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Numerical Simulations for stochastic Computer Virus Propagation Model

Computers, Materials & Continua 2020年第1期62卷 61-77页

作者： Muhammad Shoaib Arif Ali Raza Muhammad Rafiq Mairaj Bibi Javeria Nawaz Abbasi Amna Nazeer Umer Javed stochastic Analysis&Optimization Research Group Department of MathematicsAir UniversityPAF Complex E-9IslamabadPakistan Faculty of Engineering University of Central Punjab LahorePakistan Department of Mathematics Comsats UniversityChak Shahzad CampusIslamabadPakistan Department of Electrical and Computer Engineering Comsats UniversityWah CampusIslamabadPakistan

We are presenting the numerical simulations for the stochastic computer virus propagation model in this *** are comparing the solutions of stochastic and deterministic computer virus *** of a threshold number R0 hold in stochastic computer virus *** R_(0)1 shows virus rapidly spread in the computer ***,stochastic numerical techniques fail to cope with large step sizes of *** suggested structure of the stochastic non-standard finite difference technique can never violate the dynamical *** this basis,we can suggest a collection of strategies for removing virus’s propagation in the computer population.

关键词： Computer virus propagation model stochastic modelling stochastic processes stochastic techniques Convergence analysis

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stochastic Numerical Analysis for Impact of Heavy Alcohol Consumption on Transmission Dynamics of Gonorrhoea Epidemic

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Computers, Materials & Continua 2020年第3期62卷 1125-1142页

作者： Kamaleldin Abodayeh Ali Raza Muhammad Shoaib Arif Muhammad Rafiq Mairaj Bibi Muhammad Mohsin Department of Mathematics and General Sciences Prince Sultan UniversityRiyadhSaudi Arabia Stochatic Analysis&Optimization Research Group Department of MathematicsAir UniversityPAF Complex E-9Islamabad44000Pakistan Faculty of Engineering University of Central Punjab LahorePakistan Department of Mathematics Comsats UniversityChak Shahzad Campus park roadIslamabadPakistan Department of Mathematics Uppsala UniversityUppsalaSweden

This paper aims to perform a comparison of deterministic and stochastic *** stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic ***,the deterministic solution is itself mean of the stochastic solution of the *** numerical analysis,first,we developed some explicit stochastic methods,but unfortunately,they do not remain consistent in certain *** we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic *** proposed method is independent of the choice of parameters and behaves well in all ***,some theorems and simulations are presented in support of the article.

关键词： Heavy alcohol model stochastic techniques stability analysis

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A stochastic Numerical Analysis for Computer Virus Model with Vertical Transmission Over the Internet

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Computers, Materials & Continua 2019年第9期61卷 1025-1043页

作者： Muhammad Shoaib Arif Ali Raza Wasfi Shatanawi Muhammad Rafiq Mairaj Bibi Department of Mathematics Stochastic Analysis&Optimization Research GroupAir UniversityPAF Complex E-9Islamabad44000Pakistan Department of Mathematics and General Courses Prince Sultan University Riyadh Saudi Arabia Department of Medical Research China Medical University HospitalChina Medical UniversityTaichung40402Taiwan Faculty of Engineering University of Central PunjabLahore54500Pakistan Department of Mathematics Comsats UniversityChak Shahzad CampusIslamabad44000Pakistan

We are presenting the numerical analysis for stochastic SLBR model of computer virus over the internet in this *** are going to present the results of stochastic and deterministic computer virus *** of the threshold number C∗hold in stochastic computer virus *** C∗1 shows virus spread in the computer ***,stochastic numerical techniques fail to cope with large step sizes of *** suggested structure of the stochastic non-standard finite difference scheme(SNSFD)maintains all diverse characteristics such as dynamical consistency,bounded-ness and positivity as well-defined by *** this basis,we can suggest a collection of plans for eradicating viruses spreading across the internet effectively.

关键词： Computer virus model stochastic modelling stochastic techniques stability

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A Numerical Efficient Technique for the Solution of Susceptible Infected Recovered Epidemic Model

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Computer Modeling in Engineering & Sciences 2020年第8期124卷 477-491页

作者： Muhammad Shoaib Arif Ali Raza Kamaleldin Abodayeh Muhammad Rafiq Mairaj Bibi Amna Nazeer stochastic Analysis and Optimization Research Group Department of MathematicsAir UniversityPAF Complex E-9Islamabad44000Pakistan Department of Mathematics National College of Business Administration and EconomicsLahorePakistan Department of Mathematics and General Sciences Prince Sultan UniversityRiyadhSaudi Arabia Faculty of Engineering University of Central PunjabLahorePakistan Department of Mathematics Comsats University IslamabadIslamabadPakistan

The essential features of the nonlinear stochastic models are positivity,dynamical consistency and *** features have a significant role in different fields of computational biology and many *** aim of our paper,to achieve the comparison analysis of the stochastic susceptible,infected recovered epidemic *** stochastic modelling is a realistic way to study the dynamics of compartmental modelling as compared to deterministic *** effect of reproduction number has also observed in the stochastic susceptible,infected recovered epidemic *** comparison analysis,we developed some explicit stochastic techniques,but they are the time-dependent *** implicitly driven explicit technique has developed for the stochastic susceptible,infected recovered epidemic *** the support,some theorems and graphical illustration has ***,the time efficiency of this method makes it easy to find the solution of the stochastic *** comparison with other techniques shows the efficacy and reliability of the designed technique.

关键词： Epidemiolocal model stochastic differential equations stochastic techniques convergence analysis

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