Related papers: Stochastic Dynamics and Probability Analysis for a…
A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…
The rampant phenomenon of overpopulation and the remarkable increase of human movements over the last decade have caused an aggressive re-emergence of dengue fever, which made it the subject of several research fields. In this regard,…
We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic…
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…
A susceptible, asymptomatic, infectious, quarantined, and hospitalized (SAIQH) compartmental model on time scales is introduced and a suitable Lyapunov function is defined. Main results include: the proof that the system is permanent; proof…
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…
We explore a rigorous formulation of agent-based SIR epidemic dynamics as a discrete-state Markov process, capturing the stochastic propagation of infection or an invading agent on networks. Using indicator functions and corresponding…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…
Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…
It is important to study the global behavior of solutions to systems of ordinary differential equations describing the transmission dynamics of infectious disease. In this paper, we present a different approach from the Lyapunov function…
Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with…
We introduce a modified SIR model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states susceptible (${\bf S}$), infected (${\bf I}$) or recovered (${\bf R}$). In…
This paper studies qualitative properties of solutions of nonlocal infectious SIR epidemic models (1.3)-(1.5), with the homogeneous Neumann boundary conditions, Dirichlet boundary conditions and free boundary, respectively. We first use the…
We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…
We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear. randomly. Using a constructive transition approach that predicts large outbreaks, prior to their occurrence, we derive an adaptive control.…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
We propose an epidemic compartment model, which includes mortality caused by the disease, but excludes demographic birth and death processes. Individuals are represented by random walkers, which are in one of the following states…
This paper demonstrates input-to-state stability (ISS) of the SIR model of infectious diseases with respect to the disease-free equilibrium and the endemic equilibrium. Lyapunov functions are constructed to verify that both equilibria are…
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…