Related papers: A note on Exact solution of SIR and SIS epidemic m…
In this paper we generalise a simple discrete time stochastic SIR type model defined by Tuckwell and Williams. The SIR model by Tuckwell and Williams assumes a homogeneous population, a fixed infectious period, and a strict transition from…
In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…
Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…
This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…
The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The…
The results of Kermack-McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of epidemic, systematically. The basic goal is to capture the effects of…
In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size…
A stochastic SIR epidemic model taking into account the heterogeneity of the spatial environment is constructed. The deterministic model is given by a partial differential equation and the stochastic one by a space-time jump Markov process.…
This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic…
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…
In the present paper, we are concerned with an SIS epidemic reaction-diffusion model governed by mass action infection mechanism and linear birth-death growth with no flux boundary condition. By performing qualitative analysis, we study the…
We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the…
We propose a stochastic SIR model, specified as a system of stochastic differential equations, to analyse the data of the Italian COVID-19 epidemic, taking also into account the under-detection of infected and recovered individuals in the…
In this paper we investigate the asymptotic behavior of some SIR models incorporating demography, bounded random transmission coefficient and a time-dependent vaccination strategy targeting the susceptible population. In this setting, we…
A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for the same purposes. The Lie symmetry classification of the…
Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
We consider a general class of epidemic models obtained by applying a random time change to a collection of Poisson processes and we show the large deviation principle for such models. We generalize to a more general situation the approach…