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

作　　者：Umar Shafique Mohamed Mahyoub Al-Shamiri Ali Raza Emad Fadhal Muhammad Rafiq Nauman Ahmed 

机构地区：[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

出　　处：《Computer Modeling in Engineering & Sciences》2024年第10期311-329,共19页工程与科学中的计算机建模（英文）

基　　金：Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Project under Grant Number RGP2/302/45;supported by the Deanship of Scientific Research,Vice Presidency forGraduate Studies and Scientific Research,King Faisal University,Saudi Arabia(Grant Number A426).

摘　　要：Based on theWorld 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 deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,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.

关 键 词：Bacterial Meningitis disease stochastic delayed model stability analysis extinction and persistence computational methods 

分 类 号：O17[理学—数学]