A non-integer order dengue internal transmission model

Abstract

A non-linear mathematical model with non-integer order γ , 0 < γ ≤ 1, is used to analyze the dengue virus transmission in the human body. Both disease-free F 0 and endemic F * equilibria are calculated. Their stability is also described using the stability theorem of non-integer order. The threshold parameter R 0 demonstrates an important behavior in the stability of a considerable model. For R 0 < 1, the disease-free equilibrium (DFE) F 0 is an attractor. For R 0 > 1, F 0 is not stable, the endemic equilibrium (EE) F * exists, and it is an attractor. Numerical examples of the proposed model are also proven to study the behavior of the system.

Comparison of fractional order techniques for measles dynamics

“…For numerous ages, there have been many demarcations that address the idea of noninteger derivatives [6,7]. In this section, the Caputo (C), Riemann Liouville (RL) and Grunwald-Letnikov (GL) fractional derivative (FD) demarcations are presented.…”

“…for all p, τ in the purview of F and ν is the Hölder exponent. We represent the space of Hölder-continuous functions by W 0,ν " [7].…”

“…Definition 3 "The equilibrium point F of autonomous (13) is said to be stable if, for all > 0, ε > 0 exists such that if x 0 -F < ε, then x -F < , t ≥ 0; the equilibrium point F of autonomous (13) is said to be asymptotically unwavering if lim t→∞ x(τ ) = F " [7].…”

“…The geometrical and physical significance of the fractional integral having a complex and real conjugate power-law exponent has been suggested. One somatic implication of the non-integer order in non-integer derivatives concerns the index of memory [7]. Moreover, non-integer calculus displays a vivacious part of superdiffusive and subdiffusive measures, which make it an obliging instrument in the learning of syndrome transmission [6].…”

“…A significant role of modeling enterprises is that it can alert us to the paucities in our up-to-date understanding of the epidemiology of numerous infectious ailments, and propose critical queries for analysis and data that need to be collected. Lately, it has been applied to analyze dengue internal transmission model, bovine babesiosis disease and a tick population model, a HIV/AIDS epidemic model and the Lengyel-Epstein chemical reaction model [6,7,20,21]. Although the operating of the non-integer approach is more complex than the out-dated one, there are numerical approaches for cracking systems of DEs which are nonlinear.…”