Related papers: Persistence, extinction and spatio-temporal synchr…
The stochastic SIRS model is a continuous-time Markov chain modelling the spread of infectious diseases with temporary immunity, in a homogeneously-mixing population of fixed size $N$. We study the scaling behaviour of the extinction time…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the…
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number $\mathscr{R}_0$…
Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the…
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is…
Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…
Organisms modulate their fitness in heterogeneous environments by dispersing. Prior work shows that there is selection against "unconditional" dispersal in spatially heterogeneous environments. "Unconditional" means individuals disperse at…
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…
We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…
In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the…
Most infectious diseases including more than half of known human pathogens are not restricted to just one host, yet much of the mathematical modeling of infections has been limited to a single species. We investigate consequences of a…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…