Vector Disease Model Research Articles

The Asymptotic Speed of Spread and Traveling Waves for a Vector Disease Model

The asymptotic speed of spread is established for a diffusive and time-delayed integro-differential equation modeling vector disease, and its coincidence with the minimal wave speed for monotone traveling waves is proved.

Existence of Travelling Wave Fronts for a Diffusive Vector Disease Model with Delay

In this paper, the existence of monotone travelling front solutions is established for a diffusive vector disease model with a discrete delay. We show that if the delay is sufficiently small, then there exists a travelling wave fronts for the delayed diffusive model connecting the zero equilibrium with the positive equilibrium. The approach used in this paper is the upper-lower solution technique and monotone iteration method for delayed reaction-diffusion systems.

Stability of steady states and existence of travelling waves in a vector-disease model

In this paper, a host-vector model is considered for a disease without immunity in which the current density of infectious vectors is related to the number of infectious hosts at earlier times. Spatial spread in a region is modelled in the partial integro-differential equation by a diffusion term. For the general model, we first study the stability of the steady states using the contracting-convex-sets technique. When the spatial variable is one dimensional and the delay kernel assumes some special form, we establish the existence of travelling wave solutions by using the linear chain trick and the geometric singular perturbation method.

A S-I-R vector disease model with delay

We analyze a deterministic epidemic model with delay derived by the Kermack-McKendrick model. This model is suitable to describe infections transmitted by a vector. Existence, uniqueness, stability and asymptotic behavior of the solutions are studied. A threshold theorem is also proved.

Global asymptotic stability for a vector disease model with spatial spread.

We analyze the global behaviour of a vector disease model which involves spatial spread and hereditary effects. This model can be applied to investigate growth and spread of malaria. No immunization is considered. We prove that, if the recovery rate is less than or equal to a threshold value, the disease dies out, otherwise the infectious people density tends to a homogeneous distribution. Our results follow using contracting convexes techniques and agree with the results given by K. L. Cooke for the model without diffusion.

Stability analysis for a vector disease model

Stability analysis for a vector disease model