Related papers: A measure-valued stochastic model for vector-borne…

This paper describes a technique for analyzing the stochastic structure of the vectorial capacity using moment--generating functions. In such formulation, for an infectious disease transmitted by a vector, we obtain the generating function…

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider 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…

This study develops and analyzes a stochastic differential equation (SDE) model for the dynamics of hepatitis B virus (HBV) infection. While deterministic frameworks have yielded important insights into viral behavior, they cannot…

The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…

Biological processes at the cellular level are stochastic in nature, and the immune response system is no different. Therefore, models that attempt to explain this system need to also incorporate noise or fluctuations that can account for…

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…

To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state…

This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed…

Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic…

We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial $\Lambda$-Fleming-Viot (SLFV) process. The model can be described by as little as three…

We present an epidemiological model for vector-borne diseases that includes within-host viral load and antibody dynamics using structured transport equations. By incorporating the internal dynamics into the infected and recovered host…

In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…

Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…

Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…

Vector-borne diseases arise from the coupled dynamics of human mobility and mosquito ecology, producing outbreaks shaped by both spatial distributions and temporal patterns of movement. Here we develop a coarse-grained hub--leaf reduction…

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…

We develop a new structured compartmental model for the coevolutionary dynamics between susceptible and infectious individuals in heterogeneous SI epidemiological systems. In this model, the susceptible compartment is structured by a…