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Predator's management requires a detailed understanding of the ecological circumstances associated with predation. Predation by foxes has been a significant contributor to the Australian native animal reduction. This paper mainly focuses on the dissemination of rabbit hemorrhagic disease in the rabbit population and its subsequences on red fox ( Vulpes vulpes ) population, by qualitative and quantitative analyses of a designed eco-epidemiological model with simple law of mass action and sigmoid functional response. Existence of solution has been analyzed and shown to be uniformly bounded. The basic reproduction number ( R 0 ) is obtained and the occurrence of a backward bifurcation at R 0 = 1 is shown to be possible using central manifold theory. Global stability of endemic equilibrium is established by geometric approach. Criteria for diffusion-driven ecological instability caused by local random movements of European rabbits and red fox are obtained. Detailed analyses of Turing patterns formation selected by reaction-diffusion system under zero flux boundary conditions are presented. We found that transmission rate, self and cross-diffusion coefficients have appreciable influence on spatial spread of epidemics. Numerical simulation results confirm the analytical finding and generate patterns which indicate that population of red foxes might be controlled if rabbit hemorrhagic disease (RHD) is introduced into the rabbit population and thus ecological balance can be maintained. [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]