A Stochastic Semi-Parametric SEIR Model with Infectivity in an Incubation Period

Jing Zhang () and Tong Jin
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Jing Zhang: School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
Tong Jin: School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

Mathematics, 2024, vol. 12, issue 10, 1-14

Abstract: This paper introduces stochastic disturbances into a semi-parametric SEIR model with infectivity in an incubation period. The model combines the randomness of disease transmission and the nonlinearity of transmission rate, providing a flexible framework for more accurate description of the process of infectious disease transmission. On the basis of the discussion of the deterministic model, the stochastic semi-parametric SEIR model is studied. Firstly, we use Lyapunov analysis to prove the existence and uniqueness of global positive solutions for the model. Secondly, the conditions for disease extinction are established, and appropriate stochastic Lyapunov functions are constructed to discuss the asymptotic behavior of the model’s solution at the disease-free equilibrium point of the deterministic model. Finally, the specific transmission functions are enumerated, and the accuracy of the results are demonstrated through numerical simulations.

Keywords: stochastic SEIR model; semi-parametric; nonlinear incidence rate; stability; disease-free equilibrium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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