Analysis and Optimal Control of a Two-Strain SEIR Epidemic Model with Saturated Treatment Rate

Yudie Hu, Hongyan Wang and Shaoping Jiang ()
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Yudie Hu: School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
Hongyan Wang: School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China
Shaoping Jiang: School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China

Mathematics, 2024, vol. 12, issue 19, 1-17

Abstract: In this paper, we conducted a study on the optimal control problem of an epidemic model which consists of two strain with different types of incidence rates: bilinear and non-monotonic. We also considered use of the saturation treatment function. Two basic regeneration numbers are calculated from the epidemic model, which are denoted as R 1 and R 2 . The global stability of the disease-free equilibrium point was studied by the Lyapunov method, and it was proved that the disease-free equilibrium point is globally asymptotically stable when R 1 and R 2 are less than one. Finally, we formulated a time-dependent optimal control problem by Pontryagin’s maximum principle. Numerical simulations were performed to establish the effects of model parameters for disease transmission as well as the effects of control.

Keywords: optimal control; two strain; saturated treatment; global stability; Pontryagin’s maximum principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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