QUALITATIVE AND BIFURCATION ANALYSIS USING A COMPUTER VIRUS MODEL WITH A SATURATED RECOVERY FUNCTION

Abstract In this paper, we introduce a saturated treatment function into the computer virus propagation model, where the treatment function is limited for increasing number of infected computers. By carrying out global qualita-tive and bifurcation analysis, it is shown that the system exhibits some new and complicated behaviors: if the basic reproduction number is larger than unity, the number of infected computers will show persistent behavior, either converging to some positive constant or oscillating; and if the basic repro-duction number is below unity, the model may exhibit complicated behaviors including: (i) backward bifurcation; (ii) almost sure virus eradication where the number of infective computers tends to zero for all initial positions ex-cept the interior equilibria; (iii) oscillating backward bifurcation where either the number of infective computers oscillates persistently, if the initial position lies in a region covering the stable virus equilibrium, or virus eradication, if the initial position lies outside this region; (iv) virus eradication for all initial positions if the basic reproduction number is less than a turning point value