Theoretical Analysis and Simulation of a Fractional-Order Compartmental Model with Time Delay for the Propagation of Leprosy

Fractal and Fractional

article

Zafar Iqbal¹  Nauman Ahmed¹  Jorge E. Macías-Díaz² 

[1] Department of Mathematics and Statistics, The University of Lahore;Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University;Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria

关键词: fractional epidemic model;    leprosy infection with memory effects;    non-standard finite-difference scheme;    local and stability analyses;    numerical simulations30G35;    35F15;    31B10;    74B05;    35Q60;   

DOI  :  10.3390/fractalfract7010079

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

This article investigates the propagation of a deadly human disease, namely leprosy. At the outset, the mathematical model is transformed into a fractional-order model by introducing the Caputo differential operator of arbitrary order. A result is established, which ensures the positivity of the fractional-order epidemic model. The stability of the continuous model at different points of equilibria is investigated. The basic reproduction number, R 0, is obtained for the leprosy model. It is observed that the leprosy system is locally asymptotically stable at both steady states whenR 0< 1. On the other hand, the fractional-order system is globally asymptotically stable whenR 0 1. To find the approximate solutions for the continuous epidemic model, a non-standard numerical scheme is constructed. The main features of the non-standard scheme (such as positivity and boundedness of the numerical method) are also confirmed by applying some benchmark results. Simulations and a feasible test example are presented to discern the properties of the numerical method. Our computational results confirm both the analytical and the numerical properties of the finite-difference scheme.

【 授权许可】

CC BY