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This paper is concerned with the spatio-temporal dynamics of an age-structured reaction-diffusion system of KPP-epidemic type (SIS), subject to Neumann boundary conditions and incorporating $L^1$ blow-up type death rate. We first establish…

Analysis of PDEs · Mathematics 2025-07-15 Cong-Bang Trang , Hoang-Hung Vo

Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…

Populations and Evolution · Quantitative Biology 2020-08-07 Oğul Esen , Eduardo Fernández-Saiz , Cristina Sardón , Marcin Zając

Networked epidemic models have been widely adopted to describe propagation phenomena. The endemic equilibrium of these models is of great significance in the field of viral marketing, innovation dissemination, and information diffusion.…

Systems and Control · Electrical Eng. & Systems 2020-01-22 Fangzhou Liu , Shaoxuan Cui , Xianwei Li , Martin Buss

This paper is devoted to the study of an age-structured SIRS epidemic model, in which a population affected by a disease is divided into susceptible, infected, and removed individuals. We assume that the force of infection may be nonlinear…

Analysis of PDEs · Mathematics 2026-03-16 Luisa Malaguti , Stefania Perrotta

In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations modeling the motion of cancer cells, degradation of the…

Numerical Analysis · Mathematics 2023-08-02 Mario Fuest , Shahin Heydari , Petr Knobloch , Johannes Lankeit , Thomas Wick

In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…

Probability · Mathematics 2016-07-25 Stefano Bonaccorsi , Stefania Ottaviano

We study an SIR epidemic model with a seasonal contact rate and saturated treatment function. It is shown that the basic reproduction number $(\mathcal {R}_0)$ cannot be acted as a threshold that predicts the spread of an infection. Based…

Classical Analysis and ODEs · Mathematics 2014-01-06 Zhenguo Bai , Yicang Zhou

We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…

Dynamical Systems · Mathematics 2025-11-13 Francesca Scarabel , Harry Coldwell , Tyler Cassidy

In this paper, we are concerned with an epidemic reaction-diffusion system with nonlinear incidence mechanism of the form $S^qI^p\,(p,\,q>0)$. The coefficients of the system are spatially heterogeneous and time dependent (particularly time…

Analysis of PDEs · Mathematics 2021-06-15 Rui Peng , Yixiang Wu

In this paper, we study an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term $S$ that models tumor growth. We first prove the existence of global weak solutions as well as the existence…

Analysis of PDEs · Mathematics 2023-07-28 Jie Jiang , Hao Wu , Songmu Zheng

We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…

Analysis of PDEs · Mathematics 2025-11-03 Redouane Douaifia , Salem Abdelmalek , Mokhtar Kirane

We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the…

Physics and Society · Physics 2025-04-17 Gadi Fibich , Guy Rothmann

We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal…

Physics and Society · Physics 2022-09-08 Shogo Mizutaka , Kizashi Mori , Takehisa Hasegawa

We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible)…

Social and Information Networks · Computer Science 2016-10-03 Navid Azizan Ruhi , Hyoung Jun Ahn , Babak Hassibi

In this paper, we are concerned with two SIS epidemic reaction-diffusion models with mass action infection mechanism of the form $SI$, and study the spatial profile of population distribution as the movement rate of the infected individuals…

Analysis of PDEs · Mathematics 2023-01-04 Rui Peng , Zhi-an Wang , Guanghui Zhang , Maolin Zhou

The global behaviour of the compact pairwise approximation of SIS epidemic propagation on networks is studied. It is shown that the system can be reduced to two equations enabling us to carry out a detailed study of the dynamic properties…

Dynamical Systems · Mathematics 2018-07-11 Noémi Nagy , Péter L. Simon

We study a nonlocal SIS epidemic model with free boundaries, advection, and spatial heterogeneity, where the dispersal kernels are not assumed to be symmetric. The model describes the evolution of susceptible and infected populations in a…

Analysis of PDEs · Mathematics 2026-03-26 Soufiane Bentout , Hoang-Hung Vo

This study investigates an SEIS PDE model with a free boundary, which captures the dynamics of epidemic transmission, including diseases like COVID-19. This parabolic PDE system is analyzed in a rotationally symmetric domain, and the…

Analysis of PDEs · Mathematics 2025-11-11 Aesol Jeon , Ki-Ahm Lee

The quasi-deterministic limit of the generic extinction transition is considered within the framework of standard epidemiological models. The susceptible-infected-susceptible (SIS) model is known to exhibit a transition from extinction to…

Statistical Mechanics · Physics 2009-11-13 David A. Kessler , Nadav M. Shnerb

We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…

Optimization and Control · Mathematics 2022-01-26 Marcel Fang , Pierre-Alexandre Bliman