Hopf bifurcation and optimal control of a delayed SLBPS virus-patch model

Abstract

This paper formulates a Susceptible–Latent–Breaking out–Patched–Susceptible (SLBPS) virus propagation model with delay of temporary immunity. The influence of time delay on stability of the model is examined by analyzing the distribution of eigenvalues of the characteristic equation. Furthermore, we also demonstrate the direction and stability of the Hopf bifurcation. Lastly, optimal control strategies in terms of the rate at which susceptible, latent, break out nodes acquiring patches to improve performance of the model are presented. For the sake of the correctness of the theoretical analysis, some numerical simulations are also presented.