A SEIS Criss-Cross Model for Online Social Networks Communities

Social Network has become important part of our daily life. An average number of people spend a lot of time of their daily life on social network. People belonging to different classes, communities or groups share their opinion or thoughts over a particular issue through social network. These ideologies supporting the arguments either join or divide people among different group on social network. The thoughts or opinions of different people belonging to different classes or communities create a negative environment among them and this resulting in social network attack from one group over the other. Consequently, it creates a criss-cross like environment over the social network and raises an idea of developing criss-cross epidemic model in order to minimize or restrict the epidemic outbreak. In this paper we have proposed a criss-cross epidemic model for attacks on online social networks. We drive the expression for Reproduction Number for given model and analyzed stability of equilibrium point in term of reproduction number. Also establish the Global stability of the model at endemic equilibrium. Finally, numerical simulation of given model using matlab has been done.