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We study the susceptible-infected-susceptible (SIS) model on directed complex networks within the quenched mean-field approximation. Combining results from random matrix theory with an analytic approach to the distribution of fixed-point…

Physics and Society · Physics 2025-12-12 Vinícius B. Müller , Fernando L. Metz

The study of epidemic models plays an important role in mathematical epidemiology. There are many researches on epidemic models using ordinary differential equations, partial differential equations or stochastic differential equations. In…

Probability · Mathematics 2023-03-10 Yuqi Li , Lihua Zhang

We study the stochastic susceptible-infected-recovered (SIR) model with time-dependent forcing using analytic techniques which allow us to disentangle the interaction of stochasticity and external forcing. The model is formulated as a…

Populations and Evolution · Quantitative Biology 2010-11-23 Andrew J Black , Alan J McKane

We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on the networks. We derive an analytical expression of the…

Populations and Evolution · Quantitative Biology 2019-11-18 M. Ali Saif

Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…

Methodology · Statistics 2024-05-24 Sam A. Whitaker , Andrew Golightly , Colin S. Gillespie , Theodore Kypraios

During an epidemic, the infectiousness of infected individuals is known to depend on the time since the individual was infected, that is called the age of infection. Here we study the parameter identifiability of the Kermack-McKendrick…

Analysis of PDEs · Mathematics 2023-05-10 Jacques Demongeot , Quentin Griette , Yvon Maday , Pierre Magal

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing,…

Optimization and Control · Mathematics 2021-11-17 Willem Esterhuizen , Jean Lévine , Stefan Streif

In this paper, we are concerned with the stochastic susceptible-infectious-susceptible (SIS) epidemic model on the complete graph with $n$ vertices. This model has two parameters, which are the infection rate and the recovery rate. By…

Probability · Mathematics 2020-12-02 Huazheng Bu , Xiaofeng Xue

We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…

Optimization and Control · Mathematics 2022-01-26 Marcel Fang , Pierre-Alexandre Bliman

The structure of social contact networks strongly influences the dynamics of epidemic diseases. In particular the scale-free structure of real-world social networks allows unlikely diseases with low infection rates to spread and become…

Physics and Society · Physics 2012-09-13 Güven Demirel , Thilo Gross

In this paper we investigate the asymptotic behavior of some SIR models incorporating demography, bounded random transmission coefficient and a time-dependent vaccination strategy targeting the susceptible population. In this setting, we…

Populations and Evolution · Quantitative Biology 2025-10-27 Javier López-de-la-Cruz , Susana Merchán , Felipe Rivero , Javier Rodrigo

We consider a stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic defined on a configuration model random graph, in which infective individuals can infect only their neighbours in the graph during an infectious period…

Probability · Mathematics 2018-12-10 Frank Ball

The history of infections and epidemics holds famous examples where understanding, containing and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV and most computer viruses, spread person to…

Social and Information Networks · Computer Science 2013-09-26 Chris Milling , Constantine Caramanis , Shie Mannor , Sanjay Shakkottai

We analyze a class of general nonlinear epidemic models with age and space structure, including a nonlocal infection term depending on age and space. After establishing the well-posedness of the state partial differential equation, we…

Optimization and Control · Mathematics 2025-03-11 Behzad Azmi , Nicolas Schlosser

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

A standard model for epidemics is the SIR model on a graph. We introduce a simple algorithm that uses the early infection times from a sample path of the SIR model to estimate the parameters this model, and we provide a performance…

Information Theory · Computer Science 2020-08-11 Charles Clum , Dustin G. Mixon

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all…

Physics and Society · Physics 2015-07-16 L. G. Alvarez Zuzek , H. E. Stanley , L. A. Braunstein

The Susceptible-Infected-Recovered (SIR) model is studied in multilayer networks with arbitrary number of links across the layers. By following the mapping to bond percolation we give the analytical expression for the epidemic threshold and…

Populations and Evolution · Quantitative Biology 2017-03-09 Ginestra Bianconi

Infectious disease epidemiologists routinely fit stochastic epidemic models to time series data to elucidate infectious disease dynamics, evaluate interventions, and forecast epidemic trajectories. To improve computational tractability,…

We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…

Analysis of PDEs · Mathematics 2025-12-16 Giorgio Martalò , Giuseppe Toscani , Mattia Zanella