Abstract
Successful treatment of COVID-19 that outbroke worldwide since the beginning of 2020 has demonstrated the importance of effective isolation, which is aimed at asymptomatic and symptomatic infected persons in the incubation period. In this paper, to further analyze the transmission dynamics behavior of epidemics with the latent state, we construct a class of health state - latent state - infection - recovery state (SEIR) infectious disease model with heterogeneity and time delay characteristic based on considering the nonlinear incidence rate formed by psychological inhibition factors. Also, the dynamics of the epidemic, the threshold condition, and stability are studied by creating Lyapunov functions reasonably, applying LaSalle’s Invariance Principle and mean-field equation theory. The research shows that, the basic reproduction number ${R_{0}}$ of the system depends on birth rate, death rate, recovery rate, disease transmission rate, and network topology. If ${R_{0}} , the system is stable at the disease-free equilibrium point ${E^{0}}$ , and if ${R_{0}}>1$ , the system is sound at the endemic equilibrium point ${E^{*}}$ . Moreover, it is also proved that latent delay and psychological inhibitory factors can influence the peak and rate of the infected nodes in the system before their convergence to the equilibrium point, but not the system’s global stability. Meanwhile, the theoretical results are verified by numerical simulation finally
Highlights
It is well known that infectious diseases caused by pathogens or viruses will pose a significant threat to human health and social security once they develop into epidemics
This paper focuses on the nonlinear incidence rate with psychological factors in infectious diseases, besides considering the heterogeneity, delay factors, and exposed nodesto to establish a more accurate propagation dynamics model
In this paper, a nonlinear incidence SEIR propagation dynamic model with time delay based on a scale-free network is presented
Summary
It is well known that infectious diseases caused by pathogens or viruses will pose a significant threat to human health and social security once they develop into epidemics. For simulating the effects of such inhibition, basing the SIS dynamics model with nonlinear incidence rate, do Zhu et al analyze the influence of psychological inhibition factors on the propagation mechanism, and they deduce the global stability of equilibrium point by using Lyapunov functional and delay differential equation theory, and further solve the optimal immune parameters of the model[39]. Based on all these factors, this paper establishes a health state-latent state-infection state-recovery state (SEIR) epidemic model with nonlinear incidence rate and time delay, and is organized as follows. To ensure that self-consistency equality (17) on the time function Θ (t) has a unique non-zero resolution in the interval from zero to unity, the relationship that needs to be satisfied is as follows
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