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Related papers: On a Vector-host Epidemic Model with Spatial Struc…

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Time varying susceptibility of host at individual level due to waning and boosting immunity is known to induce rich long-term behavior of disease transmission dynamics. Meanwhile, the impact of the time varying heterogeneity of host…

Populations and Evolution · Quantitative Biology 2018-08-28 Yukihiko Nakata , Ryosuke Omori

We propose an epidemic model for the spread of vector-borne diseases. The model, which is built extending the classical susceptible-infected-susceptible model, accounts for two populations -- humans and vectors -- and for cross-contagion…

Systems and Control · Electrical Eng. & Systems 2025-10-21 Lorenzo Zino , Alessandro Casu , Alessandro Rizzo

We propose a nonlocal epidemic model whose spatial domain evolves over time and is represented by $[0,h(t)]$ with $h(t)$ standing for the spreading front of epidemic. It is assumed that the agents can cross the fixed boundary $x=0$, but…

Analysis of PDEs · Mathematics 2024-08-15 Xueping Li , Lei Li

A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…

Optimization and Control · Mathematics 2017-03-09 Sebastian Anita , Vincenzo Capasso

This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and…

Analysis of PDEs · Mathematics 2024-06-11 Xueping Li , Lei Li , Mingxin Wang

Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between…

Populations and Evolution · Quantitative Biology 2020-06-11 Goncalo Oliveira

In this work we consider an epidemic system modelling the evolution of a spore-producing pathogen within a multi-host population of plants. Here we focus our analysis on the study of the stationary states. We first discuss the existence of…

Analysis of PDEs · Mathematics 2020-08-03 Jean-Baptiste Burie , Arnaud Ducrot , Quentin Griette , Quentin Richard

We consider a spatially-heterogeneous generalization of a well-established model for the dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The model consists of a nonlinear system of three coupled…

Analysis of PDEs · Mathematics 2016-04-18 Stephen Pankavich , Christian Parkinson

Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the…

Optimization and Control · Mathematics 2015-03-19 Helena Sofia Rodrigues , M. Teresa T. Monteiro , Delfim F. M. Torres , Alan Zinober

We obtain conditions for eradication and permanence of infection for a nonautonomous SIQR model with time-dependent parameters, that are not assumed to be periodic. The incidence is given by functions of all compartments and the threshold…

Dynamical Systems · Mathematics 2017-01-05 César M. Silva

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a…

Analysis of PDEs · Mathematics 2019-03-25 Angel Calsina , Jozsef Z. Farkas

When an infectious disease propagates throughout society, the incidence function may rise at first due to an increase in pathogenicity and then decrease due to inhibitory effects until it reaches saturation. Effective vaccination and…

Dynamical Systems · Mathematics 2023-07-11 Sushil Pathak , G. Shirisha , K. Venkata Ratnam

This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison…

Analysis of PDEs · Mathematics 2025-09-16 Qihua Huang , Minglong Wang , Yixiang Wu

Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…

Populations and Evolution · Quantitative Biology 2020-05-19 Sebastian J. Schreiber , Shuo Huang , Jifa Jiang , Hao Wang

We consider the basic model of virus dynamics in the modeling of Human Immunodeficiency Virus (HIV), in a 2D heterogenous environment. It consists of two ODEs for the non-infected and infected $CD_4^+$ $T$ lymphocytes, $T$ and $I$, and a…

Dynamical Systems · Mathematics 2009-05-14 Claude-Michel Brauner , Danaelle Jolly , Luca Lorenzi , Rodolphe Thiebaut

A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…

Dynamical Systems · Mathematics 2025-09-12 Wael El Khateeb , Chanaka Kottegoda , Chunhua Shan

This paper aims to explore the temporal-spatial spreading and asymptotic behaviors of West Nile virus by a reaction-advection-diffusion system with free boundaries, especially considering the impact of advection term on the extinction and…

Analysis of PDEs · Mathematics 2020-01-20 Chengcheng Cheng , Zuohuan Zheng

For nearly a century, the initial reproduction number (R0) has been used as a one number summary to compare outbreaks of infectious disease, yet there is no `standard' estimator for R0. Difficulties in estimating R0 arise both from how a…

Populations and Evolution · Quantitative Biology 2020-03-25 Shannon Gallagher , Andersen Chang , William F. Eddy

We study a multitype SIR epidemic model where individuals are categorized into different types, and where infection spread is characterized by a next-generation matrix $M=\{m_{ij}\}$ with community fractions $\{\pi_j\}$ for the different…

Populations and Evolution · Quantitative Biology 2026-03-10 Andrea Bizzotto , Frank Ball , Tom Britton

We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less…

Analysis of PDEs · Mathematics 2019-10-08 Dawit Denu , Sedar Ngoma , Rachidi B. Salako