Stability analysis and optimal control of SEAIQR infectious disease model with nonlinear treatment term based on BA scale-free network

Abstract

The primary approaches to curbing the dissemination of epidemics include vaccination of susceptible individuals, quarantine and complementary cure of infected individuals. To better understand the impact of the above control measures on epidemics and develop optimal control strategies to save medical resources, this paper develops a susceptible-exposed-asymptomatic infected-symptomatic infected-quarantined-recovered (SEAIQR) model with nonlinear treatment term on a BA scale-free network. The process of solving basic reproduction number of SEAIQR model is simplified through the theory of complex networks. It is proven that the global stability of the two equilibrium points is obtained by the construction of Lyapunov functions. Furthermore, we regard the three measures of vaccination for susceptible populations, quarantine for asymptomatic populations and symptomatic populations as control of bounded time-varying inputs. The Pontryagin’s Minimum Principle allows to obtain solutions of optimal control. Finally, the simulations demonstrate that the seven control strategies are superior under the developed SEAIQR model. Our proposal achieves a balance between the cost of controlling infectious diseases and the scale of infection, which will be of immense benefit in the development of control strategies for infectious diseases.