Mathematical models on computer viruses

摘要

An attempt has been made to develop mathematical models on computer viruses infecting the system under different conditions. Mathematical model 1 discusses the situation to find the probability that at any time t how many software components are infected by virus, assuming the recovery rate and proportion of un-infected population receiving infection per unit time does not change with time. Mathematical model 2 is to estimate the proportion of software component population infected at any time and at any indefinite time under different cases. The third model is to find out the rate of change of proportion of total population with exactly j viruses (1 ⩽ j < ∞) and proportion of total population with zero virus, assuming that the total population is distributed into different groups based on the number of viruses present in a particular module. The fourth model is to find out what is the probability that at any time t, z number of software components are infected, assuming that initially (i.e. at t = 0), a number of components are infected and also there is a change from infected to uninfected or vice versa.