Related papers: A predator-prey SIR type dynamics on large complet…
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that…
We study the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents - sources…
One of the most effective strategies to mitigate the global spreading of a pandemic (e.g., COVID-19) is to shut down international airports. From a network theory perspective, this is since international airports and flights, essentially…
Given a population with dynamic pairwise connections, we ask if the entire population could be (indirectly) infected by a small group of $k$ initially infected individuals. We formalise this problem as the Temporal Reachability Dominating…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
Mathematical models of infectious diseases exhibit robust dynamics such as stable endemic or a disease-free equilibrium, or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among…
We study a susceptible-vaccinated--infected--recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…
Here we propose and implement a generalized mathematical model to find the time evolution of population in infectious diseases and apply the model to study the recent COVID-19 pandemic. Our model at the core is a non-local generalization of…
Two stochastic models of susceptible/infected/removed (SIR) type are introduced for the spread of infection through a spatially-distributed population. Individuals are initially distributed at random in space, and they move continuously…
It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of…
Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by…
Theoretical arguments and empirical evidence for the emergence of macroscopic epidemic type behavior, in the form of Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) processes in urban traffic congestion from…
In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to…
We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped…
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…
Most epidemic processes on networks can be modelled by a compartmental model, that specifies the spread of a disease in a population. The corresponding compartmental graph describes how the viral state of the nodes (individuals) changes…