Dynamics of a virtual virus infection process involving a spatial distribution of interacting computers

Abstract

In this work we introduce a theoretical model for describing the dynamics of a virtual virus infection process in a set of interacting computers, considering spatial densities of susceptible and infected equipments distributed in a two dimensional region. We consider here two possible propagation mechanisms: the transmission and reception of electronic mails and also the exchange of softwares by means of recording devices as compact disks or the commonly used floppy disks. The model gives a good idea of the infection process and trends reproducing, satisfactorily, some previously obtained results concerning the homogeneous mixing case. The new nonlinear integral equation we obtain here presents certain interesting features which are explored and enlightened in this article.

Keywords:

• Virtual viruses
• Nonlinear delay integral equations
• Population equation
• AMS Subject Classifications: 45G10
• 49K25
• 92D99