Vector Disease Model Research Articles

Dynamics of the nonlocal diffusive vector-disease model with delay and spatial heterogeneity

Dynamics of the nonlocal diffusive vector-disease model with delay and spatial heterogeneity

Stability of a delayed diffusion–advection vector-disease model with spatial heterogeneity

Existence of nonconstant positive steady state and its locally asymptotical stability of a delayed diffusion–advection vector-disease model in the heterogeneous environment are considered, by using the Rabinowitz local bifurcation theory and the distribution of associated eigenvalues. Ecologically, in the spatially heterogeneous environment, the incubation period cannot change the stability when the diffusion is large enough.

Global Dynamics and Optimal Control of Multi-Age Structured Vector Disease Model with Vaccination, Relapse and General Incidence

Global Dynamics and Optimal Control of Multi-Age Structured Vector Disease Model with Vaccination, Relapse and General Incidence

Stability of traveling wave fronts for a modified vector disease model

Stability of traveling wave fronts for a modified vector disease model

Existence and asymptotic behaviors of traveling waves of a modified vector-disease model

In this paper, we are concerned with the existence and asymptotic behavior of traveling wave fronts in a modified vector-disease model. We establish the existence of traveling wave solutions for the modified vector-disease model without delay, then explore the existence of traveling fronts for the model with a special local delay convolution kernel by employing the geometric singular perturbation theory and the linear chain trick. Finally, we deal with the local stability of the steady states, the existence and asymptotic behaviors of traveling wave solutions for the model with the convolution kernel of a special non-local delay.

Entire solutions of a lattice vector disease model

In this article, the existence and qualitative properties of entire solutions for a lattice vector disease model is considered. These entire solutions are constructed by the combinations of traveling wave solutions and the spatial independent solution of the model, which reveal some new transmission forms of the disease.

Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation

A hybrid SIR vector disease model with incubation is established, where susceptible host population satisfies the logistic equation and the recovered host individuals are commercially harvested. It is utilized to discuss the transmission mechanism of infectious disease and dynamical effect of commercial harvest on population dynamics. Positivity and permanence of solutions are analytically investigated. By choosing economic interest of commercial harvesting as a parameter, dynamical behavior and local stability of model system without time delay are studied. It reveals that there is a phenomenon of singularity induced bifurcation as well as local stability switch around interior equilibrium when economic interest increases through zero. State feedback controllers are designed to stabilize model system around the desired interior equilibria in the case of zero economic interest and positive economic interest, respectively. By analyzing corresponding characteristic equation of model system with time delay, local stability analysis around interior equilibrium is discussed due to variation of time delay. Hopf bifurcation occurs at the critical value of time delay and corresponding limit cycle is also observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied. Numerical simulations are carried out to show consistency with theoretical analysis.

Existence and critical speed of traveling wave fronts in a modified vector disease model with distributed delay

In this paper, we consider a modified disease model with distributed delay. The existence of traveling wave fronts connecting the zero equilibrium and the positive equilibrium is established by using an iterative technique and a nonstandard ordering for the set of profiles of the corresponding wave system. We also study the critical wave speed and give a detailed analysis on its location and asymptotic behavior with respect to the time delay. Our work extends some previous results.

Asymptotic speed of propagation and traveling wavefronts for a lattice vector disease model

In this paper, we study a lattice vector disease model with infinite delay and global spatial interaction. We obtain the existence of solutions of the initial value problem, the asymptotic speed of propagation and the strictly monotonic traveling waves for the system. We also confirm that the asymptotic speed of propagation coincides with the minimal wave speed for traveling wavefronts. Furthermore, some asymptotic behaviors for the traveling waves as ξ = n + c t → − ∞ are described.

Global dynamics of a vector disease model with saturation incidence and time delay

Global dynamics of a vector disease model with saturation incidence and time delay

Delay induced travelling wavefronts in a diffusive vector disease model with distributed delay

The existence of travelling wavefront solutions is established for a reaction diffusion equation with distributed delay, which models vector disease. Instead of geometric perturbation method, the approach used here is the upper---lower solution technique and monotone iteration recently developed by Wang et al. [J. Differ. Equations 222 (2006), pp. 185---232)] and the result shows that delay can indeed induce slow travelling wavefronts.

Existence of travelling waves in a diffusive vector disease model with distributed delay

This paper is concerned with a diffusive vector disease model with distributed delay. The existence of travelling wave front solutions connecting the zero equilibrium and the positive equilibrium is established by using an iterative technique and a nonstandard ordering for the set of profiles of the corresponding wave system recently developed by Wang, Li and Ruan (Travelling wave fronts in reactiondiffusion systems with spatio-temporal delays. J. Differential Equations 222 (2006), 185---232). The existence of travelling front solutions shows that there is a moving zone of transition from the disease free state to the infective state.

Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay

In this paper, we study travelling front solutions of a vector disease model incorporating time delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate the associated non-local spatial terms which account for the drift of individuals to their present positions from their possible positions at previous times. We shall show that such fronts exist for the weak generic delay kernel and sufficiently small delays by using geometric singular perturbation theory. Then, for the discrete-delay case, following Canosa’s asymptotic analysis method, we give some information on travelling front solutions.

Analysis of an SIR model with bilinear incidence rate

An SIR vector disease model with incubation time is studied under the assumption that the susceptible of host population satisfies the logistic equation and the incidence rate is the simple mass action incidence. Threshold quantity ℜ 0 is derived which determines whether the disease dies out or remains endemic. If ℜ 0 < 1 , the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears. If ℜ 0 > 1 , there will be an endemic and the disease is permanent if it initially exists. Using the time delay (i.e., incubation time) as a bifurcation parameter, the local stability of the endemic equilibrium is investigated, and the conditions for Hopf bifurcation to occur are derived. Numerical simulations are presented to illustrate our main results.

Existence, uniqueness and asymptotic behavior of traveling wave fronts for a vector disease model

Abstract This paper is concerned with the existence, uniqueness and asymptotic behavior of traveling wave fronts for a vector disease model. We first establish the existence of traveling wave fronts by using geometric singular perturbation theory. Then the asymptotic behavior and uniqueness of traveling wave fronts are obtained by using the standard asymptotic theory and sliding method. In addition, our method is also suitable to establish the uniqueness and asymptotic behavior of traveling wave fronts for a cooperative system.

Existence of travelling waves in a modified vector-disease model

In this paper, we consider travelling wave solutions for a modified vector-disease model. Special attention is paid to the model in which a susceptible vector can receive the infection not only from the infectious host but also from the infectious vector. For the strong generic delay kernel, we show that travelling wave solutions exist using the geometric singular perturbation theory.

Travelling wave fronts in a vector disease model with delay

In this paper, we study the diffusive vector disease model with delay. This problem with strong biological background has attracted much research attention. We focus on the existence of traveling wave fronts, and find that there is a moving zone for the transition from the disease-free state to the infective state. To complete the theoretical analysis, we employ the mathematical tools including the monotone iteration technique as well as the upper and lower solution method.

Errata to “The Asymptotic Speed of Spread and Traveling Waves for a Vector Disease Model”

In our recent paper [2], the existence of traveling wave solutions U(x+ct) with c>c∗ was proved via the method of upper and lower solutions. However, there is a mistake in the verification of the lower solution in the proof of [2, Theorem 3.1]. More precisely, the number M depends on the parameter ξ ∈R and is unbounded as ξ→−∞. Thus, there may not exist a constant M 1 such that U(ξ) is a lower solution for ξ ξ0 :=− lnM . The purpose of our current note is to correct this mistake. Instead of constructing an appropriate lower solution, we use the finite time-delay approximation and a limiting argument to prove the existence of traveling waves. It turns out that the theory developed in [1] can also be applied to establish both spreading speeds and traveling waves for monotone evolution equations with spatial structure and infinite time delay with the aid of the finite time-delay approximation.

Dynamics and Traveling Waves in CNN Vector Disease Model

In this brief, a cellular neural network (CNN) vector disease model is investigated from the point of view of its dynamics. Some vector-borne diseases such as malaria, yellow fever, and typhus, which arrive and spread in new areas, are one of the main public health problems throughout the world. The investigations of the spatial spread of newly introduced diseases are interesting and challenging for both theory and applications. Existence of traveling waves for such CNN vector disease model is proved. Simulations of the obtained CNN model are given, which confirm the obtained theoretical results

Periodic solution and wave front solution for delay equation

First, a general theorem on the existence of periodic solutions for equations with small discrete delay is obtained by employing a technique which is based on a result of the existence of inertial manifold for small discrete delay equation, meanwhile, this general theorem is applied to show the existence of periodic solution for a predator–prey system with small discrete delay. Second, this technique is also used to obtain the existence of travelling wave solution for a host–vector disease model with small discrete delay.