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Stochastic dynamics of an SIS epidemic on networks

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Abstract

We derive a stochastic SIS pairwise model by considering the change of the variables of this system caused by an event. Based on approximations, we construct a low-dimensional deterministic system that can be used to describe the epidemic spread on a regular network. The mathematical treatment of the model yields explicit expressions for the variances of each variable at equilibrium. Then a comparison between the stochastic pairwise model and the stochastic mean-field SIS model is performed to indicate the effect of network structure. We find that the variances of the prevalence of infection for these two models are almost equal when the number of neighbors of every individual is large. Furthermore, approximations for the quasi-stationary distribution of the number of infected individuals and the expected time to extinction starting in quasi-stationary are derived. We analyze the approximations for the critical number of neighbors and the persistence threshold based on the stochastic model. The approximate performance is then examined by numerical and stochastic simulations. Moreover, during the early development phase, the temporal variance of the infection is also obtained. The simulations show that our analytical results are asymptotically accurate and reasonable.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 11971279, 61873154).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, Shanxi, China

    Xiaojie Jing & Guirong Liu

  2. Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, China

    Zhen Jin

  3. Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, 030006, Shanxi, China

    Zhen Jin

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  1. Xiaojie Jing
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  2. Guirong Liu
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  3. Zhen Jin
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Correspondence to Guirong Liu.

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Jing, X., Liu, G. & Jin, Z. Stochastic dynamics of an SIS epidemic on networks. J. Math. Biol. 84, 50 (2022). https://doi.org/10.1007/s00285-022-01754-y

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  • DOI: https://doi.org/10.1007/s00285-022-01754-y

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