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In this paper, an e-epidemic Susceptible–Infected–Vaccinated ( S I V ) model has been proposed to analyze the effect of node immunization and worms attacking dynamics in wireless sensor network. A modified nonlinear incidence rate with cyrtoid type functional response has been considered using sleep and active mode approach. Detailed stability analysis and the sufficient criteria for the persistence of the model system have been established. We also established different types of bifurcation analysis for different equilibria at different critical points of the control parameters. We performed a detailed Hopf bifurcation analysis and determine the direction and stability of the bifurcating periodic solutions using center manifold theorem. Numerical simulations are carried out to confirm the theoretical results. The impact of the control parameters on the dynamics of the model system has been investigated and malicious chaotic signals are detected. Finally, we have analyzed the effect of time delay on the dynamics of the model system. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to understand the activity of mean membrane voltage and subsidiary system variables with moment equations (i.e., mean, variance and covariance’s) under noisy environment. We consider a biophysically plausible modified Hindmarsh–Rose (H–R) neural system injected by an applied current exhibiting spiking–bursting phenomenon. The effects of predominant parameters on the dynamical behavior of a modified H–R system are investigated. Numerically, it exhibits period-doubling, period halving bifurcation and chaos phenomena. Further, a nonlinear system has been analyzed for the first and second order moments with additive stochastic perturbations. It has been solved using fourth order Runge–Kutta method and noisy systems by Euler’s scheme. It has been demonstrated that the firing properties of neurons to evoke an action potential in a certain parameter space of the large exact systems can be estimated using an approximated model. Strong stimulation can cause a change in increase or decrease of the firing patterns. Corresponding to a fixed set of parameter values, the firing behavior and dynamical differences of the collective variables of a large, exact and approximated systems are investigated. [ABSTRACT FROM AUTHOR]

In this paper, a model with two different frameworks of an attacking class and a targeted class is introduced to study the virus mobility of an attack in a targeted network. Existence and stability of equilibrium points are discussed in equivalence with the basic reproduction number R 0. It is observed that as R 0 crosses unity, transcritical bifurcation arises in the system. The effect of firewall security is also shown graphically which has been taken as a media coverage factor in this work and it is discovered that firewall helps to bring down the virus propagation by reducing the infection peak. Optimal control concept is then introduced to propose one more measure for regulating the virus propagation. Numerical experimentations have been done to rationalize the analytical conclusions. In the end, a sensitivity analysis is executed that provides the information about relevance of parameters in deciding the virus spread in networks. • A new model governing DDoS attacks has been proposed to study the virus mobility in targeted network. • Firewall helps to control virus proliferation to a symbolic level by lowering the infection level. • Optimal control theory has been proposed as one more measure for regulating the virus propagation. • Sensitivity analysis is executed that provides information about the virus spread in networks. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to study the global dynamical behavior of a viral dynamics model incorporating both the lytic and nonlytic immune responses. The global stability of the model is analyzed in terms of two threshold parameters, namely, basic reproduction number, R 0 and immune response reproduction number, R 1. The obtained results signify that the infection dies out if R 0 ≤ 1 and persists if R 0 > 1. We establish that the global dynamic behavior of the model has no concern with the efficacy of the nonlytic component. Numerical simulations are performed to support our theoretical findings and to investigate the effects of lytic and nonlytic components on the viral dynamics model. A comparison of two different viral infection models has been performed to illustrate the effect of viral replication inhibition through nonlytic effector mechanism on the infection dynamics. Moreover, a case study of HIV-1 infected humanized mice is presented and the result manifests that the model can fairly demonstrate the chronic stage of HIV-1 infection in humanized mice. • A viral dynamic model with lytic and nonlytic immune responses has been presented. • Global stability of the model is independent of the efficacy of nonlytic strength. • Inhibition of viral replication reduces the level of infected cells and virions. • The model fairly demonstrates the chronic HIV-1 infection in humanized mice. [ABSTRACT FROM AUTHOR]

We report a method to find the complete integrability and analytical scheme of a well-known two dimensional (2D) excitable biophysical system that includes a coupled non-linear ordinary differential equations (ODEs). We demonstrate the integrability of the autonomous FitzHugh–Nagumo (FHN) dynamical system for the time evolution equations of motion and briefly describe the solution procedure using the extended Prelle–Singer (PS) scheme without perturbation and series solution method. To illustrate the mathematical formulation procedure, both the time independent and time dependent integrals have been derived by using the extended PS method. Finally, the numerical solution of the integrals has been found with the original dynamical model. It also allows us to establish the integrability of another type of an analytical technique for the deterministic system and this explores the quantitative applicability of the method. Interestingly, the method may have significant applications in other physical systems. [ABSTRACT FROM AUTHOR]