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Gao H, Liu S, Xiao Y. The limit behavior of SEIRS model in spatial grid. STOCH DYNAM 2022. [DOI: 10.1142/s0219493722400081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we study a SEIRS model with Neumann boundary condition for a population distributed in a spatial grid. We first discuss the existence and uniqueness of global positive solution with any given positive initial value. Next, we introduce the basic reproduction number of this model. Then we consider the relation between the system of PDE and the discrete ODE model. Finally, we consider the stochastic model and give two laws of large numbers.
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Affiliation(s)
- Hongjun Gao
- School of Mathematics, Southeast University, Nanjing 211189, P. R. China
| | - Shuaipeng Liu
- Jiangsu Provincial Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, P. R. China
| | - Yeyu Xiao
- School of Mathematics, Jilin University, Changchun 130012, P. R. China
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