Mathematical Analysis of Fractional Order Co-Infection TB and HIV Model

Muhammad Farman ,Muhammad Usman ,Aqeel Ahmad ,Manzoor Ahmad

doi:10.28924/2291-8639-18-2020-16

Abstract

A mathematical model of HIV/AIDS and TB including its co-infections is formulated. We find the Equilibrium points and with the help of numerical simulation, we have analyze that the sub-models of TB, HIV/AIDS and its co-infections. The Caputo and Caputo Febrizo fractional derivative operator of order α ∈ (0, 1] is employed to obtain the system of fractional differential equations. Laplace Adomian Decomposition Method was successfully used for solving the different differential equations.Laplace transform is a perfect technique in various field of biological science,engineering,pure and applied mathematics. The latest technique Laplace Adomian Decomposition Method is employed on the developed fractional order model for the numerical solutions. Finally numerical simulations are also established to investigate the influence of the system parameter on the spread of disease and which show effect of fractional parameter α on our obtained solutions.

Highlights

Mathematics plays a key role in many scientific disciplines, primarily as a mathematical modeling tool
We find the Equilibrium points and with the help of numerical simulation, we have analyzed that the sub-models of TB, HIV/AIDS and its co-infections
Laplace Adomian Decomposition Method was successfully used for solving the different differential equations.Laplace transform is a perfect technique in various field of biological science,engineering,pure and applied mathematics

Summary

Introduction

Mathematics plays a key role in many scientific disciplines, primarily as a mathematical modeling tool. The use of mathematics in biology is important because biology becomes more quantitative This new discipline has applications in the fields of biology, biomedicine and biotechnology. Tuberculosis and AIDS Tuberculosis and HIV co-infection refer to people with both HIV infection and latent or active TB. The World Health Organization (WHO) estimates that between 2005 and 2012, cooperation activities in tuberculosis prevention and treatment, including TB prevention, antiretroviral therapy and HIV testing, were reinstated at 1.3 million. As a result, these cooperative activities have infected humans by reducing tuberculosis and HIV. In people co-infected with HIV and TB, antiviral therapy may reduce the risk of developing latent tuberculosis tuberculosis.

Mathematical Model

Model parameters and its formulation

Preliminaries

Fractional Order Model with Caputo Febrizio Sense

Numerical Results and Discussion

Conclusion