Related papers: Some rigorous results for the stacked contact proc…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…
We investigate a time-dependent spatial vector-host epidemic model with non-coincident domains for the vector and host populations. The host population resides in small non-overlapping sub-regions, while the vector population resides…
Bacteria and their viruses ("bacteriophages") coexist in natural environments forming complex infection networks. Recent empirical findings suggest that phage-bacteria infection networks often possess a nested structure such that there is a…
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…
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barab\'asi-Albert (BA),…
In this paper, we use a linear birth and death process with immigration to model infectious disease propagation when contamination stems from both person-to-person contact and contact with the environment. Our aim is to estimate the…
In many real-world contagion phenomena, the number of contacts to spreading entities for adoption varies for different individuals. Therefore, we study a model of contagion dynamics with heterogeneous adoption thresholds. We derive…
Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…
The critical properties of the stochastic susceptible-exposed-infected model on a square lattice is studied by numerical simulations and by the use of scaling relations. In the presence of an infected individual, a susceptible becomes…
We study the contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infection rates and asymmetric power law tail decays of the two…
We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, and it can be infected or healthy; the infection propagates to healthy neighbors just…
Our study is devoted to a four-compartment epidemic model of a constant population of independent random walkers. Each walker is in one of four compartments (S-susceptible, C-infected but not infectious (period of incubation), I-infected…
We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
We study a stochastic model proposed recently in the genetic literature to explain the heterogeneity of cell populations or of gene products. Cells are located in two colonies, whose sizes fluctuate as birth and migration processes in…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…
This paper studies contact processes on general countable groups. It is shown that any such contact process has a well-defined exponential growth rate, and this quantity is used to study the process. In particular, it is proved that on any…