Stochastic dynamics of an SIS epidemic on networks

Jing, Xiaojie; Liu, Guirong; Zhou, Jin

doi:10.1007/s00285-022-01754-y

Cited by 7 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A straightforward approach is the stochastic perturbation of the model parameters [16,[20][21][22][23][24][25]. A more principled approach is to model the number of susceptible and infected individuals as continuous-time Markov chain birth-death processes or as branching processes [28][29][30][31][32][33][34]. Under the usual assumption that their state variables are continuous, Markov chain models lead to a system of stochastic differential equations whose noise covariance matrix is different from the parametric perturbation models [28,[35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Mamis

Farazmand

2023

Proc. R. Soc. A.

View full text Add to dashboard Cite

Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.

show abstract

Section: Introductionmentioning

confidence: 99%

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Mamis

Farazmand

2023

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…On the other hand, infected individuals recover and become susceptible individuals. The above process happens in a well-mixed population, but the SIS model has also been investigated on graphs [ 21 , 22 ] and hypergraphs [ 23 , 24 ]. Studies on introducing new factors into the SIS epidemic model continued to appear, including the study on vaccination [ 25 ], heterogeneous contacts [ 26 ], competing mechanism on complex networks [ 27 , 28 ], immigrants arriving with the same infection [ 29 ], and the external source of infection [ 30 – 32 ].…”

Section: Introductionmentioning

confidence: 99%

A simple epidemic model for semi-closed community reveals the hidden outbreak risk in nursing homes, prisons, and residential universities

Wang

2022

Int. J. Dynam. Control

View full text Add to dashboard Cite

We develop a general SIS model to study the epidemic transmission in such semi-closed communities. The community population is divided into susceptible and infected in terms of the infection state, and concerning the physical structure of the crowd, they are classified into mobile and fixed individuals. The mobile individuals can be inside or outside the community, while the fixed individuals can be only inside the community. There are fixed infection sources outside the community, measuring the epidemic severity in society. We attribute the spreading to two reasons: (i) clustered infection among the community population and (ii) the epidemic in society spreading to the community population. We discuss the model in two cases. In the first case, the epidemic spreads in society, such that reasons (i) and (ii) work together. The results show that concerning fixed individuals (e.g. the elderly in nursing homes), a more closed community always promotes the infection. In the second case, there is no epidemic spreading in society, such that only reason (i) works. The results show that restricting all individuals to the community produces equivalent consequences as allowing them going outside the community. We should evenly distribute individuals inside and outside to form isolation. A counterexample is residential universities implementing closed management, where only students are restricted to campus. The model shows such management may lead to severe epidemics, and to prevent the epidemic outbreaks, students should have free access to being on or off campus.

show abstract

Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model

Yang

Huang

2023

Numer Algor

View full text Add to dashboard Cite

Stochastic dynamics of an SIS epidemic on networks

Cited by 7 publications

References 34 publications

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

A simple epidemic model for semi-closed community reveals the hidden outbreak risk in nursing homes, prisons, and residential universities

Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model

Contact Info

Product

Resources

About