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SEIRS epidemic model with delay for transmission of malicious objects in computer network. (English) Zbl 1118.68014
Summary: An epidemic transmission model SEIRS of malicious objects in the computer network is formulated, with death rate other than attack of malicious object is constant and an excess death rate constant for infective nodes. Deaths of a node in computer network equivalently mean to say the isolation of that node from the computer network which even on continuous run by anti malicious software spread malicious objects. Latent and immune periods are assumed to be constants, and the force of infection is assumed to be of standard form, namely proportional to $I\left(t\right)/N\left(t\right)$, where $N\left(t\right)$ is the total (variable) population size and $I\left(t\right)$ is the size of infective population. The model consists of a set of integro-differential equations. When a node is recovered from the infected class, it recovers temporarily, acquiring temporary immunity with probability $p$ $\left(0⩽p⩽1\right)$ and dies from the attack of malicious object with probability $\left(1-p\right)$. Malicious objects free equilibrium is investigated and the stability of the results are stated in terms of threshold parameter.
##### MSC:
 68M10 Network design and communication of computer systems