Disease-free Equilibrium Of System Research Articles

Stochastic SIR Epidemiological Model With Two Levels of Severity

In this paper, we develop an epidemic model to analyze the spread of an infectious disease with two levels of severity within a population of varying size. Additionally, we examine the stability of the disease-free equilibrium.
 Such a model is suitable for the dynamics of COVID-19 disease spread. If the two types of infected individuals have different recovery rates, then there is no endemic equilibrium; only the disease-free equilibrium will be the subject of our study. We then study both the deterministic model and a stochastic version. The stochastic model is obtained by perturbing the contact rate using white noise. For the deterministic model, we have shown that if the basic reproduction number R_0 < 1, then the equilibrium state is globally asymptotically stable by using Lyapunov function. This implies that the disease will disappear, and the entire population will become susceptible. For the stochastic version, we demonstrate that the system admits a unique positive global solution that exists within a positively invariant domain. Under suitable conditions on the intensity of the white noise perturbations, we prove that the number of infectious individuals converge almost surely exponentially to zero and the disease-free equilibrium of system is stochastically asymptotically stable in the large provided. Finally, we give some numerical simulations to illustrate our theoretical results.

Large time behavior in a reaction diffusion epidemic model with logistic source

This paper concerns a reaction diffusion epidemic model under logistic source. First, we explore uniform boundedness of the system. Moreover, by constructing two Lyapunov functions, we show that the disease-free equilibrium of system is globally asymptotically stable and the large time dynamics of constant endemic equilibrium is also considered. Especially, we further investigate the convergence rate of the nonnegative globally bounded classical solution. Finally, two numerical simulations are displayed to confirm the results.

STABILITY ANALYSIS OF A SEIQRS EPIDEMIC MODEL ON THE FINITE SCALE-FREE NETWORK

Taking into account the quarantine for an infectious disease, a susceptible-exposed-infected-quarantined-recovery-susceptible (SEIQRS) epidemic model with time delay on the finite scale-free network is given. The basic reproduction number [Formula: see text], which is dependent not only on all kinds of transfer rates, but also on the topology of the network, is derived. By constructing the Lyapunov function, it is asserted that the disease-free equilibrium of system is locally asymptotically stable if [Formula: see text], moreover, disease-free equilibrium of system is globally asymptotically stable when [Formula: see text]. In addition, the influence of network nodes on the spread of diseases is discussed. Finally, the theoretical results are verified by corresponding numerical simulation.

On extinction of infectious diseases for multi-group SIRS models with saturated incidence rate

We generalize the deterministic and the stochastic single-group SIRS epidemic models with saturated incidence rate introduced by Lahrouz, Omari, and Kiouach to the multi-group versions. In the deterministic multi-group model, the fact is highlighted that if the threshold $\mathscr{R}_{0}\leq1$ , then the infective condition disappears and it means the extinction of the disease. If $\mathscr{R}_{0}>1$ , then there exists an endemic equilibrium in a feasible region. Allowing the noise perturbation, for the stochastic version, we utilize stochastic Lyapunov functions to show the stability of the disease-free equilibrium of system. A detailed analysis is performed on almost surely exponential stability and pth moment exponential stability of the disease-free equilibrium. We also go into several numerical simulations to illustrate how exactly the theoretical results are verified. Good agreement was observed between our theoretical results and numerical simulations. A comprehensive conclusion is provided.