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 R 0 and the equilibrium points' stability are discussed. The results show that R 0 depends on birth rate, death rate, recovery rate, vaccination rate, isolation rate, disease transmission rate, and network topology. Interestingly, the latency does not influence R . 0 And if < R 1, 0 system's disease-free equilibrium is global asymptotically stable, so is endemic equilibrium if > R 1.

Global stability and control strategies of a SIQRS epidemic model with time delay

“…Sun et al 30 introduced three improved SIS models on scale‐free networks, which considered variable population size, nonlinear infectivity, and time lag to represent the actual spread of epidemics better. More excellent time‐delay models on scale‐free networks can be found in previous studies 31–33 …”

“…More excellent time-delay models on scale-free networks can be found in previous studies. [31][32][33] In addition, the development of appropriate immunization and control strategies plays an important role in suppressing the spread of disease in complex networks, effectively reducing the epidemic level and reducing the cost of controlling the spread of the virus. In general, immunization strategies include uniform immunization, 34 proportional immunization, 35 targeted immunization, 36 acquaintance immunization, 37 active immunization, 1 and so on.…”

Complex pattern evolution of a two-dimensional space diffusion model of malware spread

“…In recent years, many scholars have made contributions to the research on the propagation of malware [18][19][20][21][22][23][24]. The analysis of Turing instability and Hopf bifurcation of malware propagation model can provide guidance for prediction and control of malware.…”