Stability and optimal control strategy analysis for a class of SEIQR model with time delay on scale-free networks

Abstract

Numerous experiences in fighting epidemic diseases have revealed that isolation before treatment is an effective way to prevent the further spread of the epidemic, which scholars in current researches mostly ignore. Also, medical research shows that most infectious diseases have an incubation period, and the length of the incubation period will affect the final therapeutic effect. Therefore, in this paper, to deeply analyze the epidemic transmission with latency and quarantine states, we construct a class of health state-latent state - infected state-quarantined state-recovered state (SEIQR), epidemic model, with a power-law distribution of nodes based on considering the non-linear incidence formed by the psychological suppressor. Furthermore, the system’s basic reproduction number and the equilibrium points’ stability are discussed. The results show that depends on birth rate, death rate, recovery rate, vaccination rate, isolation rate, disease transmission rate, and network topology. Interestingly, the latency does not influence And if system’s disease-free equilibrium is global asymptotically stable, so is endemic equilibrium if Also, we demonstrate that both the latency and psychological inhibitory factor can influence the evolutionary trend of infected nodes in the system. Similarly, this paper verifies the quarantine parameter’s effectiveness, and considers that the parameter variation within (0,0.3) is the most effective. It is worth noting that this paper focuses not only on the dynamics of the SEIQR system, but also on the control of infectious diseases’ spread. Because of this, We use Pontryagin’s maximum principle to solve optimal control solutions of multiple control system under the constraints of minimizing the objective function. Furthermore, the simulation results show that applying multiple controls can effectively inhibit the epidemic’s spread, especially when