Dynamical analysis of the avian–human influenza epidemic model using multistage analytical method

Abstract

In this paper, analytical result of avian-human influenza epidemic model has been investigated by applying homotopy analysis method (HAM) and by expanding it to hybrid numeric-analytic method which is known as multistage HAM (MSHAM). HAM is an algorithm which gives us the approximate solution of the problem in an arrangement of time interims and by modifying it to multistage one. Some advantages such as flexibility of picking the auxiliary linear operator and the auxiliary parameter are emerged, that leads us to achieve some excellent results in this work. Furthermore, in this analytical work, obtained results are compared and reported with numerical ones which were obtained previously from methods such as the Runge-Kutta (RK4) method.

Optimal Control Design of the In-vivo HIV Fractional Model

“…Over time, mathematical modeling has played an important role in analyzing the dynamics of diseases such as tuberculosis, malaria and acquired immune deficiency syndrome (AIDS). Where it played an important role in the comprehension of the epidemiological patterns of disease treatment [3,4,5]. Also, the optimal control theory is a very important and effective tool in disease modeling as it provides strategies that are appropriate for the prevention and control of diseases [6,7,8,9].…”

Optimal control of a fractional order model for the COVID – 19 pandemic

“…Over the years mathematical modeling has been used in analyzing different dynamics of diseases, like Malaria, Tuberculosis and HIV/AIDS, it also plays a very important role in understanding the epidemiological patterns of the diseases control, because it can provides short and long term prediction of the incidence of the diseases [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] .…”

A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

“…Over the past several years, various studies have been carried out to construct an appropriate mathematical model for various disease dynamics, including those of tuberculosis, malaria, and HIV [ 1 , 2 , 3 , 4 , 5 ]. Mathematical modeling of diseases plays an important role in profound understanding of the system for the purpose of disease control due to the fact that it enables long- and short-term prediction of disease incidence [ 6 , 7 , 8 , 9 , 10 , 11 ]. Since the study by [ 12 ] on the modeling of diseases, which was a breakthrough in this area, dynamical systems approaches have been used for a wide variety of diseases.…”