Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

Abstract

A novel mathematical fractional model of multistrain tuberculosis with time delay memory is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the sense of the Grünwald-Letinkov definition. Modified parameters are introduced to account for the fractional order. The stability of the equilibrium points is investigated for any time delay. Nonstandard finite deference method is proposed to solve the resulting system of fractional-order delay differential equations. Numerical simulations show that nonstandard finite difference method can be applied to solve such fractional delay differential equations simply and effectively.

Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

“…In this section, we compute the reproduction number R 0 . The basic reproduction number is the expected number of secondary cases produced, in a completely susceptible population, by a typical infective individual [32]. Method in [32] is applied to derive R 0 .…”

“…Since most of the fractional-order differential equations do not have exact analytic solutions, the approximation and numerical techniques must be used [26]. Delayed fractional differential equations (DEDEs) are also used to describe dynamical systems [32], for more details, see [33][34][35]. Recently, many papers have been devoted to DEDEs (see [36][37][38], and the references cited therein).…”

Crossover Dynamics of Rotavirus Disease under Fractional Piecewise Derivative with Vaccination Effects: Simulations with Real Data from Thailand, West Africa, and the US

“…Fractional-order (FO) models have attracted greater attention from researchers during the last 20 years [27,28]. Compared to traditional integer-order models, they provide novel, accurate, and deeper information on the complicated activity of many diseases [29,30]. Due to genetic characteristics and descriptions memory, classical-order systems are not superior to FO systems.…”

Complex Social Contagions on Weighted Networks Considering Adoption Threshold Heterogeneity

“…Besides the complicated network structure, the widely existed heterogeneity of the behavioral agents also affects the information spreading [41], [42]: Because of different position [43], social users have different opinions; Because of discrepant action capabilities [44], [45], they show different waiting and response time; Because of diverse acceptance willingness [46], [47], they usually exhibit distinctive adoption thresholds to mimic the same activity; and so on. The heterogeneity alters the effect of spreading dynamics and induces sophisticated statistical physical phenomena.…”