# Mean Latin Hypercube Runge-Kutta Method to Solve the Influenza Model

## Authors

• Shatha Jabbar Mohammed Department of Mathematics, College of Education for Pure Science / Ibn al-Haytham University of Baghdad, 47146, Baghdad, Iraq
• Maha A. Mohammed Department of Mathematics, College of Education for Pure Science / Ibn al-Haytham University of Baghdad, 47146, Baghdad, Iraq https://orcid.org/0000-0001-7209-2096

## Keywords:

Nonlinear system of ordinary differential equations, Epidemic model, Runge-Kutta (RK) method, Latin Hypercube Sampling (LHS) method, Numerical simulation methods

## Abstract

In this study, we propose a suitable solution for a non-linear system of ordinary differential equations (ODE) of the first order with the initial value problems (IVP) that contains multi variables and multi-parameters with missing real data. To solve the mentioned system, a new modified numerical simulation method is created for the first time which is called Mean Latin Hypercube Runge-Kutta (MLHRK). This method can be obtained by combining the Runge-Kutta (RK) method with the statistical simulation procedure which is the Latin Hypercube Sampling (LHS) method. The present work is applied to the influenza epidemic model in Australia in 1919  for a previous study. The comparison between the numerical and numerical simulation results is done, discussed and tabulated. The behavior of subpopulations is shown graphically. MLHRK method can reduce the number of numerical iterations of RK, and the number of LHS simulations, thus it saves time, effort, and cost.  As well as it is a faster simulation over the distribution of the LHS. The MLHRK method has been proven to be effective, reliable, and  convergent to solve a wide range of linear and nonlinear problems. The proposed method can predict the future behavior of the population under study in analyzing the behavior of some epidemiological models.

2022-03-30

## How to Cite

Mohammed, S. J. . ., & Mohammed, M. A. (2022). Mean Latin Hypercube Runge-Kutta Method to Solve the Influenza Model. Iraqi Journal of Science, 63(3), 1158–1177. https://doi.org/10.24996/ijs.2022.63.3.22

## Section

Mathematics  