Related papers: The Dynamics of Vector-Borne Relapsing Diseases
A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence…
A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have been proposed and studied. The basic reproductive number $R_0$ is defined. The dynamical behaviors of the model are analyzed with the help of persistence,…
We show that disease transmission models in a spatially heterogeneous environment can have a large number of coexisting endemic equilibria. A general compartmental model is considered to describe the spread of an infectious disease in a…
Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same…
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…
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…
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR…
The emergence or adaptation of pathogens may lead to epidemics, highlighting the need for a thorough understanding of pathogen evolution. The tradeoff hypothesis suggests that virulence evolves to reach an optimal transmission intensity…
In order to explore the impact of periodically evolving domain on the transmission of disease, we study a SIS reaction-diffusion model with logistic term on a periodically evolving domain. The basic reproduction number ${\mathcal{R}}_0$ is…
We present a deterministic mathematical model for malaria transmission with waning immunity. The model consists of five non-linear system of differential equations. We used next generation matrix to derive the basic reproduction number…
We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…
We introduce a general system of ordinary differential equations that includes some classical and recent models for the epidemic spread in a closed population without vital dynamic in a finite time horizon. The model is vectorial, in the…
We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers…
This paper conducts research on the established model and presents the main conclusions . Firstly, by separately considering the infectivity of each of the two infectious diseases and the infectivity of the population simultaneously…
In this paper, we introduce a general framework for co-infection as cooperative SIR dynamics. We first solve analytically CGCG model [1] and then the generalized model in symmetric scenarios. We calculate transition points, order parameter,…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
This study focuses on the modeling, mathematical analysis, developing theories, and numerical simulation of Influenza virus transmission. We have proved the existence, uniqueness, positivity, and boundedness of the solutions. Also,…
In this study, we develop and analyze a deterministic two-strain host-vector model for dengue transmission that incorporates key immuno-epidemiological mechanisms, including temporary cross-immunity, antibody-dependent enhancement (ADE),…
We study the problem of a policymaker who aims at taming the spread of an epidemic while minimizing its associated social costs. The main feature of our model lies in the fact that the disease's transmission rate is a diffusive stochastic…
Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without…