Dynamical Analysis of Hyper-ILSR Rumor Propagation Model with Saturation Incidence Rate.

With the development of the Internet, it is more convenient for people to obtain information, which also facilitates the spread of rumors. It is imperative to study the mechanisms of rumor transmission to control the spread of rumors. The process of rumor propagation is often affected by the interaction of multiple nodes. To reflect higher-order interactions in rumor-spreading, hypergraph theories are introduced in a Hyper-ILSR (Hyper-Ignorant-Lurker-Spreader-Recover) rumor-spreading model with saturation incidence rate in this study. Firstly, the definition of hypergraph and hyperdegree is introduced to explain the construction of the model. Secondly, the existence of the threshold and equilibrium of the Hyper-ILSR model is revealed by discussing the model, which is used to judge the final state of rumor propagation. Next, the stability of equilibrium is studied by Lyapunov functions. Moreover, optimal control is put forward to suppress rumor propagation. Finally, the differences between the Hyper-ILSR model and the general ILSR model are shown in numerical simulations.

Stability Analysis of a Fractional-Order African Swine Fever Model with Saturation Incidence.

This article proposes and analyzes a fractional-order African Swine Fever model with saturation incidence. Firstly, the existence and uniqueness of a positive solution is proven. Secondly, the basic reproduction number and the sufficient conditions for the existence of two equilibriums are obtained. Thirdly, the local and global stability of disease-free equilibrium is studied using the LaSalle invariance principle. Next, some numerical simulations are conducted based on the Adams-type predictor-corrector method to verify the theoretical results, and sensitivity analysis is performed on some parameters. Finally, discussions and conclusions are presented. The theoretical results show that the value of the fractional derivative α will affect both the coordinates of the equilibriums and the speed at which the equilibriums move towards stabilization. When the value of α becomes larger or smaller, the stability of the equilibriums will be changed, which shows the difference between the fractional-order systems and the classical integer-order system.

Dynamic properties of deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences.

The classical compartment model is often used to study the spread of an epidemic with one virus. However, there are few types of research on epidemic models with multiple viruses. The article aims to propose two new deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences. We obtain asymptotic properties of disease-free and several endemic equilibria for the deterministic model. In the stochastic case, we prove the existence and uniqueness of positive global solutions. The extinction and persistence of diseases are obtained under different threshold conditions. We analyze the existence of stationary distribution through a suitable Lyapunov function. The results indicate that the extinction or persistence of the two viruses is closely related to the intensity of white noise interference. Specifically, considerable white noise is beneficial for the extinction of diseases, while slight one can lead to long-term epidemics of diseases. Finally, numerical simulations illustrate our theoretical results and the effect of essential parameters.

The backward bifurcation of an age-structured cholera transmission model with saturation incidence.

In this paper, we consider an age-structured cholera model with saturation incidence, vaccination age of vaccinated individuals, infection age of infected individuals, and biological age of pathogens. First, the basic reproduction number is calculated. When the basic reproduction number is less than one, the disease-free equilibrium is locally stable. Further, the existence of backward bifurcation of the model is obtained. Numerically, we also compared the effects of various control measures, including basic control measures and vaccination, on the number of infected individuals.

On a population pathogen model incorporating species dispersal with temporal variation in dispersal rate.

In the present paper, we consider a mathematical model of ecosystem population interaction where the population suffers from a susceptible-infectious-susceptible disease. Dispersal of both the susceptible and the infective is incorporated using reaction-diffusion equations. We first study the stability criteria of the basic (non-spatial) model around the disease-free and the infected steady states. We find that the loss rate of the infective species controls disease prevalence. Also without predation pressure, the disease will continue to exist among the population. Then we analyze the spatial model with species dispersal in constant as well as in time-varying form. It is observed that though constant dispersal is unable to generate diffusion-driven instability, dispersal with sinusoidal variation in dispersion rate can generate diffusive instability when the wave number of the perturbation lies within a given range. Numerical simulations are performed to illustrate analytical studies.

Global dynamics of an age-structured cholera model with multiple transmissions, saturation incidence and imperfect vaccination.

In this paper, an age-structured cholera model with multiple transmissions, saturation incidence and imperfect vaccination is proposed. In the model, we consider both the infection age of infected individuals and the biological age of Vibrio cholerae in the aquatic environment. Asymptotic smoothness is verified as a necessary argument. By analysing the characteristic equations, the local stability of disease-free and endemic steady states is established. By using Lyapunov functionals and LaSalle's invariance principle, it is proved that the global dynamics of the model can be completely determined by basic reproduction number. The study of optimal control helps us seek cost-effective solutions of time-dependent vaccination strategy against cholera outbreaks. Numerical simulations are carried out to illustrate the corresponding theoretical results.

The impact of predation on the coexistence and competitive exclusion of pathogens in prey.

A two-strain epidemic model with saturating contact rate under a generalist predator is proposed. For a generalist predator which feeds on many types of prey, we assume that the predator can discriminate among susceptible and infected with each strain prey. First, mathematical analysis of the model with regard to invariance of nonnegativity, boundedness of solutions, nature of equilibria, persistence and global stability are analyzed. Second, the two strains will competitively exclude each other in the absence of predation with the strain with the larger reproduction number persisting. If predation is discriminate, then depending on the predation level, a dominant strain may occur. Thus, for some predation levels, the strain one may persist while for other predation levels strain two may persist. Furthermore, coexistence line and coexistent asymptotic-periodic solution are obtained when coexistence occur while heteroclinic is obtained when the two strains competitively exclude each other. Finally, the impact of predation is mentioned along with numerical results to provide some support to the analytical findings.

Global dynamics of an SIRS epidemic model with saturation incidence.

In this paper, the dynamical behavior of an SIRS epidemic model with birth pulse, pulse vaccination, and saturation incidence is studied. By using a discrete map, the existence and stability of the infection-free periodic solution and the endemic periodic solution are investigated. The conditions required for the existence of supercritical bifurcation are derived. A threshold for a disease to be extinct or endemic is established. The Poincaré map and center manifold theorem are used to discuss flip bifurcation of the endemic periodic solution. Moreover, numerical simulations for bifurcation diagrams, phase portraits and periodic solutions, which are illustrated with an example, are in good agreement with the theoretical analysis.