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In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical…
Capturing the structured mixing within a population is key to the reliable projection of infectious disease dynamics and hence informed control. Both heterogeneity in the number of contacts and age-structured mixing have been repeatedly…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
Recent experiments in adult mammalian tissues have found scaling relations of the voter model in the dynamics of the genetically labeled population of stem cells. Yet, the reason for this seemingly robust appearance of the voter model…
Using a stochastic Susceptible-Infected-Removed (SIR) meta-population model of disease transmission, we present analytical calculations and numerical simulations dissecting the interplay between stochasticity and the division of a…
Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others.…
Capturing the structure of a population and characterising contacts within the population are key to reliable projections of infectious disease. Two main elements of population structure -- contact heterogeneity and age -- have been…
The variability in cell size of an isogenic population of Escherichia coli has been widely reported in experiment. The probability density function (PDF) of cell lengths has been variously described by exponential and lognormal functions.…
We study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement of control measures. We show that the…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts…
Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…
Motivated by massive outbreaks of COVID-19 that occurred even in populations with high vaccine uptake, we propose a novel multi-population temporal network model for the spread of recurrent epidemic diseases. We study the effect of human…
We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge…
Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
We have further extended our compartmental model describing the spread of the infection in Italy. The model is based on the assumption that the time evolution of all of the observable quantities (number of people still positive to the…
Stochastic rearrangement of germline DNA by VDJ recombination is at the origin of immune system diversity. This process is implemented via a series of stochastic molecular events involving gene choices and random nucleotide insertions…
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…
Empirical studies suggest that contact patterns follow heterogeneous inter-event times, meaning that intervals of high activity are followed by periods of inactivity. Combined with birth and death of individuals, these temporal constraints…