Sci & Math, Beirut, Lebanon
[6] Siirt Univ, Art & Sci Fac, Dept Math, TR-56100 Siirt, Turkiye
[7] Near East Univ, Math Res Ctr, Dept Math, Near East Blvd, TR-99138 Nicosia 10, Mersin, Turkiye
[8] King Khalid Univ, Coll Appl Med Sci, Dept Clin Lab Sci, POB 61413, Abha 9088, Saudi Arabia
[9] VSB Tech Univ Ostrava, IT4Innovat, Ostrava, Czech Republic
[10] Lebanese Amer Univ, Dept Comp Sci & Math, Byblos, Lebanon
[11] Biruni Univ, Dept Comp Engn, Turkiye, TR-34010 Istanbul, Turkiye
关键词
Zika model with mutant; AB operator; Simulation results; Existence and uniqueness; Sensitivity analysis; MATHEMATICAL-MODEL; DYNAMICS; TRANSMISSION; COVID-19; SPREAD;
D O I
10.1016/j.heliyon.2023.e23390
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
We present a new mathematical model to analyze the dynamics of the Zika virus (ZV) disease with the mutant under the real confirmed cases in Colombia. We give the formulation of the model initially in integer order derivative and then extend it to a fractional order system in the sense of the Mittag-Leffler kernel. We study the properties of the model in the Mittag-Leffler kernel and establish the result. The basic reproduction of the fractional system is computed. The equilibrium points of the Zika virus model are obtained and found that the endemic equilibria exist when the threshold is greater than unity. Further, we show that the model does not possess the backward bifurcation phenomenon. The numerical procedure to solve the problem using the Atangana-Baleanu derivative is shown using the newly established numerical scheme. We consider the real cases of the Zika virus in Colombia outbreak are considered and simulate the model using the nonlinear least square curve fit and computed the basic reproduction number R0= 0.4942, whereas in previous work (Alzahrani et al., 2021) [1], the authors computed the basic reproduction number R0 = 0.5447. This is due to the fact that our work in the present paper provides better fitting to the data when using the fractional order model, and indeed the result regarding the data fitting using the fractional model is better than integer order model. We give a sensitivity analysis of the parameters involved in the basic reproduction number and show them graphically. The results obtained through the present numerical method converge to its equilibrium for the fractional order, indicating the proposed scheme's reliability.
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页数:16
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