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We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an…
The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known \textit{Susceptible-Infected-Susceptible} ($SIS$) epidemic…
We study convergence properties of competing epidemic models of the Susceptible-Infected-Susceptible (SIS) type. The SIS epidemic model has seen widespread popularity in modelling the spreading dynamics of contagions such as viruses,…
Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load…
In this work we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations…
For linear dynamical systems (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability, as…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
We revisit the SICA (Susceptible-Infectious-Chronic-AIDS) mathematical model for transmission dynamics of the human immunodeficiency virus (HIV) with varying population size in a homogeneously mixing population. We consider SICA models…
Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model…
We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…
In this paper, a mathematical analysis of the global dynamics of a partial differential equation viral infection cellular model is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both…
Interactions in biology and social systems are not restricted to pairwise but can take arbitrary sizes. Extensive studies have revealed that the arbitrary-sized interactions significantly affect the spreading dynamics on networked systems.…
The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of…
In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…
Background: Animal trade plays an important role for the spread of infectious diseases in livestock populations. As a case study, we consider pig trade in Germany, where trade actors (agricultural premises) form a complex network. The…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian…