Stability analysis and optimal control of an infectious disease model considering vaccination

Xinjie Zhu; Hua Liu; Xiaotao Han; Xiaofeng Lin

doi:10.1117/12.2686007

28 July 2023 Stability analysis and optimal control of an infectious disease model considering vaccination

Xinjie Zhu, Hua Liu, Xiaotao Han, Xiaofeng Lin

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275612 (2023) https://doi.org/10.1117/12.2686007
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

Vaccinations can prevent the propagation of infectious diseases very effectively. In this paper, we consider the effects of vaccines on the spread of infectious diseases, compute the analytical expressions of the disease-free equilibrium point and the basic reproduction number, and analyze the local asymptotic stability conditions of the disease-free equilibrium point using the Hurwitz criterion. Numerical simulations are used to examine the stability of the endemic equilibrium point. We chose the vaccination rate as a control variable, and we estimated the optimal control problem with an inequality constraint. We used the symplectic pseudospectral method to solve optimal control problems. The results indicate that increasing vaccination rate can stop the spread of infectious diseases.

Citation Download Citation

Xinjie Zhu, Hua Liu, Xiaotao Han, and Xiaofeng Lin "Stability analysis and optimal control of an infectious disease model considering vaccination", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275612 (28 July 2023); https://doi.org/10.1117/12.2686007

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