Related papers: The Basic Reproduction Number for Petri Net Models…
Accurate estimates of the reproduction ratio are crucial to project infectious disease epidemic evolution and guide public health response. Here, we prove that estimates of the reproduction ratio based on inference from surveillance data…
The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations (ODEs) to describe the co-evolution of…
Since the beginning of the corona pandemic in March 2020, various parameters for describing the spread of the disease have been specified for Germany in addition to the daily infection figures (new infections and total infections), which…
A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces. This so-called reproduction number has significant implications for the disease progression. There…
We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a…
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global…
The basic reproduction ratio is a crucial threshold parameter in infectious disease models. In nonlocal dispersal systems, its variational characterization is challenging due to the possible absence of a principal eigenvalue caused by…
Epidemic modelling on complex networks has been studied intensively all the time. The majority of relative research assumes that the time scale of the underlying network evolution is much larger compared to the propagation dynamics on it,…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
We present a methodology for systematically extending epidemic models to multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on the use of coloured stochastic and continuous Petri nets facilitating the sound…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…
In this paper, we propose and analyze a reaction-diffusion susceptible-infected-susceptible (SIS) epidemic patch model. The individuals are assumed to reside in different patches, where they are able to move inside and among the patches.…
We consider the simple epidemiological SIS model for a general heterogeneous population introduced by Lajmanovich and Yorke (1976) in finite dimension, and its infinite dimensional generalization we introduced in previous works. In this…
Malaria constitutes an important cause of human mortality. After 2009 Greece experienced a resurgence of malaria. Here, we develop a modelbased framework that integrates entomological, geographical, social and environmental evidence in…
Reconstructing who infected whom is a central challenge in analysing epidemiological data. Recently, advances in sequencing technology have led to increasing interest in Bayesian approaches to inferring who infected whom using genetic data…
This study constructs a dual-model framework integrating Ordinary Differential Equations (ODE) and Petri Nets (PN) to analyze the 2025 Chikungunya outbreak in Foshan City, China. We employ SEICR compartmental modeling to compare two…
It is a fundamental question in disease modelling how the initial seeding of an epidemic, spreading over a network, determines its final outcome. Research in this topic has primarily concentrated on finding the seed configuration which…
We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected…
Network-based epidemic models have been extensively employed to understand the spread of infectious diseases, but have generally overlooked the fact that most realistic networks are dynamical rather than static. In this paper, we study a…