On the Dynamics of Deterministic Epidemic Propagation over Networks

2017/01/11 by Wenjun Mei, Shadi Mohagheghi, Mei, Wenjun +5 · 8 citations
Medicine · Physics and Astronomy · #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1701.03137

openalex publication_date 2017/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI), susceptible-infected-susceptible (SIS), and susceptible-infected-recovered (SIR) settings. In each setting, we provide a comprehensive nonlinear analysis of equilibria, stability properties, convergence, monotonicity, positivity, and threshold conditions. For the network SI setting, specific contributions include establishing its equilibria, stability, and positivity properties. For the network SIS setting, we review a well-known deterministic model, provide novel results on the computation and characterization of the endemic state (when the system is above the epidemic threshold), and present alternative proofs for some of its properties. Finally, for the network SIR setting, we propose novel results for transient behavior, threshold conditions, stability properties, and asymptotic convergence. These results are analogous to those well-known for the scalar case. In addition, we provide a novel iterative algorithm to compute the asymptotic state of the network SIR system.

Citations

• Some discrete-time SI, SIR, and SIS epidemic models
• A deterministic model for gonorrhea in a nonhomogeneous population
• The Mathematics of Infectious Diseases

Cited by

• Multiple-Timescale Solutions to the Susceptible-Infected-Recovered (SIR) Epidemic Model Equations in the Case of High Basic Reproduction Number
• Effective Delayed Patching for Transient Malware Control on Networks
• A Human-Vector Susceptible-Infected-Susceptible Model for Analyzing and Controlling the Spread of Vector-Borne Diseases
• A Physics-Informed Neural Networks-Based Model Predictive Control Framework for SIR Epidemics
• A Quantum-Compliant Formulation for Network Epidemic Control
• A Quantum Approach for Optimal Transient Control in Network-Based Epidemic Models
• Network Behavioral-Feedback SIR Epidemic Model
• Recent trends in socio-epidemic modelling: behaviours and their determinants

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