Investigation of computer virus propagation with optimal control strategies: impacts of social media coverage and saturated treatment

In this paper, a model of computer virus propagation with social media coverage and saturated treatment is established to obtain an optimal control strategy so that the number of infected computers is minimized while controlling costs as low as possible. Firstly, we show that the virus-free equilibrium is asymptotically stable for R 0 < 1, indicating computer virus disappears eventually. The global stability of the positive equilibrium is investigated through the Li-Muldowney geometric approach. Secondly, sensitivity analysis is performed by applying Latin hypercube sampling(LHS) to understand how each parameter affects virus spread. Based on the sensitivity analysis of parameters, we propose an optimal control system whose objective function is to both minimize the number of infected computers and reduce the costs of implemented control measures. The necessary conditions for optimal control are derived by applying Pontryagin’s maximum principle. Furthermore, the optimal control strategies are characterized by means of the numerical simulations to verify our results. Finally, a brief discussion is presented.