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In this paper, we investigate a novel 3-compartment model of HIV infection of CD4$^+$ T-cells with a mass action term by including two versions: one baseline ODE model and one delay-differential equation (DDE) model with a constant discrete…

Populations and Evolution · Quantitative Biology 2021-01-05 Hoang Anh Ngo , Hung Dang Nguyen , Mehmet Dik

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…

Probability · Mathematics 2024-04-22 Yuanfei Huang , Adrian Röllin

In several practical applications, particularly healthcare, clinical data of each patient is individually recorded in a database at irregular intervals as required. This causes a sparse and irregularly sampled time series, which makes it…

Machine Learning · Computer Science 2025-04-09 Mincheol Kim , Soo-Yong Shin

We prove a Central Limit Theorem for the proportion of infected individuals for an epidemic model by dealing with a discrete time system of simple random walks on a complete graph with n vertices. Each random walk makes a role of a virus.…

Probability · Mathematics 2010-11-17 F. Machado , H. Mashurian , H. Matzinger

We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution.…

Dynamical Systems · Mathematics 2024-09-17 Márcia Lemos-Silva , Sandra Vaz , Delfim F. M. Torres

In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by…

Dynamical Systems · Mathematics 2024-02-08 Luis Sanz-Lorenzo , Rafael Bravo de la Parra

We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for…

Classical Analysis and ODEs · Mathematics 2019-08-12 Abdelhai Elazzouzi , Abdesslem Lamrani Alaoui , Mouhcine Tilioua , Delfim F. M. Torres

An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…

Chaotic Dynamics · Physics 2012-09-21 K. B. Blyuss , Y. N. Kyrychko

The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the SIR. In…

Physics and Society · Physics 2023-12-19 Louis Bremaud , Olivier Giraud , Denis Ullmo

We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we…

Physics and Society · Physics 2017-10-05 Matthieu Nadini , Kaiyuan Sun , Enrico Ubaldi , Michele Starnini , Alessandro Rizzo , Nicola Perra

Deep Equilibrium Models (DEQs) have emerged as a powerful paradigm in deep learning, offering the ability to model infinite-depth networks with constant memory usage. However, DEQs incur significant inference latency due to the iterative…

Machine Learning · Computer Science 2026-02-04 Junchao Lin , Zenan Ling , Jingwen Xu , Robert C. Qiu

In this work, we study the epidemic SIR model on a system which takes into consideration face-to-face interaction networks. This approach has been used as prototype to describe people interactions in different kinds of social organizations…

We study an individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity. Each individual is associated with a random infection-age dependent…

Probability · Mathematics 2025-10-21 Guodong Pang , Etienne Pardoux

We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents. Broken links are either permanently removed or reconnected…

Populations and Evolution · Quantitative Biology 2007-11-07 Damian H. Zanette , Sebastian Risau Gusman

In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDEs),…

Physics and Society · Physics 2015-08-19 Istvan Z. Kiss , Gergely Röst , Zsolt Vizi

This paper proposes a novel discrete-time multi-virus SIR (susceptible-infected-recovered) model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level…

Systems and Control · Electrical Eng. & Systems 2022-04-05 Ciyuan Zhang , Sebin Gracy , Tamer Basar , Philip E. Pare

In this paper, we propose a new real-time differential virus transmission model, which can give more accurate and robust short-term predictions of COVID-19 transmitted infectious disease with benefits of near-term trend projection.…

Populations and Evolution · Quantitative Biology 2020-05-05 Sheldon X. D. Tan , Liang Chen

We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…

Dynamical Systems · Mathematics 2017-02-03 Sue Ann Campbell , Israel Ncube

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…

Dynamical Systems · Mathematics 2017-08-15 Yilei Tang , Dongmei Xiao , Weinian Zhang , Di Zhu

Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of…

Physics and Society · Physics 2020-09-08 Bnaya Gross , Shlomo Havlin