Related papers: Oscillation in the SIRS model
We investigate the dynamics of an epidemiological susceptible-infected-susceptible (SIS) model on an adaptive network. This model combines epidemic spreading (dynamics on the network) with rewiring of network connections (topological…
In this paper, we conduct mathematical and numerical analyses to address the following crucial questions for COVID-19: (Q1) Is it possible to contain COVID-19? (Q2) When will be the peak and the end of the epidemic? (Q3) How do the…
We modelled emergence and spread of the Omicron variant of SARS-CoV-2 in Australia between December 2021 and June 2022. This pandemic stage exhibited a diverse epidemiological profile with emergence of co-circulating sub-lineages of…
In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions…
A numerical study of synchronization and extinction is done for a SIRS model with fixed infective and refractory periods, in the regime of high infectivity, on one- and two-dimensional networks for which the connectivity probability decays…
In this paper, we study a stochastic susceptible-infected-susceptible (SIS) epidemic model that includes an additional immigration process. In the presence of multiplicative noise, generated by environmental perturbations, the model…
How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider…
Susceptible-Infected-Recovered (SIR) models have been used for decades to understand epidemic outbreak dynamics. We develop an SIR model specifically designed to study the effects of population behavior with respect to health and…
We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…
Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model…
We study supercritical spatial SIR epidemics on $\mathbb{Z}^2\times \{1,2,\ldots, N\}$, where each site in $\mathbb{Z}^2$ represents a village and $N$ stands for the village size. We establish several key asymptotic results as $N\to\infty$.…
We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several of these (epidemic) models to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new…
The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do…
We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…
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…
Although previous infection and vaccination provide protection against SARS-CoV-2 infection, both reinfection and breakthrough infection are possible events whose occurrence would increase with time after first exposure to the antigen and…
The spread of an infectious disease is known to change people's behavior, which in turn affects the spread of disease. Adaptive network models that account for both epidemic and behavior change have found oscillations, but in an extremely…
The COVID-19 pandemic has had worldwide devastating effects on human lives, highlighting the need for tools to predict its development. Dynamics of such public-health threats can often be efficiently analysed through simple models that help…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
The rapidly spreading Covid-19 that affected almost all countries, was first reported at the end of 2019. As a consequence of its highly infectious nature, countries all over the world have imposed extremely strict measures to control its…