Related papers: Approximating time to extinction for endemic infec…
A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…
We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers…
We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…
Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…
Networked epidemic models have been widely adopted to describe propagation phenomena. The endemic equilibrium of these models is of great significance in the field of viral marketing, innovation dissemination, and information diffusion.…
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 study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large…
We consider the problem of identifying an infection source based only on an observed set of infected nodes in a network, assuming that the infection process follows a Susceptible-Infected-Susceptible (SIS) model. We derive an estimator…
We consider a stochastic SIS infection model for a population partitioned into $m$ households assuming random mixing. We solve the model in the limit $m \to \infty$ by using the self-consistent field method of statistical physics. We derive…
In this work, we aim to understand the influence of the heterogeneity of infection rates on the Susceptible-Infected-Susceptible (SIS) epidemic spreading. Employing the classic SIS model as the benchmark, we study the influence of the…
The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models…
We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…
The emergence and spread of deadly pandemics has repeatedly occurred throughout history, causing widespread infections and loss of life. The rapid spread of pandemics have made governments across the world adopt a range of actions,…
In this paper, we consider a discrete-time stochastic SIR model, where the transmission rate and the true number of infectious individuals are random and unobservable. An advantage of this model is that it permits us to account for random…
We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…