Analysis and Optimal Control of a Multistrain SEIR Epidemic Model with Saturated Incidence Rate and Treatment

In this paper, we study the dynamic of a multi-strain SEIR model with both saturated incidence and treatment functions. Two basic reproduction numbers are extracted from the epidemic model, noted R 0 , 1 and R 0 , 2 . Using the Lyapunov method, we investigate the global stability of the disease free...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 31; no. 4; pp. 907 - 923
Main Authors Bentaleb, Dounia, Harroudi, Sanaa, Amine, Saida, Allali, Karam
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.10.2023
Springer Nature B.V
Subjects
Computer Science
Engineering
Epidemics
Mathematical models
Mathematics
Mathematics and Statistics
Optimal control
Original Research
Saturated incidence
Multi-strain
MSC 34-00
Global stability
Optimal control
Treatment function
MSC 92D30
MSC 34D23
SEIR
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Summary:In this paper, we study the dynamic of a multi-strain SEIR model with both saturated incidence and treatment functions. Two basic reproduction numbers are extracted from the epidemic model, noted R 0 , 1 and R 0 , 2 . Using the Lyapunov method, we investigate the global stability of the disease free equilibrium and prove that it is globally asymptotically stable when R 0 , 1 and R 0 , 2 are less than one. Moreover, we formulate the optimal control problem, solve it, and perform some numerical simulations, to support the analytical results and test how well the proposed model may be applied in practice.
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ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-020-00544-6