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Numerical Treatment for Stochastic Computer Virus Model

Computer Modeling in Engineering & Sciences 2019年第8期120卷 445-465页

作者： Ali Raza Muhammad Shoaib Arif Muhammad Rafiq Mairaj Bibi Muhammad Naveed Muhammad Usman Iqbal Zubair Butt Hafiza Anum Naseem Javeria Nawaz Abbasi Department of Mathematics Stochastic Analysis&Optimization Research GroupAir UniversityPAF Complex E-9IslamabadPakistan Faculty of Engineering University of Central Punjab LahorePakistan Department of Mathematics Comsats UniversityPark Road Chak Shahzad CampusIslamabadPakistan Faculty of Computing National College of Business Administration and Economics LahorePakistan

This writing is an attempt to explain a reliable numerical treatment for stochastic computer virus model.We are comparing the solutions of stochastic and deterministic computer virus models.This paper reveals that a stochastic computer virus paradigm is pragmatic in contrast to the deterministic computer virus model.Outcomes of threshold number C^?hold in stochastic computer virus model.If C^?1 shows virus persists in the computer population.Unfortunately,stochastic numerical methods fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference scheme(Snsfd)maintains all diverse characteristics such as dynamical consistency,boundedness and positivity as defined by Mickens.The numerical treatment for the stochastic computer virus model manifested that increasing the antivirus ability ultimates small virus dominance in a computer community.

关键词： Computer virus,euler maruyama scheme stochastic differential equations stochastic euler scheme stochastic runge-kutta scheme stochastic nsfd scheme stability

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On a diffusive bacteriophage dynamical model for bacterial infections

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生物数学学报:英文版 2023年第7期16卷 47-89页

作者： Hyacinthe M.Ndongmo Teytsa Berge Tsanou Jean Lubuma Samuel Bowong Department of Mathematics and Computer Science University of Dschang P.O.Bor 67DschangCameroon Department of Mathematics and Applied Mathematics University of Pretoria Pretoria 0002South Africa IRD UMI 209 UMMISCO University of Yaounde I P..Bor 337YaoundeCameroon LIRIMA-EPITAG Team Project University of Yaounde I P.O.Bor 812YaoundeCameroon Department of Mathematics and Computer Science University of Douala P.0.Bor 24157DoualaCameroon

Bacteriophages or phages are viruses that infect bacteria and are increasingly used to control bacterial infections.We develop a reaction-diffusion model coupling the interactive dynamic of phages and bacteria with an epidemiological bacteria-borne disease model.For the submodel without phage absorption,the basic reproduction number Ro is computed.The disease-free equilibrium(DFE)is shown to be globally asymptotically stable whenever Ro is less than one,while a unique globally asymptotically endemic equilibrium is proven whenever Ro exceeds one.In the presence of phage absorption,the above stated classical condition based on Ro,as the average number of secondary human infections produced by susceptible/lysogen bacteria during their entire lifespan,is no longer suficient to guarantee the global stability of the DFE.We thus derive an additional threshold No,which is the average offspring number of lysogen bacteria produced by one infected human during the phage-bacteria interactions,and prove that the DFE is globally asymptotically stable whenever both Ro and No are under unity,and infections persist uniformly whenever Ro is greater than one.Finally,the discrete counterpart of the continuous partial differential equation model is derived by constructing a nonstandard finite difference scheme which is dynamically consistent.This consistency is shown by constructing suitable discrete Lyapunov functionals thanks to which the global stability results for the continuous model are replicated.This scheme is implemented in MatLab platform and used to assess the impact of spatial distribution of phages,on the dynamic of bacterial infections.

关键词： Bacterial infections diffusion nsfd phage absorption global stability

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一类具有非线性发生率的戒烟模型动力学分析

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数学的实践与认识 2019年第23期49卷 262-268页

作者：李志民苏宁亚张太雷长安大学理学院

对一类具有非线性发生率的PLSQ戒烟模型进行研究.首先,确定了模型的基本再生数,并分析了模型平衡点的存在性.然后,讨论了模型平衡点的局部稳定性和全局稳定性.最后,将发生率具体化,采用微分方程的非标准差分法(nsfd)求解戒烟模型,并将... 详细信息

对一类具有非线性发生率的PLSQ戒烟模型进行研究.首先,确定了模型的基本再生数,并分析了模型平衡点的存在性.然后,讨论了模型平衡点的局部稳定性和全局稳定性.最后,将发生率具体化,采用微分方程的非标准差分法(nsfd)求解戒烟模型,并将数值结果与ODE23和ODE45的计算结果比较.

关键词：非线性发生率全局稳定性 nsfd ODE23 ODE45

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