Epidemic Model and Mathematical Study of Impact of Vaccination for the Control of Malware in Computer Network
Titus Ifeanyi Chinebu
*
Department of Physical Sciences, Federal College of Dental Technology and Therapy, P. M. B. 01473 Trans Ekulu Enugu, Nigeria.
Ikechukwu Valentine Udegbe
Department of Computer Science, Madonna University Nigeria, Elele, Nigeria.
Adanma Cecilia Eberendu
Department of Computer Science, Madonna University Nigeria, Elele, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Malware remains a significant threat to computer network. In this paper, we consideredthe problem which computer malware cause to personal computers with its control by proposing a compartmental model SVEIRS (Susceptible Vaccinated-Exposed-infected-Recovered-Susceptible) for malware transmission in computer network using nonlinear ordinary differential equation. Through the analysis of the model, the basic reproduction number were obtained, and the malware free equilibrium was proved to be locally asymptotical stable if is less than unity and globally asymptotically stable if Ro is less than some threshold using a Lyapunov function. Also, the unique endemic equilibrium exists under certain conditions and the model underwent backward bifurcation phenomenon. To illustrate our theoretical analysis, some numerical simulation of the system was performed with RungeKutta fourth order (KR4) method in Mathlab. This was used in analyzing the behavior of different compartments of the model and the results showed that vaccination and treatment is very essential for malware control.
Keywords: Epidemic model, malware, vaccination, malicious software, computer network