Open Access

ARTICLE

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Umar Shafique^1,*, Mohamed Mahyoub Al-Shamiri², Ali Raza³, Emad Fadhal^4,*, Muhammad Rafiq^5,6, Nauman Ahmed^5,7

1 Department of Mathematics, National College of Business Administration and Economics, Lahore, 54660, Pakistan
2 Department of Mathematics, Applied College, Mahayl Assir, King Khalid University, Abha, 62529, Saudi Arabia
3 Department of Physical Sciences, The University of Chenab, Gujrat, 50700, Pakistan
4 Department of Mathematics & Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa, 31982, Saudi Arabia
5 Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1102-2801, Lebanon
6 Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, 54000, Pakistan
7 Department of Mathematics and Statistics, University of Lahore, Lahore, 54000, Pakistan

* Corresponding Authors: Umar Shafique. Email: ; Emad Fadhal. Email:

(This article belongs to the Special Issue: Mathematical Aspects of Computational Biology and Bioinformatics-II)

Computer Modeling in Engineering & Sciences 2024, 141(1), 311-329. https://doi.org/10.32604/cmes.2024.052383

Received 31 March 2024; Accepted 28 June 2024; Issue published 20 August 2024

Abstract

Based on the World Health Organization (WHO), Meningitis is a severe infection of the meninges, the membranes covering the brain and spinal cord. It is a devastating disease and remains a significant public health challenge. This study investigates a bacterial meningitis model through deterministic and stochastic versions. Four-compartment population dynamics explain the concept, particularly the susceptible population, carrier, infected, and recovered. The model predicts the nonnegative equilibrium points and reproduction number, i.e., the Meningitis-Free Equilibrium (MFE), and Meningitis-Existing Equilibrium (MEE). For the stochastic version of the existing deterministic model, the two methodologies studied are transition probabilities and non-parametric perturbations. Also, positivity, boundedness, extinction, and disease persistence are studied rigorously with the help of well-known theorems. Standard and nonstandard techniques such as Euler Maruyama, stochastic Euler, stochastic Runge Kutta, and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model. Unfortunately, standard methods fail to restore the biological properties of the model, so the stochastic nonstandard finite difference approximation is offered as an efficient, low-cost, and independent of time step size. In addition, the convergence, local, and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero. The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

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