The Dynamic Behavior of a Stochastic SEIRM Model of COVID-19 with Standard Incidence Rate

Yuxiao Zhao, Hui Wang () and Dongxu Wang ()
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Yuxiao Zhao: School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
Hui Wang: School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
Dongxu Wang: School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China

Mathematics, 2024, vol. 12, issue 19, 1-15

Abstract: This paper studies the dynamic behavior of a stochastic SEIRM model of COVID-19 with a standard incidence rate. The existence of global solutions for dynamic system models is proven by integrating stochastic process theory and the concept of stopping times, together with the contradiction method. Moreover, we construct appropriate Lyapunov functions to analyze system stability and apply Dynkin’s formula and Fatou’s lemma to handle stopping times and expectations of stochastic processes. Notably, the extinction study provides mathematical proof that under the given system dynamics, the total population does not grow indefinitely but tends to stabilize over time. The properties of the diffusion matrix are harnessed to guarantee the system’s stationary distribution. Conclusively, numerical simulations confirm the model’s extinction outcomes.

Keywords: SEIRM; standard incidence rate; dynamic behavior; extinction; stationary distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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