TY  - EJOU
AU  - Shafique, Umar 
AU  - Al-Shamiri, Mohamed Mahyoub 
AU  - Raza, Ali 
AU  - Fadhal, Emad 
AU  - Rafiq, Muhammad 
AU  - Ahmed, Nauman 

TI  - Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2024
VL  - 141
IS  - 1
SN  - 1526-1506

AB  - 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.
KW  - Bacterial Meningitis disease; stochastic delayed model; stability analysis; extinction and persistence; computational methods

DO  - 10.32604/cmes.2024.052383