An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator

Abstract

The present study aims to investigate a new fractional model describing the dynamical behaviour of the tuberculosis infection. In this new formulation, we use a recently introduced fractional operator with Mittag-Leffler nonsingular kernel. To solve and simulate the proposed model, a new and efficient numerical method is developed based on the product-integration rule. Simulation results are provided and some discussions are given to verify the theoretical analysis. The results indicate that employing the nonsingular operator can extract the hidden aspects of the model under consideration while these features are invisible when we use the ordinary time-derivatives. Therefore, the non-integer calculus supplies more flexible models describing the asymptotic behaviours of the real-world phenomena and helps us to better understand their complex dynamics.

A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

“…With this change, the right and left sides will not have the same dimension. To solve this problem, we use an auxiliary parameter λ , having the dimension of sec., to change the fractional operator so that the sides have the same dimension [29] . According to the explanation presented, the corona virus transmission fractional model for t > 0 and η ∈ (0, 1) is given by where initial conditions are .…”

A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

“…With this change, the right-and left-hand sides will not have the same dimension. To solve this problem, we use an auxiliary parameter ρ, having the dimension of sec., to change the fractional operator so that the sides have the same dimension [43]. According to the explanation presented, the COVID-19 transmission fractional model for t ≥ 0 and η ∈ (0, 1) is given as follows:…”

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

“…The ordinary derivative has an inverse second dimension and the fractional derivative has a dimension of . To solve this problem, we use an auxiliary parameter θ that has a second dimension s and is called the cosmic time [ 41 ]. By the parameter, from a physical point of view, we will have .…”