Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection

Samad Noeiaghdam,Sanda Micula

doi:10.3390/math9091031

Abstract

This study focuses on solving the nonlinear bio-mathematical model of malaria infection. For this aim, the HATM is applied since it performs better than other methods. The convergence theorem is proven to show the capabilities of this method. Instead of applying the FPA, the CESTAC method and the CADNA library are used, which are based on the DSA. Applying this method, we will be able to control the accuracy of the results obtained from the HATM. Also the optimal results and the numerical instabilities of the HATM can be obtained. In the CESTAC method, instead of applying the traditional absolute error to show the accuracy, we use a novel condition and the CESTAC main theorem allows us to do that. Plotting several ℏ-curves the regions of convergence are demonstrated. The numerical approximations are obtained based on both arithmetics.

Highlights

Modeling different phenomena, solving the model by efficient methods and control and adjust their parameters are one of the important topics of bio-mathematics which have direct relation with human life
We focused on solving the nonlinear bio-mathematical model of malaria infection
Because of reflexibility of the HATM, we applied this method to find the approximate solutions of the problem

Summary

Introduction

Modeling different phenomena, solving the model by efficient methods and control and adjust their parameters are one of the important topics of bio-mathematics which have direct relation with human life. HATM is one the semi analytical methods for solving different linear and nonlinear problems. Solving integral equations [15,16,17,18], system of equations [6,10] and engineering problems [19,20] are only some of the applications of this method In this method, we have some freedom to choose the initial values, the auxiliary functions and the auxiliary parameters. We have some freedom to choose the initial values, the auxiliary functions and the auxiliary parameters One of these parameters is h , which is used to adjust and control the convergence region of the HATM. Using this parameter we can plot some h -curves and after that we will be able to find the convergence region

Objectives

Methods

Findings

Conclusion