Combining Epidemic Model and Deep Learning to Study Cyber Attacks
Pascal Sungu Ngoy, Kaninda Musumbu, Duncan Kioi Gathungu · 2021
Mathematical modeling has been proven to be a remarkably effective approach for bio-mathematician to study and understand the behavior of various malicious objects in a computer system. Due to the connection that exist between computer virus and disease infection, a SEIAR compartmental model has been proposed to model and analyses cyberspace attack where S stands for Susceptible, E for Exposed, I for Infected, A for Asymptomatic and R for Recovered. The dynamic of the above model is governed by a set of differential equations which are generally solved by finite difference methods such as Euler method, Crank-Nicolson method, Runge-Kutta method. However, solutions obtained by these methods are stored in a discretized form that presents some limitations in terms of space memory occupied when high resolution result are required or an accumulation of approximation error on every step of a finite-difference methods. In that regards, a deep neural learning approach has been implemented to solve the system of ordinary differential equation of the epidemic model. It has been found that neural network with one hidden layer shows good capacity in approximating the solution of the differential equation and it required less storage comparing to the traditional finite difference methods. For the convergence of the neural network model, BFGS has been a good optimization method compering to the Conjugate Gradient as well as the Limited Memory BFGS methods.