Network Benign And Malignant Worms Interaction Model Analysis

With the development of the information technology, the worm viruses have become common computer viruses. The viruses mainly use networks (often through the Internet and E-mail) to reproduce and spread. The traditional methods of killing worm viruses are:downloading and installing antivirus software, firewalls, and fixing bugs, etc. However, Sapon Tanachaiwiwat and so on put forward using benign worms to curb the spread of malignant worms. Malignant worms have harmful effects (such as changing users’ files, etc.), but benign worms do not have such harmful effects, however they still take up the space, and should not be stored in the computers for a long time.Nowadays, using mathematical tools to study the changing rules of the computer worm viruses’ quantity and trying to use the research results to control the spread of the computer worm viruses are very meaningful works. In this paper, according to the patching malignant worms and non-patching malignant worms (i.e., whether malignant worms are immune to benign worms), based on the theories of ordinary differential equations, I set up two worms interaction models (predator-prey interaction model and predator-patching prey interaction model); do some detailed analysis for these two models; get no worms equilibrium points, boundary equilibrium points and endemic equilibrium points; calculate the basic reproduction numbers; and obtain critical conditions for the stability of the equilibrium points.In chapter2and chapter3through some concrete analysis, we have:①when the constant input A, the infection rate of prey to susceptible class (n) a and the infection rate of predator to susceptible class (n) c are sufficiently small, malignant and benign worms will disappear finally;②when the infection rate of prey to susceptible class (n) a is sufficiently small and the infection rate of predator to susceptible class (n) c is sufficiently large, malignant worms will disappear and benign worms will stay in the network finally;③when the infection rate of prey to susceptible class (n) a is sufficiently large, the infection rate of predator to susceptible class (n) c and the infection rate of predator to prey b are sufficiently small, malignant worms will stay in the network and benign worms will disappear finally;④When condition Λcb<δ<Λabis r2 satisfied (with8=br1-cr2+ar3), both malignant and benign worms will exist in the network finally;⑤for the predator-patching prey interaction model, if the proportion of the patching prey p is sufficiently large, it’s likely that only malignant worms would stay in the network but benign worms would disappear.In chapter4, we carry on the numerical simulation experiment, and assign values to each of the parameters of the two models, use mathematica software to simulate all kinds of trends of computer quantity, the experimental results have proved the correctness of the models and the analysis that have done for the models.