Related papers: Stochastic two-patch epidemic model with nonlinear…
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…
In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global…
Assessing the practical identifiability of epidemic models is essential for determining whether parameters can be meaningfully estimated from observed data. Monte Carlo (MC) methods provide an accessible and intuitive framework; however,…
Physiological stress fundamentally alters disease susceptibility in aquatic environments. In this paper, we develop a stress-structured epidemiological model where host vulnerability is dynamically driven by water quality. Analytically, we…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant…
We investigate a discrete-time two-strain symbiotic epidemic model on complex networks with both random and long-range interactions. Our analysis examines how the co-infection recovery rate ($\mu$), the long-range decay exponent ($\alpha$),…
Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We study an individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity. Each individual is associated with a random infection-age dependent…
We develop a stochastic framework for viral population dynamics at the cellular level that explicitly incorporates the replication cycle with random stage durations. The model is formulated as a structured birth-death process coupled with a…
We propose a lattice dynamical system that arises in a discrete diffusive two-group epidemic model with latency in a patchy environment. The model considers the SIS form and latency of the disease in group 1, while the SIR form without…
Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with…
Among various possible causes of autoimmune disease, an important role is played by infections that can result in a breakdown of immune tolerance, primarily through the mechanism of "molecular mimicry". In this paper we propose and analyse…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of $n$ cities. In the model a fraction $f_{jk}$ of individuals from city $k$ commute to city $j$,…