Simplicial epidemic model with birth and death

Author:

Leng Hui1,Zhao Yi1ORCID,Luo Jianfeng12,Ye Yong1ORCID

Affiliation:

1. School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China

2. CAS AMSS-PolyU Joint Laboratory of Applied Mathematics (Shenzhen), The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, China

Abstract

In this paper, we propose a simplicial susceptible-infected-susceptible (SIS) epidemic model with birth and death to describe epidemic spreading based on group interactions, accompanying with birth and death. The site-based evolutions are formulated by the quenched mean-field probability equations for each site, which is a high-dimensional differential system. To facilitate a theoretical analysis of the influence of system parameters on dynamics, we adopt the mean-field method for our model to reduce the dimension. As a consequence, it suggests that birth and death rates influence the existence and stability of equilibria, as well as the appearance of a bistable state (the coexistence of the stable disease-free and endemic states), which is then confirmed by extensive simulations on empirical and synthetic networks. Furthermore, we find that another type of the bistable state in which a stable periodic outbreak state coexists with a steady disease-free state also emerges when birth and death rates and other parameters satisfy the certain conditions. Finally, we illustrate how the birth and death rates shift the density of infected nodes in the stationary state and the outbreak threshold, which is also verified by sensitivity analysis for the proposed model.

Funder

Natural Science Foundation of Guangdong Province

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

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