Related papers: A vector-host epidemic model with spatial structur…
Magal, Webb and Wu [Nonlinearity 31, 5589-5614 (2018)] studied the model describing outbreak of Zika in Rio De Janerio, and provided a complete analysis of dynamical properties for the solutions. In this note we first use a very simple…
To describe the propagation of West Nile virus and/or Zika virus, in this paper, we propose and study a time-periodic reaction-diffusion model with general boundary conditions in heterogeneous environments and with four unknowns:…
In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number $R_0$ and show that $R_0$ is a threshold parameter: if $R_0\le 1$ the disease free steady state is globally stable; if $R_0>1$…
Background: A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting. The disease is borne by vectors to susceptible hosts through criss-cross dynamics. The model is focused on an epidemic…
Insect-borne diseases are diseases carried by insects affecting humans, animals or plants. They have the potential to generate massive outbreaks such as the Zika epidemic in 2015-2016 mostly distributed in the Americas, the Pacific and…
Epidemic models play a crucial role in population dynamics, offering valuable insights into disease transmission while aiding in epidemic prediction and control. In this paper, we analyze the mathematical model of the time-fractional Zika…
In this paper we study a diffusive age structured epidemic model with disease transmission between vector and host populations. The dynamics of the populations are described by reaction-diffusion equations, with infection age structure of…
This paper is devoted to the study of asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems in the case of small and large diffusion coefficients. We first establish the continuity of the basic…
We introduce a stochastic household model for vector-borne diseases, in particular as relevant to prominent vectors belonging to the Aedes genus and hence the Zika, chikungunya, and dengue viruses. In this model, vectors remain local to…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
Aedes Aegypti is the vector of several deadly diseases, including Zika. Effective and sustainable vector control measures must be deployed to keep A. aegypti numbers under control. The distribution of A. Aegypti is subject to spatial and…
Vector-borne diseases arise from the coupled dynamics of human mobility and mosquito ecology, producing outbreaks shaped by both spatial distributions and temporal patterns of movement. Here we develop a coarse-grained hub--leaf reduction…
In this paper we describe the dynamics of a vector-borne relapsing disease, such as tick-borne relapsing fever, using the methods of compartmental models. After some motivation, model description, and a brief overview of the theory of…
In this paper, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Infection dynamics are based on a simplified model for cross infection between…
In the present paper, we study the dynamics of a nine compartmental vector-host model for Zika virus infection where the predatory fish Gambusia Affinis is introduced into the system to control the zika infection by preying on the vector.…
This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and…
Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic…
In this paper, we study a simplified version of a West Nile virus model discussed by Lewis et al. [28], which was considered as a first approximation for the spatial spread of WNv. The basic reproduction number $R_0$ for the non-spatial…
We present an epidemiological model for vector-borne diseases that includes within-host viral load and antibody dynamics using structured transport equations. By incorporating the internal dynamics into the infected and recovered host…
In this paper we study some deterministic mathematical models that seek to explain the expansion of zika virus, as a viral epidemic, using published data for Brazil. SIR type models are proposed and validated using the epidemic data found,…