Analysis of dengue transmission using fractional order scheme - Nisar, Kottakkaran Sooppy; Ahmad, Aqeel; İnç, Mustafa; Farman, Muhammad; Rezazadeh, Hadi; Akinyemi, Lanre; Akram, Muhammad Mannan (Amer Inst Mathematical Sciences-Aims, 2022)
In this paper, we will check the existence and stability of the dengue internal transmission model with fraction order derivative as well as analyze it qualitatively. The solution has been determined using Atangana-Baleanu in Caputo sense (ABC) with the help of Sumudu transform (ST). Atangana-Toufik (AT) and fractal fractional operator are used to analyze the dengue transmission which is an advanced approach for such types of biological models. Existence theory and uniqueness for the equilibrium solution are provided via nonlinear functional analysis and fixed point theory. Global stability of the system was also proved by using the Lyapunov function. Such kind of study helps us to analyze dengue transmission which shows the actual effect of dengue transmission in society, also will be helpful in future analysis and control strategies.
Keywords: dengue model; Sumudu transform; Atangana-Toufik scheme; uniqueness; fractal fractional operator