Threshold dynamics and optimal control of a dengue epidemic model with time delay and saturated incidence

In this paper, an epidemic model of dengue fever with time delay and saturated incidence rate is studied. The basic reproduction number is calculated by the next-generation matrix method. The local stability of each of feasible equilibria is obtained by analyzing the corresponding characteristic equ...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2023-02, Vol.69 (1), p.871-893
Main Authors: Wang, Bian, Tian, Xiaohong, Xu, Rui, Song, Chenwei
Format: Article
Language:English
Subjects:
Applied mathematics
Asymptotic properties
Computational Mathematics and Numerical Analysis
Disease control
Eigenvalues
Eigenvectors
Epidemics
Mathematical and Computational Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Matrix methods
Optimal control
Original Research
Principles
Sensitivity analysis
Stability analysis
Theory of Computation
Time lag
Viral diseases
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Summary:In this paper, an epidemic model of dengue fever with time delay and saturated incidence rate is studied. The basic reproduction number is calculated by the next-generation matrix method. The local stability of each of feasible equilibria is obtained by analyzing the corresponding characteristic equations. Lyapunov functional method and LaSalle’s invariance principle are used to prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1; when the basic reproduction number is greater than 1, the endemic equilibrium is globally asymptotically stable. Further, optimal control strategy for the prevention and control of dengue fever infection is suggested based on Pontryagin’s minimum principle with delay. In addition, sensitivity analysis is carried out on basic reproduction number and numerical simulation of the dengue outbreak in Guangdong, in 2014, is given to illustrate the rationality of the model.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-022-01766-3