Solving the Model of the Risk of Microcephaly Induced by the Zika Virus (ZIKV) by a Modified Moving least Squares Method

TL;DR

This paper applies modified moving least squares meshfree methods to solve stiff ODE systems, including a Zika virus model, demonstrating improved accuracy and reliability over traditional MLS techniques.

Contribution

Introduces a modified MMLS method that reduces computational cost and avoids singular matrices, enhancing the solution of stiff ODE systems including ZIKV models.

Findings

GMLS reduces computational cost significantly.

MMLS improves accuracy and stability for stiff ODEs.

Validated methods effectively solve ZIKV-induced microcephaly model.

Abstract

The aim of this work is the application of the Meshfree methods for solving systems of stiff ordinary differential equations. These methods are based on the Moving least squares (MLS), generalized moving least squares (GMLS) approximation and Modified Moving least squares (MMLS) method. GMLS makes a considerable reduction in the cost of numerical methods. In fact, GMLS method is effect operator on the basis polynomial rather than the complicated MLS shape functions. Besides that the modified MMLS approximation method avoids undue a singular moment matrix. This allows the base functions to be of order greater than two with the same size of the support domain as the linear base functions. We also show the estimation of the error propagation obtained of the numerical solution of the systems of stiff ordinary differential equation. Some examples are provided to show that the GMLS and MMLS methods are more reliable (accurate) than classic MLS method.Finally, the (our) proposed methods are validated by solving ZIKV model which is a system of ODEs.