Related papers: Exact solution for a discrete-time SIR model
In this paper, we propose a time-dependent Susceptible-Exposed-Infectious-Recovered-Died (SEIRD) reaction-diffusion system for the COVID-19 pandemic and we deal with its derivation from a kinetic model. The derivation is obtained by…
We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the…
We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient and recruitment rate. Initially, we conduct an extensive analysis of the autonomous scenario, covering aspects such as local and…
In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for…
Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time…
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
Individual-based model (IBM) has been used to simulate and to design control strategies for dynamic systems that are subject to stochasticity and heterogeneity, such as infectious diseases. In the IBM, an individual is represented by a set…
We study the minimum eradication time problem for controlled Susceptible-Infected-Recovered (SIR) epidemic models that incorporate vaccination control and time-varying infected and recovery rates. Unlike the SIR model with constant rates,…
The simplest epidemiologic model composed by mutually exclusive compartments SIR (susceptible-infected-susceptible) is presented to describe a reality. From health concerns to situations related with marketing, informatics or even…
We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the…
We analytically study the SEIR (Susceptible Exposed Infectious Removed) epidemic model. The aim is to provide simple analytical expressions for the peak and asymptotic values and their characteristic times of the populations affected by the…
With the outbreak of COVID-19, how to mitigate and suppress its spread is a big issue to the government. Department of public health need powerful models to model and predict the trend and scale of such pandemic. And models that could…
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR…
The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource…
We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we…
We study a symmetric two-disease SIR co-infection model on networks in which co-infected individuals recover at a rate distinct from that of single infections. The model explicitly represents all co-infection states and features absorbing…
It's well-known that in a traditional discrete-time autonomous linear systems, the eigenvalues of the weigth (system) matrix solely determine the stability of the system. If the spectral radius of the system matrix is larger than 1, then…