Modeling the virus dynamics in computer network with SVEIR model and nonlinear incident rate

Upadhyay, Ranjit Kumar; Kumari, Sangeeta; Misra, Arvind

doi:10.1007/s12190-016-1020-0

Cited by 57 publications

(37 citation statements)

References 25 publications

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“…In the field of studying epidemic model behavior, one of the most important parts is to analyze steady states together with their stability [6]. In general, there are two distinct techniques named Lyapunov's direct method and Li-Muldowney's geometric approach to give sufficient conditions of global stability for the equilibrium states (see, for example, [7][8][9][10][11][12][13][14]). We would like to mention some related work concerned with the existence of positive solutions for the discrete fractional boundary value problem [15], the sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions [16] and the nonexistence of global in time solution of the mixed problem for the nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model [17].…”

Section: Introductionmentioning

confidence: 99%

“…Many researchers have adopted different nonlinear incidence rates in their works. For more details, we refer the reader to [8][9][10][11][12][13][14][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] and the references therein. When it comes to control of a disease, it is generally known that the spread of many diseases can be prevented by vaccinating.…”

Section: Introductionmentioning

confidence: 99%

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Global stability analysis of an SVEIR epidemic model with general incidence rate

et al. 2018

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In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function f (S, I). The role that temporary immunity (vaccinated-induced) and treatment of infected people play in the spread of disease, is incorporated in the model. The basic reproduction number R 0 is found, under certain conditions on the incidence rate and treatment function. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on R 0 as well as on the treatment rate. If R 0 > 1, then the endemic equilibrium is globally asymptotically stable with the help of the Li and Muldowney geometric approach applied to four dimensional systems. Numerical simulations are also presented to illustrate our main results. MSC: 92D25; 92D30; 34D23; 37B25

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global stability analysis of an SVEIR epidemic model with general incidence rate

et al. 2018

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“…As stated in [26], the dynamics of a model system heavily depends on the choice of the incidence rate. Gan et al have considered the different incidence rate functions / ( ) in their work [27,28].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

Zhang

Wang

Guerrini

2018

Advances in Mathematical Physics

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This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results.

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“…Based on the fact that some virus can infect an arbitrary vulnerable computer through random scanning, the homogeneous models regard the propagation network as fully connected, such as the 1-n-n-1 type D-SEIR malicious propagation model proposed by Mishra et al [3], SCIR model and SEIRS model proposed by Guillén et al [4,5], SLAR model by Dong et al [6], SIP model proposed by Abazari et al [7], SVEIR model proposed by Upadhyay et al [8], and SLBS model proposed by Yang et al [9,10]. Instead, the heterogeneous model assumes that the virus could only spread between the direct topological neighbors.…”

Section: Introductionmentioning

confidence: 99%

State-Based Switching for Optimal Control of Computer Virus Propagation with External Device Blocking

Zhu

Loke

Zhang

2018

Security and Communication Networks

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The rapid propagation of computer virus is one of the greatest threats to current cybersecurity. This work deals with the optimal control problem of virus propagation among computers and external devices. To formulate this problem, two control strategies are introduced: (a) external device blocking, which means prohibiting a fraction of connections between external devices and computers, and (b) computer reconstruction, which includes updating or reinstalling of some infected computers. Then the combination of both the impact of infection and the cost of controls is minimized. In contrast with previous works, this paper takes into account a state-based cost weight index in the objection function instead of a fixed one. By using Pontryagin's minimum principle and a modified forward-backward difference approximation algorithm, the optimal solution of the system is investigated and numerically solved. Then numerical results show the flexibility of proposed approach compared to the regular optimal control. More numerical results are also given to evaluate the performance of our approach with respect to various weight indexes.

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Modeling the virus dynamics in computer network with SVEIR model and nonlinear incident rate

Cited by 57 publications

References 25 publications

Global stability analysis of an SVEIR epidemic model with general incidence rate

Global stability analysis of an SVEIR epidemic model with general incidence rate

Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

State-Based Switching for Optimal Control of Computer Virus Propagation with External Device Blocking

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