Fractal-fractional Anthroponotic Cutaneous Leishmania model study in sense of Caputo derivative

• Published in: Alexandria engineering journal Vol. 61; no. 6; pp. 4423 - 4433
• Main Authors: Zhang, Lei, Rahman, Mati ur, Haidong, Qu, Arfan, Muhammad, Adnan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2022; Elsevier
• Subjects: Anthroponotic Cutaneous Leshmania model; Epidemic model; Fractal-fractional Caputo derivative; Numerical simulations; Fractal-fractional Caputo derivative; Numerical simulations; Epidemic model; Anthroponotic Cutaneous Leshmania model
• ISSN: 1110-0168
• DOI: 10.1016/j.aej.2021.10.001

The current paper is the analysis of an Anthroponotic Cutaneous Leishmania infection caused by a parasite known as Leishmania Tropica under the Caputo fractal-fractional operator. The problem has seven compartmental agents having two categories of human and vector population. By using the fixed point theory we show the existence and uniqueness of solutions of the system. Applying the methods of basic theorems of fractal-fractional calculus and the iterative numerical techniques of fractional Adams–Bashforth method for approximate solution. For the simulation of the model, we have considered different values for fractional-order ϱ and fractal dimension χ and compare the results with integer order for real data. The fractal-fractional calculus technique is applied as a beneficial technique to know about the real-world problem and also to controls the whole world situation of the aforesaid pandemic in the different continents and territories of the world. Finally, numerical simulations are performed to elaborate on the significance of the arbitrary order derivative. Our analysis indicates that the fractal-fractional order derivatives are more informative about the complexity of the dynamics of the proposed Leishmania model.