Related papers: The network-level reproduction number and extincti…
We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…
We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
The basic reproduction number R0 -- the number of individuals directly infected by an infectious person in an otherwise susceptible population -- is arguably the most widely used estimator of how severe an epidemic outbreak can be. This…
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…
Many biological systems exhibit multiscale dynamics, where some species occur in high copy numbers while others remain rare. This heterogeneity necessitates hybrid modelling approaches: deterministic models are computationally efficient but…
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…
Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In…
The basic reproduction number ($R_0$) is a threshold parameter for disease extinction or survival in isolated populations. However no human population is fully isolated from other human or animal populations. We use compartmental models to…
The initial phase of an epidemic is often characterized by an exponential increase in the number of infected individuals. In this paper, we predict the exponential spreading rate of an epidemic on a complex network. We first find an…
Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account, by assuming that the relevant information to study…
Extrinsic environmental factors influence the distribution and population dynamics of many organisms, including insects that are of concern for human health and agriculture. This is particularly true for vector-borne infectious diseases,…
We consider the propagation of a contagion process (epidemic) on a network and study the problem of dynamically allocating a fixed curing budget to the nodes of the graph, at each time instant. For bounded degree graphs, we provide a lower…
We propose a variation of the GMS model of evolution of species. In this version, as in the GMS model, at each birth, the new species in the system is labeled with a random fitness mark, but in our variation, to each extinction event is…
We consider epidemic extinction in finite networks with broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or…
We study the persistent recoverable prevalence and the extinction of computer viruses via e-mails on a growing scale-free network with new users, which structure is estimated form real data. The typical phenomenon is simulated in a…
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…