Open Access

ARTICLE

Analysis of Pneumonia Model via Efficient Computing Techniques

by Kamaledin Abodayeh¹, Ali Raza^2,3,*, Muhammad Rafiq⁴, Muhammad Shoaib Arif⁵, Muhammad Naveed⁵, Zunir Zeb³, Syed Zaheer Abbas³, Kiran Shahzadi³, Sana Sarwar³, Qasim Naveed³, Badar Ul Zaman³, Muhammad Mohsin⁶

1 Department of Mathematics and General Sciences, Prince Sultan University Riyadh, 66833, Saudi Arabia
2 Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, 52000, Punjab Higher Education Department (PHED), Lahore, 54000, Pakistan
3 Department of Mathematics, National College of Business Administration and Economics Lahore, 54660, Pakistan
4 Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, 54500, Pakistan
5 Department of Mathematics, Air University, Islamabad, 44000, Pakistan
6 Department of Mathematics, Technische Universitat Chemnitz, 62 09111, Germany

* Corresponding Author: Ali Raza. Email:

(This article belongs to the Special Issue: Emerging Trends and Real-World Applications of Intelligent Computing Techniques)

Computers, Materials & Continua 2022, 70(3), 6073-6088. https://doi.org/10.32604/cmc.2022.020732

Received 06 June 2021; Accepted 20 August 2021; Issue published 11 October 2021

Abstract

Pneumonia is a highly transmissible disease in children. According to the World Health Organization (WHO), the most affected regions include south Asia and sub-Saharan Africa. Worldwide, 15% of pediatric deaths can be attributed to pneumonia. Computing techniques have a significant role in science, engineering, and many other fields. In this study, we focused on the efficiency of numerical techniques via computer programs. We studied the dynamics of the pneumonia-like infections of epidemic models using numerical techniques. We discuss two types of analysis: dynamical and numerical. The dynamical analysis included positivity, boundedness, local stability, reproduction number, and equilibria of the model. We also discuss well-known computing techniques including Euler, Runge Kutta, and non-standard finite difference (NSFD) for the model. The non-standard finite difference (NSFD) technique shows convergence to the true equilibrium points of the model for any time step size. However, Euler and Runge Kutta do not work well over large time intervals. Computing techniques are the suitable tool for crosschecking the theoretical analysis of the model.

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Citations