Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence

Luo, Yantao; Zhang, Long; Zheng, Tianhang; Teng, Zhidong

doi:10.1016/j.physa.2019.122415

Cited by 20 publications

(16 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this subsection, on the existence and uniqueness of global solutions as well as the ultimate boundedness for system (4)-(6), we can establish the following results. The similar conclusion as those in Ref s. [17,16] implies that the subsequent lemma holds. Lemma 1.…”

Section: 1supporting

confidence: 87%

“…Preliminaries. In this subsection, we first give some notations and some preliminaries which will be used frequently hereafter through Ref s. [17,4,16,40]. Normally, denote by R 3 + the positive cone in R 3 , where…”

Section: 1mentioning

confidence: 99%

“…The rumor propagation models we mentioned above, it is worth noting, are based on the assumption of "homogeneous mixing", with users mixing uniformly, without regard to location. It has been universally accepted that spatial diffusion and environmental heterogeneity are crucial factors that should be considered in the infectious disease transmission [17,25,33,20]. Since the pioneering work of Allen et al [2] on the influence of the environmental heterogeneity and the movement of individuals on disease transmission, there are many scholars begin to study the reaction-diffusion equations in a spatially heterogeneous environment [3,4,15,41].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A theoretical approach to understanding rumor propagation dynamics in a spatially heterogeneous environment

Zhu¹,

Liu²,

Zhang³

2021

DCDS-B

View full text Add to dashboard Cite

Most of the previous work on rumor propagation either focus on ordinary differential equations with temporal dimension or partial differential equations (PDE) with only consideration of spatially independent parameters. Little attention has been given to rumor propagation models in a spatiotemporally heterogeneous environment. This paper is dedicated to investigating a SCIR reaction-diffusion rumor propagation model with a general nonlinear incidence rate in both heterogeneous and homogeneous environments. In spatially heterogeneous case, the well-posedness of global solutions is established first. The basic reproduction number R 0 is introduced, which can be used to reveal the threshold-type dynamics of rumor propagation: if R 0 < 1, the rumor-free steady state is globally asymptotically stable, while R 0 > 1, the rumor is uniformly persistent. In spatially homogeneous case, after introducing the time delay, the stability properties have been extensively studied. Finally, numerical simulations are presented to illustrate the validity of the theoretical analysis and the influence of spatial heterogeneity on rumor propagation is further demonstrated.

show abstract

Section: 1supporting

confidence: 87%

Section: 1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A theoretical approach to understanding rumor propagation dynamics in a spatially heterogeneous environment

Zhu¹,

Liu²,

Zhang³

2021

DCDS-B

View full text Add to dashboard Cite

show abstract

“…Throughout this paper, we use the notations similar to Ref s. [14,23]. Denote R 3 + be the positive cone in R 3 by…”

Section: 1mentioning

confidence: 99%

“…From the mathematical models themselves, both system (1) and system (2) are derived under the assumption that the environment is "homogeneous mixing", that is, the location of network users are not taken into account. As is well-known, spatial diffusion and environmental heterogeneity are core factors that affects the spatial spread of infectious diseases and should be reflected in modelling [14,23]. Reaction-diffusion equations have been shown to be an effective and valuable tool to incorporate the spatial motion of the population into the model by assuming some random movements [39].…”

mentioning

confidence: 99%

Spatial dynamics and optimization method for a network propagation model in a shifting environment

Zhu¹,

Liu²

2021

Discrete &Amp; Continuous Dynamical Systems - A

View full text Add to dashboard Cite

In this paper, a reaction-diffusion ISCT rumor propagation model with general incidence rate is proposed in a spatially heterogeneous environment. We first summarize the well-posedness of global solutions. Then the basic reproduction number R 0 is introduced for the model which contains the spatial homogeneity as a special case. The threshold-type dynamics are also established in terms of R 0 , including the global asymptotic stability of the rumor-free steady state and the uniform persistence of all positive solutions. Furthermore, by applying a controller to this model, we investigate the optimal control problem. Employing the operator semigroup theory, we prove the existence, uniqueness and some estimates of the positive strong solution to the controlled system. Subsequently, the existence of the optimal control strategy is established with the aid of minimal sequence techniques and the first order necessary optimality conditions for the optimal control is deduced. Finally, some numerical simulations are performed to validate the main analysis. The results of our study can theoretically promote the regulation of rumor propagation on the Internet.

show abstract

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

Zhang

et al. 2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

This paper is concerned with the existence and nonexistence of traveling waves of a virus infection model with humoral immunity, cell‐to‐cell transmission, and general nonlinear incidence. Our results show that the existence of traveling wave solutions is determined not only by the basic reproduction number of virus infection and the antibody response reproduction number but also by the critical wave speed . More precisely, we obtain the existence of traveling wave solution connecting infection‐free equilibrium and antibody‐free infection equilibrium for , and and connecting infection‐free equilibrium and antibody‐present infection equilibrium for , and . The existence of traveling wave solution connecting infection‐free equilibrium and antibody‐present infection equilibrium is discussed. Some numerical simulations are carried out to illustrate our analytical results.

show abstract

Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence

Cited by 20 publications

References 25 publications

A theoretical approach to understanding rumor propagation dynamics in a spatially heterogeneous environment

A theoretical approach to understanding rumor propagation dynamics in a spatially heterogeneous environment

Spatial dynamics and optimization method for a network propagation model in a shifting environment

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

Contact Info

Product

Resources

About