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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…
SIR models, also with age structure, can be used to describe the evolution of an infective disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered…
Numerous elements drive the spread of infectious diseases in complex real-world networks. Of particular interest is social behaviors that evolve in tandem with the spread of disease. Moreover, recent studies highlight the importance of…
In this article we use global and regional data from the SARS epidemic in conjunction with a model of susceptible, exposed, infective, diagnosed, and recovered classes of people (``SEIJR'') to extract average properties and rate constants…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…
The study of epidemiological systems has generated deep interest in exploring the dynamical complexity of common infectious diseases driven by seasonally varying contact rates. Mathematical modeling and field observations have shown that,…
China adjusted the zero-COVID strategy in late 2022, triggering an unprecedented Omicron wave. We estimated the time-varying reproduction numbers of 32 provincial-level administrative divisions from December 2022 to January 2023. We found…
Detections of mutations of the SARS-CoV-2 virus gave rise to new packages of interventions. Among them, international travel restrictions have been one of the fastest and most visible responses to limit the spread of the variants. While…
This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments…
In this work, we revisit the basic reproduction rate $\mathcal{R}_{0}$ definition for analysis of epidemic-non-epidemic phases describing the dynamics of the discrete stochastic version of the epidemic $SIR$ model based on the Master…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…
We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the…
This paper extends the canonical model of epidemiology, the SIRD model, to allow for time-varying parameters for real-time measurement and prediction of the trajectory of the Covid-19 pandemic. Time variation in model parameters is captured…
Non-pharmaceutical interventions(NPIs) play an important role in the early stage control of COVID-19 pandemic. Vaccination is considered to be the inevitable course to stop the spread of SARS-CoV-2. Based on the mechanism, a SVEIR COVID-19…
In this paper, we derive and analyse a model for the control of arboviral diseases which takes into account an imperfect vaccine combined with some other mechanisms of control already studied in the literature. We begin by analyse the basic…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
A linearization-based feedback-control strategy for a SEIR epidemic model is discussed. The vaccination objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously…
The mobility patterns of individuals in China during the early outbreak of the COVID-19 pandemic exhibit reversible changes -- in many regions, the mobility first decreased significantly and later restored. Based on this observation, here…
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,…